Dynamics of vesicles in a wall-bounded shear flow

Lift at low Reynolds number

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Cell deformability heterogeneity recognition by unsupervised machine learning from in-flow motion parameters

Cell deformability is a well-established marker of cell states for diagnostic purposes. However, the measurement of a wide range of different deformability levels is still challenging, especially in cancer, where a large heterogeneity of rheological/mechanical properties is present. Therefore, a simple, versatile and cost-effective recognition method for variable rheological/mechanical properties of cells is needed. Here, we introduce a new set of in-flow motion parameters capable of identifying heterogeneity among cell deformability, properly modified by the administration of drugs for cytoskeleton destabilization. Firstly, we measured cell deformability by identification of in-flow motions, rolling (R), tumbling (T), swinging (S) and tank-treading (TT), distinctively associated with cell rheological/mechanical properties. Secondly, from a pool of motion and structural cell parameters, an unsupervised machine learning approach based on principal component analysis (PCA) revealed dominant features: the local cell velocity (V_Cell/V_Avg), the equilibrium position (Y_Eq) and the orientation angle variation (Δφ). These motion parameters clearly defined cell clusters in terms of motion regimes corresponding to specific deformability. Such correlation is verified in a wide range of rheological/mechanical properties from the elastic cells moving like R until the almost viscous cells moving as TT. Thus, our approach shows how simple motion parameters allow cell deformability heterogeneity recognition, directly measuring rheological/mechanical properties.

Flow-induced "waltzing" red blood cells: Microstructural reorganization and the corresponding rheological response

We investigate flow-induced structural organization in a dilute suspension of tumbling red blood cells (RBCs) under confined shear flow. For small Reynolds (Re = 0.1) and capillary numbers (Ca), with fully coupled hydrodynamic interaction (HI) and without interparticle adhesion, we find that HI between the biconcave discoid particles prompts the formation of layered RBC chains and synchronized rotating RBC pairs, referred here as "waltzing doublets." As the volume fraction ϕ increases, more waltzing doublets appear in RBC files. Stronger shear stress disrupts structural arrangements at higher Ca. We find that the flow-induced organization of waltzing doublets changes how the suspension viscosity varies with ϕ qualitatively. The intrinsic viscosity is particularly sensitive to microstructural rearrangement, increasing (decreasing) with ϕ at low (high) Ca that correlates with the change in the fraction of doublets. We verified flow-induced collective motion with comparison to two-cell simulations in which the cell volume fraction is controlled by varying the domain volume.

Multiple-Streams Focusing-Based Cell Separation in High Viscoelasticity Flow

Viscoelastic flow has been widely used in microfluidic particle separation processes, in which particles get focused on the channel center in diluted viscoelastic flow. In this paper, the transition from single-stream focusing to multiple-streams focusing (MSF) in high viscoelastic flow is observed, which is applied for cell separation processes. Particle focusing stream bifurcation is caused by the balance between elastic force and viscoelastic secondary flow drag force. The influence of cell physical properties, such as cell dimension, shape, and deformability, on the formation of multiple-streams focusing is studied in detail. Particle separation is realized utilizing different separation criteria. The size-based separation of red (RBC) and white (WBC) blood cells is demonstrated in which cells get focused in different streams based on their dimension difference. Cells with different deformabilities get stretched in the viscoelastic flow, leading to the change of focusing streams, and this property is harnessed to separate red blood cells infected with the malaria parasite, Plasmodium falciparum. The achieved results promote our understanding of particle movement in the high viscoelastic flow and enable new particle manipulation and separation processes for sample treatment in biofluids.

Shear-induced migration of confined flexible fibers

We report an experimental study of the shear-induced migration of flexible fibers in suspensions confined between two parallel plates. Non-Brownian fiber suspensions are imaged in a rheo-microscopy setup, where the top and the bottom plates counter-rotate and create a Couette flow. Initially, the fibers are near the bottom plate due to sedimentation. Under shear, the fibers move with the flow and migrate towards the center plane between the two walls. Statistical properties of the fibers, such as the mean values of the positions, orientations, and end-to-end lengths of the fibers, are used to characterize the behaviors of the fibers. A dimensionless parameter Λ_eff, which compares the hydrodynamic shear stress and the fiber stiffness, is used to analyze the effective flexibility of the fibers. The observations show that the fibers that are more likely to bend exhibit faster migration. As Λ_eff increases (softer fibers and stronger shear stresses), the fibers tend to align in the flow direction and the motions of the fibers transition from tumbling and rolling to bending. The bending fibers drift away from the walls to the center plane. Further increasing Λ_eff leads to more coiled fiber shapes, and the bending is more frequent and with larger magnitudes, which leads to more rapid migration towards the center. Different behaviors of the fibers are quantified with Λ_eff, and the structures and the dynamics of the fibers are correlated with the migration.

