Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • Li-Tao Zhu
  • Zhe Chen*
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

bθ

tθ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

in

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

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Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

재료 분사를 통한 다중 재료 3D 유체 장치의 액체-고체 공동 인쇄

Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

BrandonHayes,Travis Hainsworth, Robert MacCurdy
University of Colorado Boulder, Department of Mechanical Engineering, Boulder, 80309, CO, USA

Abstract

다중 재료 재료 분사 적층 제조 공정은 3차원(3D) 부품을 레이어별로 구축하기 위해 다양한 모델 및 지지 재료의 미세 액적을 증착합니다.

최근의 노력은 액체가 마이크로/밀리 채널에서 쉽게 퍼지할 수 있는 지지 재료로 작용할 수 있고 구조에 영구적으로 남아 있는 작동 유체로 작용할 수 있음을 보여주었지만 인쇄 프로세스 및 메커니즘에 대한 자세한 이해가 부족합니다.

액체 인쇄의 제한된 광범위한 적용. 이 연구에서 광경화성 및 광경화성 액체 방울이 동시에 증착되는 액체-고체 공동 인쇄라고 하는 “한 번에 모두 가능한” 다중 재료 인쇄 프로세스가 광범위하게 특성화됩니다. 액체-고체 공동 인쇄의 메커니즘은 실험적인 고속 이미징 및 CFD(전산 유체 역학) 연구를 통해 설명됩니다.

이 연구는 액체의 표면 장력이 액체 표면에서 광중합하여 재료의 단단한 층을 형성하는 분사된 광중합체 미세 방울을 지지할 수 있음을 보여줍니다.

마이크로/밀리 유체 소자의 액체-고체 공동 인쇄를 위한 설계 규칙은 믹서, 액적 발생기, 고도로 분기되는 구조 및 통합된 단방향 플랩 밸브와 같은 평면, 3D 및 복합 재료 마이크로/메조 유체 구조에 대한 사례 연구뿐만 아니라 제시됩니다.

우리는 액체-고체 공동 인쇄 과정을 마이크로/메조플루이딕 회로, 전기화학 트랜지스터, 칩 장치 및 로봇을 포함한 응용 프로그램을 사용하여 3D, 통합된 복합 재료 유체 회로 및 유압 구조의 단순하고 빠른 제작을 가능하게 하는 적층 제조의 핵심 새로운 기능으로 구상합니다.

Multi-material material jetting additive manufacturing processes deposit micro-scale droplets of different model and support materials to build three-dimensional (3D) parts layer by layer. Recent efforts have demonstrated that liquids can act as support materials, which can be easily purged from micro/milli-channels, and as working fluids, which permanently remain in a structure, yet the lack of a detailed understanding of the print process and mechanism has limited widespread applications of liquid printing. In this study, an “all in one go” multi-material print process, herein termed liquid–solid co-printing in which non photo-curable and photo-curable liquid droplets are simultaneous deposited, is extensively characterized. The mechanism of liquid–solid co-printing is explained via experimental high speed imaging and computational fluid dynamic (CFD) studies. This work shows that a liquid’s surface tension can support jetted photopolymer micro-droplets which photo-polymerize on the liquid surface to form a solid layer of material. Design rules for liquid–solid co-printing of micro/milli-fluidic devices are presented as well as case studies of planar, 3D, and multi-material micro/mesofluidic structures such as mixers, droplet generators, highly branching structures, and an integrated one-way flap valve. We envision the liquid–solid co-printing process as a key new capability in additive manufacturing to enable simple and rapid fabrication of 3D, integrated print-in-place multi-material fluidic circuits and hydraulic structures with applications including micro/mesofluidic circuits, electrochemical transistors, lab-on-a-chip devices, and robotics.

Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting
Liquid-solid co-printing of multi-material 3D fluidic devices via material jetting

Keywords

Additive manufacturing; Mesofluidics; Modeling and simulation; Multi-material; Material jetting

Fig.1 Schematic diagram of the novel cytometric device

Fabrication and Experimental Investigation of a Novel 3D Hydrodynamic Focusing Micro Cytometric Device

Yongquan Wang*a , Jingyuan Wangb, Hualing Chenc

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P. R. China
a yqwang@mail.xjtu.edu.cn,, bwjy2006@stu.xjtu.edu.cn,, c hlchen@mail.xjtu.edu.cn,

Abstract:

This paper presents the fabrication of a novel micro-machined cytometric device, and the experimental investigations for its 3D hydrodynamic focusing performance. The proposed device is simple in structure, with the uniqueness that the depth of its microchannels is non-uniform. Using the SU-8 soft lithography containing two exposures, as well as micro-molding techniques, the PDMS device is successfully fabricated. Two kinds of experiments, i.e., the red ink fluidity observation experiments and the fluorescent optical experiments, are then performed for the device prototypes with different step heights, or channel depth differences, to explore the influence laws of the feature parameter on the devices hydrodynamic focusing behaviors. The experimental results show that the introducing of the steps can efficiently enhance the vertical focusing performance of the device. At appropriate geometry and operating conditions, good 3D hydrodynamic focusing can be obtained.