Stability and Deformation of Vesicles in a Cylindrical Flow

In this work, we used dissipative particle dynamics to study the stability, deformation, and rupture of polymer vesicles confined in cylindrical channels under the flow field. The morphological evolution, elongation, and rupture of vesicles and the corresponding mechanisms were intensively investigated. Bullet-like vesicles, leaking vesicles, spherical micelles, hamburger-like micelles, and bilayers were observed by changing the degree of confinement and dimensionless shear rate. We found that increasing the dimensionless shear rate and the degree of confinement can cause the deformation or rupture of polymeric vesicles. The asphericity parameter was utilized to describe the degree of elongation of vesicles deviating from the sphere in the direction of the flow. The results show that the aggregates are more likely to be spherical when the confinement is weak, while they become elongated bullet-like shapes when the confinement is strong. The investigation of dynamics reveals that the degree of confinement and the dimensionless shear rate can affect the chain stretching and reorganization during the process of vesicle elongation. Furthermore, the rupture time of the vesicle shows a nonlinear decrease with an increase in the dimensionless shear rate, and the confinement also contributes to the rupture. The results are very useful for guiding the application of vesicles in a flow environment.

Public-Health-Driven Microfluidic Technologies: From Separation to Detection

Separation and detection are ubiquitous in our daily life and they are two of the most important steps toward practical biomedical diagnostics and industrial applications. A deep understanding of working principles and examples of separation and detection enables a plethora of applications from blood test and air/water quality monitoring to food safety and biosecurity; none of which are irrelevant to public health. Microfluidics can separate and detect various particles/aerosols as well as cells/viruses in a cost-effective and easy-to-operate manner. There are a number of papers reviewing microfluidic separation and detection, but to the best of our knowledge, the two topics are normally reviewed separately. In fact, these two themes are closely related with each other from the perspectives of public health: understanding separation or sorting technique will lead to the development of new detection methods, thereby providing new paths to guide the separation routes. Therefore, the purpose of this review paper is two-fold: reporting the latest developments in the application of microfluidics for separation and outlining the emerging research in microfluidic detection. The dominating microfluidics-based passive separation methods and detection methods are discussed, along with the future perspectives and challenges being discussed. Our work inspires novel development of separation and detection methods for the benefits of public health.

The influence of cell elastic modulus on inertial positions in Poiseuille microflows

Microchannels are used as a transportation highway for suspended cells both in vivo and ex vivo. Lymphatic and cardiovascular systems transfer suspended cells through microchannels within the body, and microfluidic techniques such as lab-on-a-chip devices, flow cytometry, and CAR T-cell therapy utilize microchannels of similar sizes to analyze or separate suspended cells ex vivo. Understanding the forces that cells are subject to while traveling through these channels are important because certain applications exploit these cell properties for cell separation. This study investigated the influence that cytoskeletal impairment has on the inertial positions of circulating cells in laminar pipe flow. Two representative cancer cell lines were treated using cytochalasin D, and their inertial positions were investigated using particle streak imaging and compared between benign and metastatic cell lines. This resulted in a shift in inertial positions between benign and metastatic as well as treated and untreated cells. To determine and quantify the physical changes in the cells that resulted in this migration, staining and nanoindentation techniques were then used to determine the cells' size, circularity, and elastic modulus. It was found that the cells' exposure to cytochalasin D resulted in decreased elastic moduli of cells, with benign and metastatic cells showing decreases of 135 ± 91 and 130 ± 60 Pa, respectively, with no change in either size or shape. This caused benign, stiffer cancer cells to be more evenly distributed across the channel width than metastatic, deformable cancer cells; additionally, a decrease in the elastic moduli of both cell lines resulted in increased migration toward the channel center. These results indicate that the elastic modulus may play more of a part in the inertial migration of such cells than previously thought.

Dielectrophoresis-field flow fractionation for separation of particles: A critical review

Dielectrophoresis-field flow fractionation (DEP-FFF) has emerged as an efficient in-vitro, non-invasive, and label-free mechanism to manipulate a variety of nano- and micro-scaled particles in a continuous-flow manner. The technique is mainly used to fractionate particles/cells based on differences in their sizes and/or dielectric properties by employing dielectrophoretic force as an external force field applied perpendicular to the flow direction. The dielectrophoretic force is the result of a spatially non-uniform electric field in the microchannel that can be generated either by exploiting microchannel geometry or using special arrangements of microelectrode arrays. Several two-dimensional (e.g., coplanar interdigitated, castellated) and three-dimensional (e.g., top-bottom, side-wall) microelectrode designs have been successfully utilized to perform fractionation of heterogeneous samples. Although originally introduced as a separation technique, DEP-FFF has attracted increasing interest in performing other important operations such as switching, focusing, dipping, and surface functionalization of target particles. Nonetheless, the technique still suffers from limitations such as low throughput and joule heating. By comparatively analyzing recent developments that address these shortcomings, this work is a step forward towards realizing the full potential of DEP-FFF as an ideal candidate for point-of-care (POC) devices with diverse applications in the fields of biomedical, chemical, and environmental engineering.

Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels

OBJECTIVE

The flow behavior of blood is strongly affected by red blood cell (RBC) properties, such as the viscosity ratio C between cytosol and suspending medium, which can significantly be altered in several pathologies (e.g. sickle-cell disease, malaria). The main objective of this study is to understand the effect of C on macroscopic blood flow properties such as flow resistance in microvessels, and to link it to the deformation and dynamics of single RBCs.

METHODS

We employ mesoscopic hydrodynamic simulations to investigate flow properties of RBC suspensions with different cytosol viscosities for various flow conditions in cylindrical microchannels.