Korea Abstract

이 논문은 새로운 마이크로 머신 세포 측정 장치의 제조와 3D 유체 역학적 초점 성능에 대한 실험적 조사를 제시합니다. 제안 된 장치는 구조가 단순하며, 마이크로 채널의 깊이가 균일하지 않다는 독특함이 있습니다. 두 가지 노출이 포함 된 SU-8 소프트 리소그래피와 마이크로 몰딩 기술을 사용하여 PDMS 장치가 성공적으로 제작되었습니다. 그런 다음 두 종류의 실험, 즉 적색 잉크 유동성 관찰 실험과 형광 광학 실험을 단계 높이 또는 채널 깊이 차이가 다른 장치 프로토 타입에 대해 수행하여 장치 유체 역학적 초점에 대한 기능 매개 변수의 영향 법칙을 탐색합니다. 행동. 실험 결과는 단계의 도입이 장치의 수직 초점 성능을 효율적으로 향상시킬 수 있음을 보여줍니다. 적절한 형상과 작동 조건에서 우수한 3D 유체 역학적 초점을 얻을 수 있습니다.

Keywords

Flow cytometer, Hydrodynamic focusing, Three-dimensional (3D), Micro-machined

Fig.1 Schematic diagram of the novel cytometric device
Fig.1 Schematic diagram of the novel cytometric device
Fig.2 Overview of the cytometric device fabrication process
Fig.2 Overview of the cytometric device fabrication process
Fig.3 The fabricated micro cytometric device Fig.4 Experiment setup for focusing performance
Fig.3 The fabricated micro cytometric device Fig. 4 Experiment setup for focusing performance
Fig.5 Horizontal focusing images of two devices with and without steps
Fig.5 Horizontal focusing images of two devices with and without steps
Fig.6 Channel cross-section fluorescence images for different step heights
Fig.6 Channel cross-section fluorescence images for different step heights

References 

Fig.7 Effect of the step height on the 3D focusing at different velocity ratios
Fig.7 Effect of the step height on the 3D focusing at different velocity ratios

Conclusions

In this paper, we presented a novel micro-machined cytometric device and its fabrication process,
emphasizing on the experimental investigations for its 3D hydrodynamic focusing performance. The
proposed device is simple in structure, low cost, and easy to be batch produced. Besides this, as a
device based on standard micro-fabrication methodology, it can be conveniently integrated with other
micro-fluidic and/or micro-optical units to form a complete detection and analysis system.
The experimental tests for the prototype devices not only verified the design conception, but also
gave us a comprehensive understanding of the device hydro-focusing performance. The experimental
results show that, as the uniqueness of this design, the introducing of the feature steps can
significantly enhance the vertical focusing performance of the devices, which is crucial for the
achievement of 3D focusing. In summary, for the proposed novel device, good 3D hydrodynamic
focusing can be attained at appropriate geometry and operating conditions.
In addition, an improved design can be obtained by replacing the flat cover with an identical
device unit, in other words, the same two device units are bonded together (The channels are inward
and aligned) to form a new device. Then the sample stream can focused to the center of the assembly
outlet channel due to the hydrodynamic forces equally in both horizontal and vertical directions, and
thus avoiding the adsorption or friction issues of cells/particles to the top channel wall.

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Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

1Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
2William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, OH 43210, USA
*Author to whom correspondence should be addressed.
Sensors 202020(11), 3030; https://doi.org/10.3390/s20113030
Received: 16 April 2020 / Revised: 21 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
(This article belongs to the Special Issue Lab-on-a-Chip and Microfluidic Sensors)

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

Keywords: particle magnetophoresisCFDcross sectionchip fabrication

Korea Abstract

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를위한 기능화 된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드를 자기 적으로 회수하여 분석 또는 진단 테스트를 수행 할 수 있습니다. 연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 

따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다. 그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는 데있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜주의를 기울였습니다. 

여기에서 우리는 자기 비드가 혈액에서 분리되고 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 YY 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다. 

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증 된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다. 우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 

따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.

Numerical Analysis of Bead Magnetophoresis from Flowing Blood in a Continuous-Flow Microchannel: Implications to the Bead-Fluid Interactions

Scientific Reports volume 9, Article number: 7265 (2019) Cite this article

Abstract

이 연구에서는 비드 운동과 유체 흐름에 미치는 영향에 대한 자세한 분석을 제공하기 위해 연속 흐름 마이크로 채널 내부의 비드 자기 영동에 대한 수치 흐름 중심 연구를 보고합니다.

수치 모델은 Lagrangian 접근 방식을 포함하며 영구 자석에 의해 생성 된 자기장의 적용에 의해 혈액에서 비드 분리 및 유동 버퍼로의 수집을 예측합니다.

다음 시나리오가 모델링됩니다. (i) 운동량이 유체에서 점 입자로 처리되는 비드로 전달되는 단방향 커플 링, (ii) 비드가 점 입자로 처리되고 운동량이 다음으로부터 전달되는 양방향 결합 비드를 유체로 또는 그 반대로, (iii) 유체 변위에서 비드 체적의 영향을 고려한 양방향 커플 링.