RESULTS

Starting from a dispersed cell configuration which approximates RBC dispersion at vessel bifurcations in the microvasculature, we find that the flow convergence and development of RBC-free layer (RBC-FL) depend only weakly on C, and require a convergence length in the range of 25D-50D, where D is channel diameter. In vessels with D ≤ 20 μ m , the final resistance of developed flow is nearly the same for C = 5 and C = 1, while for D = 40 μ m , the flow resistance for C = 5 is about 10% larger than for C = 1. The similarities and differences in flow resistance can be explained by viscosity-dependent RBC-FL thicknesses, which are associated with the viscosity-dependent dynamics of single RBCs.

CONCLUSIONS

The weak effect on the flow resistance and RBC-FL explains why RBCs can contain a high concentration of hemoglobin for efficient oxygen delivery, without a pronounced increase in the flow resistance. Furthermore, our results suggest that significant alterations in microvascular flow in various pathologies are likely not due to mere changes in cytosolic viscosity.

Changes of Inertial Focusing Position in a Triangular Channel Depending on Droplet Deformability and Size

Studies on cell separation with inertial microfluidics are often carried out with solid particles initially. When this condition is applied for actual cell separations, the efficiency typically becomes lower because of the polydispersity and deformability of cells. Therefore, the understanding of deformability-induced lift force is essential to achieve highly efficient cell separation. We investigate the inertial focusing positions of viscous droplets in a triangular channel while varying Re, deformability, and droplet size. With increasing Re and decreasing droplet size, the top focusing position splits and shifts along the sidewalls. The threshold size of the focusing position splitting increases for droplets with larger deformability. The overall path of the focusing position shifts with increasing Re also has a strong dependency on deformability. Consequently, droplets of the same size can have different focusing positions depending on their deformability. The feasibility of deformability-based cell separation is shown by different focusing positions of MCF10a and MCF7 cells.

Deformability-induced lift force in spiral microchannels for cell separation

Cell sorting and isolation from a heterogeneous mixture is a crucial task in many aspects of cell biology, biotechnology and medicine. Recently, there has been an interest in methods allowing cell separation upon their intrinsic properties such as cell size and deformability, without the need for use of biochemical labels. Inertial focusing in spiral microchannels has been recognised as an attractive approach for high-throughput cell sorting for myriad point of care and clinical diagnostics. Particles of different sizes interact to a different degree with the fluid flow pattern generated within the spiral microchannel and that leads to particles ordering and separation based on size. However, the deformable nature of cells adds complexity to their ordering within the spiral channels. Herein, an additional force, deformability-induced lift force (FD), involved in the cell focusing mechanism within spiral microchannels has been identified, investigated and reported for the first time, using a cellular deformability model (where the deformability of cells is gradually altered using chemical treatments). Using this model, we demonstrated that spiral microchannels are capable of separating cells of the same size but different deformability properties, extending the capability of the previous method. We have developed a unique label-free approach for deformability-based purification through coupling the effect of FD with inertial focusing in spiral microchannels. This microfluidic-based purification strategy, free of the modifying immuno-labels, allowing cell processing at a large scale (millions of cells per min and mls of medium per minute), up to high purities and separation efficiency and without compromising cell quality.

Lateral migration of viscoelastic droplets in a viscoelastic confined flow: role of discrete phase viscoelasticity

The cross-stream motion of viscoelastic droplets in viscoelastic fluids has received little attention since the classical study of migration of drops in a second order fluid. In this work, going beyond the existing classical theory, we experimentally elucidate the effect of drop-to-medium viscosity ratio k and elasticity ratio ξ on wall and center migration of viscoelastic droplets in a Poiseuille flow of a viscoelastic medium (PVP) at low Reynolds numbers (Re ≪ 1). We observed a contrasting migration behavior of Newtonian and viscoelastic droplets having the same viscosity ratios and propose the presence of a lift force F_VD due to the viscoelasticity of the droplet phase. We use analytical scaling and empirical modelling to show that the force F_VD scales with a prefactor that depends upon the Weissenberg number Wi_D and drop-to-medium viscosity ratio k and elasticity ratio ξ. Further, we utilize the proposed force for sorting of viscoelastic and Newtonian droplets.

Oblate to prolate transition of a vesicle in shear flow

Vesicles are micrometric soft particles whose membrane is a two-dimensional incompressible fluid governed by bending resistance leading to a zoology of shapes. The dynamics of deflated vesicles in shear flow with a bottom wall, a first minimal configuration to consider confined vesicles, is investigated using numerical simulations. Coexistence under flow of oblate (metastable) and prolate (stable) shapes is studied in details. In particular, we discuss the boundaries of the region of coexistence in the (v, Ca -plane where v is the reduced volume of the vesicle and Ca the Capillary number. We characterize the transition from oblate to prolate and analyse the divergence of the transition time near the critical capillary number. We then analyse the lift dynamics of an oblate vesicle in the weak flow regime.

Depletion layer dynamics of polyelectrolyte solutions under Poiseuille flow

The interfacial physics of complex liquids under flow remains a long-standing problem in fluid mechanics that is important for fields ranging from lubrication to nanofluidics. Liquids containing small amounts of high-molecular weight polymers are found to flow through channels faster than expected, a phenomenon attributed to the formation of boundary depletion layers that relaxes the no-slip boundary condition and allows the bulk of the fluid to slip past the walls. This work provides the most direct measurement to date of the dimension and composition of depletion layers of a polymer solution under flow. We anticipate extending this approach to help understand fluid dynamics in different regimes, such as flow in nanoconfinement and turbulence.

Complex liquids flow through channels faster than expected, an effect attributed to the formation of low-viscosity depletion layers at the boundaries. Characterization of depletion layer length scale, concentration, and dynamics has remained elusive due in large part to the lack of suitable real-space experimental techniques. The short length scales associated with depletion layers have traditionally prohibited direct imaging. By overcoming this limitation via adaptations of stimulated emission depletion (STED) microscopy, we directly measure the concentration profile of polymer solutions at a nonadsorbing wall under Poiseuille flow. Using this approach, we 1) confirm the theoretically predicted concentration profile governed by entropically driven depletion, 2) observe depletion layer narrowing at low to intermediate shear rates, and 3) report depletion layer composition that approaches pure solvent at unexpectedly low shear rates.

Droplet encapsulation of particles in different regimes and sorting of particle-encapsulating-droplets from empty droplets

Encapsulation of microparticles in droplets has profound applications in biochemical assays. We investigate encapsulation of rigid particles (polystyrene beads) and deformable particles (biological cells) inside aqueous droplets in various droplet generation regimes, namely, squeezing, dripping, and jetting. Our study reveals that the size of the positive (particle-encapsulating) droplets is larger or smaller compared to that of the negative (empty) droplets in the dripping and jetting regimes but no size contrast is observed in the squeezing regime. The size contrast of the positive and negative droplets in the different regimes is characterized in terms of capillary number C a and stream width ratio ω (i.e., ratio of stream width at the throat to particle diameter ω = w / d p ). While for deformable particles, the positive droplets are always larger compared to the negative droplets, for rigid particles, the positive droplets are larger in the dripping and jetting regimes for 0.50 ≤ ω ≤ 0.80 but smaller in the jetting regime for ω < 0.50 . We exploit the size contrast of positive and negative droplets for sorting across the fluid-fluid interface based on noninertial lift force (at R e ≪ 1 ), which is a strong function of droplet size. We demonstrate sorting of the positive droplets encapsulating polystyrene beads and biological cells from the negative droplets with an efficiency of ∼95% and purity of ∼65%. The proposed study will find relevance in single-cell studies, where positive droplets need to be isolated from the empty droplets prior to downstream processing.

Self-organization of red blood cell suspensions under confined 2D flows

Dynamic self-organized structures with long-range order have been observed in emulsions and suspensions of particles under confined flows. Here, experiments on red blood cell suspensions under quasi-2D confined flows and numerical simulations were combined to explore long-distance self-organization as a function of the channel width, red blood cell concentration and flow rate. They reveal and quantitatively describe the existence of red blood cell long-range alignments and heterogeneous cross-stream concentration profiles characterized by red blood cell-enriched bands parallel to the flow. Numerical simulations show that, in addition to the degree of lateral confinement, the key factor for the structural self-organization of a suspension of particles under a confined flow is the deformability of the constituent particles.

Non-inertial lift induced migration for label-free sorting of cells in a co-flowing aqueous two-phase system

We present a novel label-free passive microfluidic technique for isolation of cancer cells (EpCAM+ and CD45−) from peripheral blood mononuclear cells (PBMCs) (CD45+ and EpCAM−) in aqueous two-phase system (ATPS).

On Stability of Specific Adhesion of Particles to Membranes in Simple Shear Flow

Adhesion of carrier particles to the luminal surface of endothelium under hemodynamic flow conditions is critical for successful vascular drug delivery. Endothelial cells line the inner surface of blood vessels. The effect of mechanical behavior of this compliant surface on the adhesion of blood-borne particles is unknown. In this contribution, we use a phase-plane method, first developed by Hammer and Lauffenburger [Biophysical Journal, 52, 475 (1987)], to analyze the stability of specific adhesion of a spherical particle to a compliant interface layer. We construct a phase diagram that predicts the state of particle adhesion, subjected to an incident simple shear flow, in terms of interfacial elasticity, shear rate, binding affinity of cell adhesive molecules, and their surface density. The main conclusion is that the local deformation of the flexible interface inhibits the stable adhesion of the particle. In comparison with adhesion to a rigid substrate, a greater ligand density is required to establish a stable adhesion between a particle and a compliant interface. The results can be used for the rational design of particles in vascular drug delivery.

Internal Viscosity-Dependent Margination of Red Blood Cells in Microfluidic Channels

Cytoplasmic viscosity-dependent margination of red blood cells (RBC) for flow inside microchannels was studied using numerical simulations, and the results were verified with microfluidic experiments. Wide range of suspension volume fractions or hematocrits was considered in this study. Lattice Boltzmann method for fluid-phase coupled with spectrin-link method for RBC membrane deformation was used for accurate analysis of cell margination. RBC margination behavior shows strong dependence on the internal viscosity of the RBCs. At equilibrium, RBCs with higher internal viscosity marginate closer to the channel wall and the RBCs with normal internal viscosity migrate to the central core of the channel. Same margination pattern has been verified through experiments conducted with straight channel microfluidic devices. Segregation between RBCs of different internal viscosity is enhanced as the shear rate and the hematocrit increases. Stronger separation between normal RBCs and RBCs with high internal viscosity is obtained as the width of a high aspect ratio channel is reduced. Overall, the margination behavior of RBCs with different internal viscosities resembles with the margination behavior of RBCs with different levels of deformability. Observations from this work will be useful in designing microfluidic devices for separating the subpopulations of RBCs with different levels of deformability that appear in many hematologic diseases such as sickle cell disease (SCD), malaria, or cancer.