결과는 세 가지 시나리오에서 비드 궤적에 약간의 차이가 있지만 특히 높은 자기력이 비드에 적용될 때 유동장에 상당한 변화가 있음을 나타냅니다.

따라서 높은 자기력을 사용할 때 비드 운동과 유동장의 체적 효과를 고려한 정확한 전체 유동 중심 모델을 해결해야 합니다. 그럼에도 불구하고 비드가 중간 또는 낮은 자기력을 받을 때 계산적으로 저렴한 모델을 안전하게 사용하여 자기 영동을 모델링 할 수 있습니다.

Sketch of the magnetophoresis process in the continuous-flow microdevice.
Sketch of the magnetophoresis process in the continuous-flow microdevice.
Schematic view of the microdevice showing the working conditions set in the simulations.
Schematic view of the microdevice showing the working conditions set in the simulations.
Bead trajectories for different magnetic field conditions, magnet placed at different distances “d” from the channel: (a) d = 0; (b) d = 1 mm; (c) d = 1.5 mm; (d) d = 2 mm
Bead trajectories for different magnetic field conditions, magnet placed at different distances “d” from the channel: (a) d = 0; (b) d = 1 mm; (c) d = 1.5 mm; (d) d = 2 mm
Separation efficacy as a function of the magnet distance. Comparison between one-way and two-way coupling.
Separation efficacy as a function of the magnet distance. Comparison between one-way and two-way coupling.
(a) Fluid velocity magnitude including velocity vectors and (b) blood volumetric fraction contours with magnet distance d = 0 mm for scenario 1 (t = 0.25 s).
(a) Fluid velocity magnitude including velocity vectors and (b) blood volumetric fraction contours with magnet distance d = 0 mm for scenario 1 (t = 0.25 s).
luid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 2: (a,b) Magnet distance d = 0 mm at t = 0.4 s; (c,d) Magnet distance d = 1 mm at t = 0.4 s.
luid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 2: (a,b) Magnet distance d = 0 mm at t = 0.4 s; (c,d) Magnet distance d = 1 mm at t = 0.4 s.
Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.
Fluid velocity magnitude including velocity vectors and blood volumetric fraction contours for scenario 3: (a,b) Magnet distance d = 0; (c,d) Magnet distance d = 1 mm.
Blood volumetric fraction contours. Scenario 1: (a) Magnet distance d = 0 and (b) Magnet distance d = 1 mm; Scenario 2: (c) Magnet distance d = 0 and (d) Magnet distance d = 1 mm; and Scenario 3: (e) Magnet distance d = 0 and (f) Magnet distance d = 1 mm.
Blood volumetric fraction contours. Scenario 1: (a) Magnet distance d = 0 and (b) Magnet distance d = 1 mm; Scenario 2: (c) Magnet distance d = 0 and (d) Magnet distance d = 1 mm; and Scenario 3: (e) Magnet distance d = 0 and (f) Magnet distance d = 1 mm.

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Author information

  1. Edward P. Furlani is deceased.

Affiliations

  1. Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005, Santander, SpainJenifer Gómez-Pastora, Eugenio Bringas & Inmaculada Ortiz
  2. Flow Science, Inc, Santa Fe, New Mexico, 87505, USAIoannis H. Karampelas
  3. Department of Chemical and Biological Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
  4. Department of Electrical Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USAEdward P. Furlani
Modeling of contactless bubble–bubble interactions in microchannels with integrated inertial pumps

Modeling of contactless bubble–bubble interactions in microchannels with integrated inertial pumps

통합 관성 펌프를 사용하여 마이크로 채널에서 비접촉식 기포-기포 상호 작용 모델링

Physics of Fluids 33, 042002 (2021); https://doi.org/10.1063/5.0041924 B. Hayesa) G. L. Whitingb), and  R. MacCurdyc)

ABSTRACT

In this study, the nonlinear effect of contactless bubble–bubble interactions in inertial micropumps is characterized via reduced parameter one-dimensional and three-dimensional computational fluid dynamics (3D CFD) modeling. A one-dimensional pump model is developed to account for contactless bubble-bubble interactions, and the accuracy of the developed one-dimensional model is assessed via the commercial volume of fluid CFD software, FLOW-3D. The FLOW-3D CFD model is validated against experimental bubble dynamics images as well as experimental pump data. Precollapse and postcollapse bubble and flow dynamics for two resistors in a channel have been successfully explained by the modified one-dimensional model. The net pumping effect design space is characterized as a function of resistor placement and firing time delay. The one-dimensional model accurately predicts cumulative flow for simultaneous resistor firing with inner-channel resistor placements (0.2L < x < 0.8L where L is the channel length) as well as delayed resistor firing with inner-channel resistor placements when the time delay is greater than the time required for the vapor bubble to fill the channel cross section. In general, one-dimensional model accuracy suffers at near-reservoir resistor placements and short time delays which we propose is a result of 3D bubble-reservoir interactions and transverse bubble growth interactions, respectively, that are not captured by the one-dimensional model. We find that the one-dimensional model accuracy improves for smaller channel heights. We envision the developed one-dimensional model as a first-order rapid design tool for inertial pump-based microfluidic systems operating in the contactless bubble–bubble interaction nonlinear regime