Elastic particle deformation in rectangular channel flow as a measure of particle stiffness

In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.

Margination of Stiffened Red Blood Cells Regulated By Vessel Geometry

Margination of stiffened red blood cells has been implicated in many vascular diseases. Here, we report the margination of stiffened RBCs in vivo, and reveal the crucial role of the vessel geometry in the margination by calculations when the blood is seen as viscoelastic fluid. The vessel-geometry-regulated margination is then confirmed by in vitro experiments in microfluidic devices, and it establishes new insights to cell sorting technology and artificial blood vessel fabrication.

Effects of membrane deformability and bond formation/dissociation rates on adhesion dynamics of a spherical capsule in shear flow

Cellular adhesion plays a critical role in biological systems and biomedical applications. Cell deformation and biophysical properties of adhesion molecules are of significance for the adhesion behavior. In the present work, dynamic adhesion of a deformable capsule to a planar substrate, in a linear shear flow, is numerically simulated to investigate the combined influence of membrane deformability (quantified by the capillary number) and bond formation/dissociation rates on the adhesion behavior. The computational model is based on the immersed boundary-lattice Boltzmann method for the capsule-fluid interaction and a probabilistic adhesion model for the capsule-substrate interaction. Three distinct adhesion states, detachment, rolling adhesion and firm adhesion, are identified and presented in a state diagram as a function of capillary number and bond dissociation rate. The impact of bond formation rate on the state diagram is further investigated. Results show that the critical bond dissociation rate for the transition of rolling or firm adhesion to detachment is strongly related to the capsule deformability. At the rolling-adhesion state, smaller off rates are needed for larger capillary number to increase the rolling velocity and detach the capsule. In contrast, the critical off rate for firm-to-detach transition slightly increases with the capillary number. With smaller on rate, the effect of capsule deformability on the critical off rates is more pronounced and capsules with moderate deformability are prone to detach by the shear flow. Further increasing of on rate leads to large expansion of both rolling-adhesion and firm-adhesion regions. Even capsules with relatively large deformability can maintain stable rolling adhesion at certain off rate.

Direct Tracking of Particles and Quantification of Margination in Blood Flow

Margination refers to the migration of particles toward blood vessel walls during blood flow. Understanding the mechanisms that lead to margination will aid in tailoring the attributes of drug-carrying particles for effective drug delivery. Most previous studies evaluated the margination propensity of these particles via an adhesion mechanism, i.e., by measuring the number of particles that adhered to the channel wall. Although particle adhesion and margination are related, adhesion also depends on other factors. In this study, we quantified the margination propensity of particles of varying diameters (0.53, 0.84, and 2.11 μm) and apparent wall shear rates (30, 61, and 121 s^-1) by directly tracking fluorescent particles flowing through a microfluidic channel. The margination parameter, M, is defined as the total number of particles found within the cell-free layers normalized by the total number of particles that passed through the channel. In this study, an M-value of 0.2 indicated no margination, which was observed for all particle sizes in water. In the case of blood, larger particles were found to have higher M-values and thus marginated more effectively than smaller particles. The corresponding M-values at the device outlet were 0.203, 0.223, and 0.285 for 0.53-, 0.84-, and 2.11-μm particles, respectively. At the inlet, the M-values for all particle sizes in blood were <0.2, suggesting that non-fully-developed flow and constriction may lead to demargination. For particle velocities transverse to the flow direction (v_y), all particle sizes showed a larger standard deviation of v_y as well as a higher effective diffusivity when the particles were suspended in blood relative to water. These higher values are attributed to collisions between the blood cells and particles, further supporting recent simulation results. In terms of flow rates, for a given particle size, the higher the flow rate, the higher the M-value.

Evaluation and comparison of two microfluidic size separation strategies for vesicle suspensions

Two size-based separation strategies are evaluated for suspensions consisting of giant unilamellar vesicles with a broad, continuous distribution of diameters. Microfluidic devices were designed to separate an initial suspension into larger and smaller particles via either filtration or inertial focusing. These separation mechanisms were tested with suspensions of vesicles and suspensions of rigid spheres separately to illustrate the effect of deformability on separation ability. We define several separation metrics to assess the separation ability and to enable comparison between separation strategies. The filtration device significantly reduced the polydispersity of the separated vesicle fractions relative to the starting suspension and displayed an ability to separate vesicle suspensions at high throughputs. The device that utilized inertial focusing exhibited adequate polydispersity reduction and performed best with diluted vesicle suspensions. The inertial device had fewer issues with debris and trapped air, leading to short device preparation times and indicating a potential for continuous separation operation.

Focusing and alignment of erythrocytes in a viscoelastic medium

Viscoelastic fluid flow-induced cross-streamline migration has recently received considerable attention because this process provides simple focusing and alignment over a wide range of flow rates. The lateral migration of particles depends on the channel geometry and physicochemical properties of particles. In this study, digital in-line holographic microscopy (DIHM) is employed to investigate the lateral migration of human erythrocytes induced by viscoelastic fluid flow in a rectangular microchannel. DIHM provides 3D spatial distributions of particles and information on particle orientation in the microchannel. The elastic forces generated in the pressure-driven flows of a viscoelastic fluid push suspended particles away from the walls and enforce erythrocytes to have a fixed orientation. Blood cell deformability influences the lateral focusing and fixed orientation in the microchannel. Different from rigid spheres and hardened erythrocytes, deformable normal erythrocytes disperse from the channel center plane, as the flow rate increases. Furthermore, normal erythrocytes have a higher angle of inclination than hardened erythrocytes in the region near the side-walls of the channel. These results may guide the label-free diagnosis of hematological diseases caused by abnormal erythrocyte deformability.

Dynamics of Aqueous Droplets at the Interface of Coflowing Immiscible Oils in a Microchannel

We report the dynamics of aqueous droplets of different size and viscosity at the interface of a coflowing stream of immiscible oils (i.e., primary and secondary continuous phases) in a microchannel, at low Re. The lateral migration of droplets introduced into the primary continuous phase toward the interface and subsequent selective migration of droplets across the interface into the secondary continuous phase is investigated. The interplay between the competing noninertial lift and interfacial tension forces, which govern the interfacial migration of the droplets, is presented and discussed. The velocity and strain rate profiles, and interface location, which are critical for calculating the lift force and migration behavior of droplets, are presented. The trajectories of droplets of different size and viscosity in the primary continuous phase are obtained for different interface locations. During interfacial migration, the deformation behavior of droplets of different viscosities is studied. Finally, sorting of droplets based on size contrast is demonstrated and sorting efficiency is found. A new paradigm of migration and sorting of droplets is reported, which could find importance in chemical and biological applications.

Microfluidic assessment of mechanical cell damage by extensional stress

Mammalian cells have been widely used in bioreactors to produce biological products such as pharmaceutical materials. The productivity of such bioreactors is vastly affected by flow-induced cell damage in complicated flow environments, such as agitation-driven turbulence and oxygen bubble bursting at the interface between the culturing medium and air. However, there is no systematic approach to diagnose the cell damage caused by the hydrodynamic stress. In this work, we propose a novel microfluidic method to accurately assess the mechanical cell damage under a controlled extensional stress field, generated in a microfluidic cross-slot geometry. The cell damage in the extensional field is related to the oxygen bubble bursting process. We employed viscoelasticity-induced particle focusing to align the cells along the shear-free channel centerline, so that all the cells experience a similar extensional stress field, which also precludes the cell damage due to wall shear stress. We applied our novel microfluidic sensor to find the critical extensional stress to damage Chinese hamster ovary (CHO) cells; the critical stress is found to be ∼250 Pa. Our current results are relevant in the design of practical bioreactors, as our results clearly demonstrate that the control of the bubble bursting process is critical in minimizing cell damage in bioreactor applications. Further, our results will provide useful information on the biophysical cell properties under fluid flow environments.

Ellipsoidal Relaxation of Deformed Vesicles

Theoretical analysis and experimental quantification on the ellipsoidal relaxation of vesicles are presented. The current work reveals the simplicity and universal aspects of this process. The Helfrich formula is shown to apply to the dynamic relaxation of moderate-to-high tension membranes, and a closed-form solution is derived which predicts the vesicle aspect ratio as a function of time. Scattered data are unified by a time scale, which leads to a similarity behavior, governed by a distinctive solution for each vesicle type. Two separate regimes in the relaxation are identified, namely, the "entropic" and the "constant-tension" regimes. The bending rigidity and the initial membrane tension can be simultaneously extracted from the data analysis, posing the current approach as an effective means for the mechanical analysis of biomembranes.

Microfluidic Strategies for Understanding the Mechanics of Cells and Cell-Mimetic Systems

Microfluidic systems are attracting increasing interest for the high-throughput measurement of cellular biophysical properties and for the creation of engineered cellular microenvironments. Here we review recent applications of microfluidic technologies to the mechanics of living cells and synthetic cell-mimetic systems. We begin by discussing the use of microfluidic devices to dissect the mechanics of cellular mimics, such as capsules and vesicles. We then explore applications to circulating cells, including erythrocytes and other normal blood cells, and rare populations with potential disease diagnostic value, such as circulating tumor cells. We conclude by discussing how microfluidic devices have been used to investigate the mechanics, chemotaxis, and invasive migration of adherent cells. In these ways, microfluidic technologies represent an increasingly important toolbox for investigating cellular mechanics and motility at high throughput and in a format that lends itself to clinical translation.

Lateral migration of a spherical capsule near a plane wall in Stokes flow

Lateral migration is the motion of a particle perpendicular to the direction of the surrounding flow. One of the factors leading to the lateral migration of a deformable particle in Stokes flow is the presence of a nearby wall. We numerically investigate the lateral migration of a capsule in a near-wall simple shear flow using a boundary integral method coupled with a finite element method. We find that asymmetrical deformation of the capsule induced by the wall is correlated with a reduction in the lift velocity relative to the lift velocity predicted by a far-field analytical solution. A combination of this asymmetrical deformation, which decreases the lift velocity, and an increase in the value of the capsule stresslet near the wall, which works to increase the lift velocity, leads to a migration velocity that is nearly independent of capillary number and membrane constitutive law at large deformation near the wall.