이 연구에서 관성 마이크로 펌프에서 비접촉 기포-기포 상호 작용의 비선형 효과는 감소 된 매개 변수 1 차원 및 3 차원 전산 유체 역학 (3D CFD) 모델링을 통해 특성화됩니다. 비접촉식 기포-버블 상호 작용을 설명하기 위해 1 차원 펌프 모델이 개발되었으며, 개발 된 1 차원 모델의 정확도는 유체 CFD 소프트웨어 인 FLOW-3D의 상용 볼륨을 통해 평가됩니다.

FLOW-3D CFD 모델은 실험적인 거품 역학 이미지와 실험적인 펌프 데이터에 대해 검증되었습니다. 채널에 있는 두 저항기의 붕괴 전 및 붕괴 후 기포 및 유동 역학은 수정 된 1 차원 모델에 의해 성공적으로 설명되었습니다. 순 펌핑 효과 설계 공간은 저항 배치 및 발사 시간 지연의 기능으로 특징 지어집니다.

1 차원 모델은 내부 채널 저항 배치 (0.2L <x <0.8L, 여기서 L은 채널 길이)로 동시 저항 발생에 대한 누적 흐름과 시간 지연시 내부 채널 저항 배치로 지연된 저항 발생을 정확하게 예측합니다. 증기 방울이 채널 단면을 채우는 데 필요한 시간보다 큽니다.

일반적으로 1 차원 모델 정확도는 저수지 근처의 저항 배치와 1 차원 모델에 의해 포착되지 않는 3D 기포-저수지 상호 작용 및 가로 기포 성장 상호 작용의 결과 인 짧은 시간 지연에서 어려움을 겪습니다. 채널 높이가 작을수록 1 차원 모델 정확도가 향상됩니다. 우리는 개발 된 1 차원 모델을 비접촉 기포-기포 상호 작용 비선형 영역에서 작동하는 관성 펌프 기반 미세 유체 시스템을 위한 1 차 빠른 설계 도구로 생각합니다.

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Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

Cristina González Fernández,1 Jenifer Gómez Pastora,2 Arantza Basauri,1 Marcos Fallanza,1 Eugenio Bringas,1 Jeffrey J. Chalmers,2 and Inmaculada Ortiz1,*
Author information Article notes Copyright and License information Disclaimer

생체 유체에서 자성 입자의 연속 흐름 분리 : 마이크로 장치 형상이 분리 성능을 어떻게 결정합니까?

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를 위한 기능화된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드는 자기적으로 회수되어 분석 또는 진단 테스트를 수행 할 수 있습니다.

연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다.

그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는데 있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜 주의를 기울였습니다.

여기에서 우리는 자기 비드가 혈액에서 분리되어 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 Y-Y 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다.

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다.

우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩 온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Keywords: particle magnetophoresis, CFD, cross section, chip fabrication

Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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Figure 2. Simulation of droplet separation by EWOD

Non-Linear Electrohydrodynamics in Microfluidic Devices

미세 유체 장치의 비선형 전기 유체 역학

by Jun ZengHewlett-Packard Laboratories, Hewlett-Packard Company, 1501 Page Mill Road, Palo Alto, CA 94304, USAInt. J. Mol. Sci.201112(3), 1633-1649; https://doi.org/10.3390/ijms12031633Received: 24 January 2011 / Revised: 10 February 2011 / Accepted: 24 February 2011 / Published: 3 March 2011

Abstract

Since the inception of microfluidics, the electric force has been exploited as one of the leading mechanisms for driving and controlling the movement of the operating fluid and the charged suspensions. Electric force has an intrinsic advantage in miniaturized devices. Because the electrodes are placed over a small distance, from sub-millimeter to a few microns, a very high electric field is easy to obtain. The electric force can be highly localized as its strength rapidly decays away from the peak. This makes the electric force an ideal candidate for precise spatial control. The geometry and placement of the electrodes can be used to design electric fields of varying distributions, which can be readily realized by Micro-Electro-Mechanical Systems (MEMS) fabrication methods. In this paper, we examine several electrically driven liquid handling operations. The emphasis is given to non-linear electrohydrodynamic effects. We discuss the theoretical treatment and related numerical methods. Modeling and simulations are used to unveil the associated electrohydrodynamic phenomena. The modeling based investigation is interwoven with examples of microfluidic devices to illustrate the applications. 

Keywords: dielectrophoresiselectrohydrodynamicselectrowettinglab-on-a-chipmicrofluidicsmodelingnumerical simulationreflective display

요약

미세 유체학이 시작된 이래로 전기력은 작동 유체와 충전 된 서스펜션의 움직임을 제어하고 제어하는 ​​주요 메커니즘 중 하나로 활용되어 왔습니다. 전기력은 소형 장치에서 본질적인 이점이 있습니다. 전극이 밀리미터 미만에서 수 미크론까지 작은 거리에 배치되기 때문에 매우 높은 전기장을 쉽게 얻을 수 있습니다. 

전기력은 강도가 피크에서 멀어지면서 빠르게 감소하기 때문에 고도로 국부화 될 수 있습니다. 이것은 전기력을 정밀한 공간 제어를 위한 이상적인 후보로 만듭니다.

전극의 기하학적 구조와 배치는 다양한 분포의 전기장을 설계하는 데 사용될 수 있으며, 이는 MEMS (Micro-Electro-Mechanical Systems) 제조 방법으로 쉽게 실현할 수 있습니다. 

이 논문에서 우리는 몇 가지 전기 구동 액체 처리 작업을 검토합니다. 비선형 전기 유체 역학적 효과에 중점을 둡니다. 이론적 처리 및 관련 수치 방법에 대해 논의합니다. 모델링과 시뮬레이션은 관련된 전기 유체 역학 현상을 밝히는 데 사용됩니다. 모델링 기반 조사는 응용 분야를 설명하기 위해 미세 유체 장치의 예와 결합됩니다. 

키워드 : 유전 영동 ; 전기 유체 역학 ; 전기 습윤 ; 랩 온어 칩 ; 미세 유체 ; 모델링 ; 수치 시뮬레이션 ; 반사 디스플레이

Droplet processing array Droplet based BioFlip
igure 1. Example of droplet-based digital microfluidics architecture. Above is an elevation view showing the layered structure of the chip. Below is a diagram illustrating the system (Adapted from [4]).
Figure 2. Simulation of droplet separation by EWOD
Figure 2. Simulation of droplet separation by EWOD. The top two figures illustrate the device configuration. Electric voltages are applied to all four electrodes embedded in the insulating material. The bottom left figure shows transient simulation solution. It illustrates the process of separating one droplet into two via EWOD. The bottom right figure shows the electric potential distribution inside the device. The color indicates the electric potential; the iso-potential surfaces are also drawn. The image shows the electric field is absent within the droplet body indicating the droplet is either conductive or highly polarizable.
Figure 4. Transient sequence of the Taylor cone formation
Figure 4. Transient sequence of the Taylor cone formation: simulation and experiment comparison. Experimental images are shown in the top row. Simulation results are shown in the bottom row. Their correspondence is indicated by the vertical alignment (Adapted from [4]).
Figure 6. Simulation of charge screening effect using a parallel-plate cell
Figure 6. Simulation of charge screening effect using a parallel-plate cell. Top-left image shows the electric current as function of time and driving voltage, top-right image shows the evolution of the species concentration as function of time and space, the bottom image shows the electric current readout after switching the applied voltage.
Figure 7. Transient simulation of electrohydrodynamic instability and the development of the cellular convective flow pattern.
Figure 7. Transient simulation of electrohydrodynamic instability and the development of the cellular convective flow pattern.
Figure 3. Simulation of dielectrophoresis driven axon migration
Figure 3. Simulation of dielectrophoresis driven axon migration. The set of small images on the left shows a transient simulation of single axon migration under an electric field generated by a pin electrode. The image on the right is a snapshot of a simulation where two axons are fused by dielectrophoresis using a pin electrode. Axons are outlined in white. Also shown are the iso-potential curves.

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Electrokinetics

Dielectrophoresis

유전 영동은 분극성 입자에 힘을 생성하여 균일하지 않은 전기장 (일반적으로 AC 전기장)에서 움직임을 유도합니다. 유전 영동력은 마이크로스케일 및 나노스케일 바이오 입자를 특성화, 처리 또는 조작하는 데 사용할 수 있습니다. 여기에는 세포, 바이러스, 박테리아, DNA 등의 분류, 포획 및 분리가 포함될 수 있습니다. 유전 영동은 FLOW-3D에서 완전히 설명 할 수 있으며 날카로운 인터페이스가 있거나 없는 단일 유체 또는 2 유체 흐름과 같이 코드에서 사용할 수있는 다른 모든 유체 흐름 옵션과 함께 활성화 될 수 있습니다.

Electro-wetting

전도성 액적에서 액체와 전극 사이에 인가되는 얇은 유전체 코팅 전위를 갖는 전극 상에 배치되면, 드롭 평면화와 전극 표면 확산이 일어납니다. 이 현상은 종종electro-wetting라 부릅니다. 현상은 전하 층의 발달과 관련되어 있으므로, 외부 전기장을 그들을 이동, 합체, 깨지거나 하는 원인을 조작하기 위해 사용될 수 있습니다.