Trapping and release of giant unilamellar vesicles in microfluidic wells

We describe the trapping and release of giant unilamellar vesicles (GUVs) in a thin and wide microfluidic channel, as they cross indentations etched in the channel ceiling. This trapping results from the reduction of the membrane elastic energy, which is stored in the GUV as it squeezes to enter into the thin channel. We demonstrate that GUVs whose diameter is slightly larger than the channel height can be trapped and that they can be untrapped by flowing the outer fluid beyond a critical velocity. GUVs smaller than the channel height flow undisturbed while those much larger cannot squeeze into the thin regions. Within the range that allows trapping, larger GUVs are anchored more strongly than smaller GUVs. The ability to trap vesicles provides optical access to the GUVs for extended periods of time; this allows the observation of recirculation flows on the surface of the GUVs, in the forward direction near the mid-plane of the channel and in the reverse direction elsewhere. We also obtain the shape of GUVs under different flow conditions through confocal microscopy. This geometric information is used to derive a mechanical model of the force balance that equates the viscous effects from the outer flow with the elastic effects based on the variation of the membrane stretching energy. This model yields good agreement with the experimental data when values of the stretching moduli are taken from the scientific literature. This microfluidic approach provides a new way of storing a large number of GUVs at specific locations, with or without the presence of an outer flow. As such, it constitutes a high-throughput alternative to micropipette manipulation of individual GUVs for chemical or biological applications.

Inertial microfluidic physics

Microfluidics has experienced massive growth in the past two decades, and especially with advances in rapid prototyping researchers have explored a multitude of channel structures, fluid and particle mixtures, and integration with electrical and optical systems towards solving problems in healthcare, biological and chemical analysis, materials synthesis, and other emerging areas that can benefit from the scale, automation, or the unique physics of these systems. Inertial microfluidics, which relies on the unconventional use of fluid inertia in microfluidic platforms, is one of the emerging fields that make use of unique physical phenomena that are accessible in microscale patterned channels. Channel shapes that focus, concentrate, order, separate, transfer, and mix particles and fluids have been demonstrated, however physical underpinnings guiding these channel designs have been limited and much of the development has been based on experimentally-derived intuition. Here we aim to provide a deeper understanding of mechanisms and underlying physics in these systems which can lead to more effective and reliable designs with less iteration. To place the inertial effects into context we also discuss related fluid-induced forces present in particulate flows including forces due to non-Newtonian fluids, particle asymmetry, and particle deformability. We then highlight the inverse situation and describe the effect of the suspended particles acting on the fluid in a channel flow. Finally, we discuss the importance of structured channels, i.e. channels with boundary conditions that vary in the streamwise direction, and their potential as a means to achieve unprecedented three-dimensional control over fluid and particles in microchannels. Ultimately, we hope that an improved fundamental and quantitative understanding of inertial fluid dynamic effects can lead to unprecedented capabilities to program fluid and particle flow towards automation of biomedicine, materials synthesis, and chemical process control.

Numerical simulation of the pairwise interaction of deformable cells during migration in a microchannel

Leukocytes and other circulating cells deform and move relatively to the channel flow in the lateral and translational directions. Their migratory property is important in immune response, hemostasis, cancer progression, delivery of nutrients, and microfluidic technologies such as cell separation and enrichment, and flow cytometry. Using our three-dimensional computational algorithm for multiphase viscoelastic flow, we have investigated the effect of pairwise interaction on the lateral and translational migration of circulating cells in a microchannel. The numerical simulation data show that when two cells with the same size and small separation distance interact, repulsive interaction take place until they reach the same lateral equilibrium position. During this process, they undergo swapping or passing, depending on the initial separation distance between each other. The threshold value of this distance increases with cell deformation, indicating that the cells experiencing larger deformation are more likely to swap. When a series of closely spaced cells with the same size are considered, they generally undergo damped oscillation in both lateral and translational directions until they reach equilibrium positions where they become evenly distributed in the flow direction (self-assembly phenomenon). A series of cells with a large lateral separation distance could collide repeatedly with each other, eventually crossing the centerline and entering the other side of the channel. For a series of cells with different deformability, more deformable cells, upon impact with less deformable cells, move to an equilibrium position closer to the centerline. The results of our study show that the bulk deformation of circulating cells plays a key role in their migration in a microchannel.

Particle margination and its implications on intravenous anticancer drug delivery

"Margination" refers to the movement of particles in flow toward the walls of a channel. The term was first coined in physiology for describing the behavior of white blood cells (WBCs) and platelets in blood flow. The margination of particles is desirable for anticancer drug delivery because it results in the close proximity of drug-carrying particles to the endothelium, where they can easily diffuse into cancerous tumors through the leaky vasculature. Understanding the fundamentals of margination may further lead to the rational design of particles and allow for more specific delivery of anticancer drugs into tumors, thereby increasing patient comfort during cancer treatment. This paper reviews existing theoretical and experimental studies that focus on understanding margination. Margination is a complex phenomenon that depends on the interplay between inertial, hydrodynamic, electrostatic, lift, van der Waals, and Brownian forces. Parameters that have been explored thus far include the particle size, shape, density, stiffness, shear rate, and the concentration and aggregation state of red blood cells (RBCs). Many studies suggested that there exists an optimal particle size for margination to occur, and that nonspherical particles tend to marginate better than spherical particles. There are, however, conflicting views on the effects of particle density, stiffness, shear rate, and RBCs. The limitations of using the adhesion of particles to the channel walls in order to quantify margination propensity are explained, and some outstanding questions for future research are highlighted.