 

Lab-On-Chip Electro-wetting Applications

Lab-on-chip 기반electro-wetting 은 분리된 물방울을 조절할 수 있어 설계자들이 복잡한 절차를 전통적인 실험실 장치를 달지만 훨씬 작은 volumes 으로 비슷한 실험을 수행할 수 있습니다. 이러한 기기는 효율적으로 운송, 병합되어 있으며 분리된 물방울들이 요구합니다. FLOW-3D는 사용자가이 장치를 조작하는 데 사용되는 기하학적 파라미터들 및 전압의 영향을 시뮬레이션 할 수 있도록 하여 설계 프로세스에 유용한 도구가 될 수 있습니다.

아래의 애니메이션은 수송 시뮬레이션 병합 및 분할 방울에 FLOW-3D의 기능을 보여줍니다. Lab-on-chip은 약 300 ㎛로 분리 된 두 개의 평행 한 플레이트로 구성됩니다. 바닥 판은 방울을 조작하기 위해 사용되는 그 안에 삽입 된 전극을 보유하고 있습니다. 액 적은 물 (약간 도전성) 실리콘 오일에 의해 둘러싸여 있습니다. 액체 방울의 부피가 800nl 관한 것입니다.

This lab-on-a-chip electrowetting simulation demonstrates an electric field being applied in order to split a small droplet.

Here an electric field is being applied in order to merge two small droplets.

This simulation shows an electric field being applied to a small droplet to control its motion.

Lab-on-a-chip

다양한 표면 장력을 사용하는 패턴화된 표면

마이크로 채널의 패턴화된 표면은 액체 사이의 실제 물리적 벽 없이도 여러 액체가 나란히 흐르는 특정 경로를 따라 한 저장소에서 다른 저장소로 액체를 운반하는 데 사용할 수 있습니다. 패턴화된 표면은 랩 온어 칩 (lab-on-a-chip), 바이오어세이, 마이크로 리액터 및 화학적 및 생물학적 감지를 통해 유체를 운반하는 데 사용됩니다. 이 경우 표면 장력은 패턴화된 흐름을 생성하기 위해 마이크로 채널의 유체 흐름을 조작하는데 사용됩니다. 고체 표면에서 유체의 친수성 또는 소수성 거동을 이용하여 마이크로 채널을 통한 여러 유체의 움직임을 제어합니다. 마이크로 채널 내부의 유체 흐름은 층상이므로 여러 유체 흐름 (이 경우 2 개)이 난류 혼합없이 나란히 흐를 수 있습니다. 유체 흐름의 측면에는 물리적 벽이 없기 때문에 흐름은 소위 가상 벽에 의해 제한됩니다. 이 벽은 기본적으로 두 유체 사이의 친수성 경계입니다.

Patterned surfaces in micro channels
Experimental results showing the three phases – A, B and C (left to right), Bin Zhao et al.

위 그림은 마이크로 채널의 실험을 보여줍니다. 중앙 수평 채널의 중간 스트립은 친수성이지만 상부 및 하부 수직 채널과 함께 나머지 채널은 소수성의 정도가 다릅니다. 소수성은 접촉각의 몇도 정도만 다릅니다. 상부 채널의 접촉각은 118o이고 하부 채널의 접촉각은 112o입니다. 그러나 접촉각의 작은 차이는 유체가 이러한 영역으로 흐르기 위해 상당히 다른 압력을 필요로합니다.

Numerical Simulation

처음에는 모든 채널이 다른 유체(투명)로 채워집니다. 분홍색 액체가 수평 채널로 밀리면 중앙 영역(단계 A)의 친수성 경로를 사용합니다. 압력이 증가하면 유체는 하부 친수성-수성 장벽을 깨고 하부 친수성 영역(단계 B)으로 흐르기 시작합니다. 압력을 더 높이면 마침내 유체가 상부 친수성-수소성 장벽을 부수고 상부 영역에서도 흐르기 시작합니다(Phase C).

Numerical results - patterned surfaces using varied surface tension
Numerical results showing the three phases – A, B and C.

위의 수치 결과는 둘 사이에 중요한 차이가 있다는 점을 고려할 때 실험에서 패턴화된 표면 연구의 전반적인 아이디어와 합리적인 비교 가능성을 보여줍니다. 위에 표시된 수치 결과는 과도 상태 (압력이 지속적으로 증가)이므로 유체 경계가 실험 결과와 정확히 유사하지 않습니다. 마찬가지로 유체 특성은 실험에 사용 된 특성과 정확히 유사하지 않습니다. 그럼에도 불구하고 유체 1은 실험에서와 같이 압력이 증가함에 따라 단계 A, B 및 C를 통과합니다. 단계 B에서 투명한 유체는 계속해서 위쪽 채널을 통해 흐르지 만 분홍색 유체만 아래쪽 영역으로 흐릅니다. 이것은 실험과 일치합니다. 흥미로운 것은 C 단계에서 나타난 기포 형성입니다. C 단계에서 기포 형성과 같은 흥미로운 물리학에 대한 계시와 연구는 미세 유체 장치의 설계 및 제작 과정에 중요 할 수 있습니다.

FLOW-3D Results

아래 애니메이션은 위의 실험에 대한 FLOW-3D의 시뮬레이션 결과를 보여줍니다. 유체 1 (하늘색)은 실험의 분홍색 유체와 동일합니다. 처음에는 전체 도메인이 Fluid 2 (투명 유체)로 채워집니다. 압력은 단계적으로 증가하고 시뮬레이션이 진행됨에 따라 세 단계를 모두 볼 수 있습니다.

Evolution of fluid flow with increasing pressure in patterned micro channels created by varying contact angles.

Ref: Bin Zhao, Jeffrey S. Moore, David J. Beebe, Surface-Directed Liquid Flow Inside Microchannels, Science 291, 1023 (2001)

Learn more about the power and versatility of modeling microfluidic applications with FLOW-3D

Continuous Flow Microfluidics

Continuous Flow Microfluidics

연속 흐름 미세 유체는 연속성을 깨지 않고 제작 된 마이크로 채널을 통해 액체 흐름을 조작하는 것입니다. 유체 흐름은 마이크로 펌프 (예 : 연동 펌프 또는 주사기 펌프)와 같은 외부 소스 또는 전기, 자기 또는 모세관 힘과 같은 내부 메커니즘에 의해 설정됩니다. 연속 유동 미세 유체 학은 미세 및 나노 입자 분리기, 입자 집속, 화학적 분리는 물론 단순한 생화학 적 응용을 포함한 다양한 응용 분야에서 응용 분야를 찾아 내지 만 높은 수준의 제어가 필요한 경우에는 선택 방법이 아닐 수 있습니다.

이 범주에 속하며 FLOW-3D를 사용하여 성공적으로 시뮬레이션한 프로세스 또는 장치로는 Joule 가열, 액체 게이트, 마이크로 유체 회로, 전기-오토믹 밸브, 입자 집중, 분류 및 분리, POC(Point-of-Care) 모세관 유량 장치 및 패턴 있는 표면 장치가 있습니다.

Sketch of cross section of the device
Capillary Flows
Electro osmosis
Electro-osmosis
Simulating joule heating
Joule Heating
Patterned surfaces in micro channels
Lab-on-a-chip
Magnetic fields
Magnetic Fields
Pneumatic valve
Microfluidic Circuits
Hong chamber simulations
Mixing Dynamics
Buoyancy dominant sorting
Particle Sorting

Lab-on-a-chip – Optofluidics (광 유체)

Optofluidics (광 유체)

  • 광학과 미세 유체의 조합
    – 다른 매체에서 빛의 속도 변화
  • 응용
    – 의료 진단 분야
    – 음식과 농업 분야
    – 물의 염분 제거 분야
    – 에너지 분야

광 유체의 L2 렌즈

  • 팽창 실 내부에 L2렌즈(곡률)가 형성됨
    – 피복 및 코어 유입구의 상대 유량
  • 렌즈의 곡률은 빛을 집중시킬 수 있음
  • 기존 렌즈 대비 장점
    – 동적으로 재구성 가능
    – 렌즈의 매끄러운 인터페이스
    – 손쉬운 통합 및 사전 정렬

FLOW-3D를 이용한 곡률 검증

  • 유량에 따른 곡률 변화
    – 가변 코어 유량 (VCF) 비율 사례 연구
    – 고정 코어 유량 (FCF) 비율 사례 연구

다양한 렌즈의 구성 – VCF와 FCF


실험과 FLOW-3D의 결과에 대한 검증

  • 실험 데이터와의 정확한 일치
  • 인터페이스 곡률을 기반으로 렌즈 특성을 예측하는데 FLOW-3D를 사용할 수 있음

Lab-on-a-chip – Joule heating and circulation in conducting fluid (전도성 유체의 줄 가열 및 순환)

Joule heating and circulation in conducting fluid (전도성 유체의 줄 가열 및 순환)

  • 줄 가열은 전류가 전도성 유체를 통과 할 때 발생함
    – 유체가 유전체인 경우에 전기장이 있을 경우 분극이 발생하여 유동이 발생
  • 많은 미세 유체의 공정은 마이크로 채널 내부의 유체를 조작하기 위해 외부의 자기력 및 전기력을 필요로 함
    – 유체에 대하여 이러한 외력이 미치는 영향을 이해하는 것이 중요함

FLOW-3D에서의 줄 가열 및 유동 시뮬레이션

  • 시뮬레이션 파라미터
    – 파란색 전극은 +9V, 분홍색 전극은 -9V
    – 전극 위의 유전체 유체 전도
  • 줄 가열은 유체의 온도를 500도로 상승시킴
  • 분극 유체는 전기장 윤곽을 따라 유체의 속도를 유도함

Lab-on-a-chip – Micromixer (마이크로 믹서)

Micromixer (마이크로 믹서)

  • 마이크로 믹싱의 어려움
    – 난류는 혼합을 유도하지만 미세 유체 유동은 층류가 강함 (레이놀즈 수가 낮기 때문)
    – 미세 유동의 흐름은 유체의 확산으로 인해 혼합되기전에 장거리 이동을 해야할 수 있음 (Peclet 수가 높기 때문)
  • 비침습 곡선 마이크로 채널을 사용하여 혼합을 유도할 수 있음
    – 섬세한 생물학적인 샘플은 분해되지 않습니다

곡선형 마이크로 믹서

  • Dean 수는 관성 및 원심력 대 점성력의 비율
  • 적절한 Dean 수에서, 횡류 장은 마이크로 채널로 유도 될 수 있음

믹싱 증가를 위한 마이크로 믹서 디자인 최적화

  • 최신 최적화 알고리즘을 사용하여 최적화 된 믹서 설계
  • 색다른 채널 모양이 믹싱을 개선

Lab-on-a-chip – Thermocapillary actuation (열 모세관 작동)

Thermocapillary actuation (열 모세관 작동)

  • 열 효과를 사용한 랩온어칩의 미세 액체의 길
    – 온도에 의존하는 표면 장력
    – 외부의 기계적인 힘이 필요하지 않음
    – 프로그래밍이 가능한 마이크로 히터 어레이를 통해 열 효과 추가
  • 유체의 고유한 습윤성으로 인해 유체 손실이 발생
    – 열 모세관 작동 외에도 패턴화 된 (친수성 또는 소수성) 표면을 배치하여 손실을 최소화 할 수 있음

공간의 다양한 표면 장력

  • 차가운 유체에서 표면 장력이 높기 때문에 공간의 변화가 발생함
    – 높은 표면 장력으로 유체를 함께 유지
    – 유체가 따뜻한 곳에서 차가운 곳으로 당겨짐
    – 유체의 움직임은 다음의 식을 통해 알 수 있음

FLOW-3D에서의 시뮬레이션

  • 미세 액체는 인접 구역의 온도에 따라 움직임 (소수성과 친수성)

Micro/Biofluidics with FLOW-3D (미세/생명 유체공학)

미세/생명유체공학에 관한 모델링

  • In-Vitro Diagnostics(IVD) : 체외 진단
  • Drug Delivery : 약물 전달
  • Point of Care Devices : 현장 진료 장비
  • Microarrays : 마이크로어레이
  • Lab-on-a-chip : 랩온어칩
  • MEMS(MicroElectroMechanical Systems) : 미세전자기계시스템

미세/생명유체공학에 관한 개념

  • 대류/확산 효과
  • 표면 장력
  • 자유 표면 역학
  • 점도 효과
  • 관성 효과
  • 다공성 매체
  • 전기 역학
  • 미립자 역학
  • 반응 속도론

Lab-on-a-chip

다양한 표면 장력을 사용하여 도장된 표면

마이크로 채널의 패턴 표면은 액체 사이의 실제 물리적 벽 없이 여러 액체가 나란히 흐르는 특정 경로를 따라 한 저장 장치에서 다른 저장 장치로 액체를 운반하는 데 사용될 수 있습니다. 패턴이 있는 표면은 액체를 lab-on-a-chip, 생물학적 경로, 마이크로 프로세서 및 화학적, 생물학적 감지 장치로 운반하는 데 사용됩니다.

이 경우 표면 장력은 미세 채널의 유체 흐름을 조작하여 패턴이 있는 흐름을 만드는 데 사용됩니다. 고체 표면에 있는 유체의 친수성 또는 소수성 거동은 마이크로 채널을 통해 복수 유체의 움직임을 제어하기 위해 이용됩니다.

마이크로 채널 내부의 유체 흐름은 층류로, 이는 다중 유체 흐름(이 경우 2개)이 난류 혼합 없이 나란히 흐를 수 있음을 의미합니다. 유체 스트림 측면에 물리적 벽이 없기 때문에 스트림은 이른바 가상 벽으로 제한됩니다. 이 벽들은 기본적으로 두 액체 사이의 친수성 경계입니다.

세가지 단계를 보여 주는 실험 결과 – A, B및 C(왼쪽에서 오른쪽으로), Bin Zhao et al.

위의 그림은 실험에서의 마이크로 채널을 보여준다. 중앙 수평 채널의 중간 스트립은 친수성인 반면, 상단 및 하단 수직 채널과 함께 남아 있는 채널은 친수성의 정도가 다릅니다. 그들은 단지 몇도의 접촉점 각도에 의해서만 그들의 친수성이 다릅니다. 상부 채널의 접점 각도는 118o 이고 하부 채널의 접점 각도는 112o입니다. 그러나 이러한 접촉 각도의 작은 차이는 유체가 이러한 영역으로 흐르기 위해 상당히 다른 압력을 필요로 합니다.

수치해석 시뮬레이션

처음에는 모든 채널에 각기 다른 유체가 주입됩니다(투명). 분홍색 유체를 수평 채널로 밀어 넣으면 중앙 영역의 친수성 경로(PhaseA)를 따라 이동합니다. 압력이 증가함에 따라, 유체는 하부 친수성-친수성 장벽을 깨고 바닥 소수성 구역으로 흐르기 시작합니다(상 B). 압력이 더욱 증가하면 유체가 마침내 상부 친수성-친수성 장벽을 깨고 상부 영역에서도 흐르기 시작합니다(단계 C).