Hydrodynamic lift of vesicles and red blood cells in flow--from Fåhræus & Lindqvist to microfluidic cell sorting

Hydrodynamic lift forces acting on cells and particles in fluid flow receive ongoing attention from medicine, mathematics, physics and engineering. The early findings of Fåhræus & Lindqvist on the viscosity change of blood with the diameter of capillaries motivated extensive studies both experimentally and theoretically to illuminate the underlying physics. We review this historical development that led to the discovery of the inertial and non-inertial lift forces and elucidate the origins of these forces that are still not entirely clear. Exploiting microfluidic techniques induced a tremendous amount of new insights especially into the more complex interactions between the flow field and deformable objects like vesicles or red blood cells. We trace the way from the investigation of single cell dynamics to the recent developments of microfluidic techniques for particle and cell sorting using hydrodynamic forces. Such continuous and label-free on-chip cell sorting devices promise to revolutionize medical analyses for personalized point-of-care diagnosis. We present the state-of-the-art of different hydrodynamic lift-based techniques and discuss their advantages and limitations.

Fluid vesicles in flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.

Axial nanoscale localization by normalized total internal reflection fluorescence microscopy

We present a simple modification of a standard total internal reflection fluorescence microscope to achieve nanometric axial resolution, typically ≈10  nm. The technique is based on a normalization of total internal reflection images by conventional epi-illumination images. We demonstrate the potential of our method to study the adhesion of phopholipid giant unilamellar vesicles.

Inertia- and deformation-driven migration of a soft particle in confined shear and Poiseuille flow

Non-linear soft particle lift caused by inertia- and deformation-driven lateral migration, leading to a migration-free zone in shear flow.

Sorting of circulating tumor cells (MV3-melanoma) and red blood cells using non-inertial lift

We demonstrate the method of non-inertial lift induced cell sorting (NILICS), a continuous, passive, and label-free cell sorting approach in a simple single layer microfluidic device at low Reynolds number flow conditions. In the experiments, we exploit the non-inertial lift effect to sort circulating MV3-melanoma cells from red blood cell suspensions at different hematocrits as high as 9%. We analyze the separation process and the influence of hematocrit and volume flow rates. We achieve sorting efficiencies for MV3-cells up to EMV3 = 100% at Hct = 9% and demonstrate cell viability by recultivation of the sorted cells.

Slow sedimentation and deformability of charged lipid vesicles

The study of vesicles in suspension is important to understand the complicated dynamics exhibited by cells in in vivo and in vitro. We developed a computer simulation based on the boundary-integral method to model the three dimensional gravity-driven sedimentation of charged vesicles towards a flat surface. The membrane mechanical behavior was modeled using the Helfrich Hamiltonian and near incompressibility of the membrane was enforced via a model which accounts for the thermal fluctuations of the membrane. The simulations were verified and compared to experimental data obtained using suspended vesicles labelled with a fluorescent probe, which allows visualization using fluorescence microscopy and confers the membrane with a negative surface charge. The electrostatic interaction between the vesicle and the surface was modeled using the linear Derjaguin approximation for a low ionic concentration solution. The sedimentation rate as a function of the distance of the vesicle to the surface was determined both experimentally and from the computer simulations. The gap between the vesicle and the surface, as well as the shape of the vesicle at equilibrium were also studied. It was determined that inclusion of the electrostatic interaction is fundamental to accurately predict the sedimentation rate as the vesicle approaches the surface and the size of the gap at equilibrium, we also observed that the presence of charge in the membrane increases its rigidity.

Hydrodynamic mechanisms of cell and particle trapping in microfluidics

Focusing and sorting cells and particles utilizing microfluidic phenomena have been flourishing areas of development in recent years. These processes are largely beneficial in biomedical applications and fundamental studies of cell biology as they provide cost-effective and point-of-care miniaturized diagnostic devices and rare cell enrichment techniques. Due to inherent problems of isolation methods based on the biomarkers and antigens, separation approaches exploiting physical characteristics of cells of interest, such as size, deformability, and electric and magnetic properties, have gained currency in many medical assays. Here, we present an overview of the cell/particle sorting techniques by harnessing intrinsic hydrodynamic effects in microchannels. Our emphasis is on the underlying fluid dynamical mechanisms causing cross stream migration of objects in shear and vortical flows. We also highlight the advantages and drawbacks of each method in terms of throughput, separation efficiency, and cell viability. Finally, we discuss the future research areas for extending the scope of hydrodynamic mechanisms and exploring new physical directions for microfluidic applications.

Dielectrophoresis has broad applicability to marker-free isolation of tumor cells from blood by microfluidic systems

The number of circulating tumor cells (CTCs) found in blood is known to be a prognostic marker for recurrence of primary tumors, however, most current methods for isolating CTCs rely on cell surface markers that are not universally expressed by CTCs. Dielectrophoresis (DEP) can discriminate and manipulate cancer cells in microfluidic systems and has been proposed as a molecular marker-independent approach for isolating CTCs from blood. To investigate the potential applicability of DEP to different cancer types, the dielectric and density properties of the NCI-60 panel of tumor cell types have been measured by dielectrophoretic field-flow fractionation (DEP-FFF) and compared with like properties of the subpopulations of normal peripheral blood cells. We show that all of the NCI-60 cell types, regardless of tissue of origin, exhibit dielectric properties that facilitate their isolation from blood by DEP. Cell types derived from solid tumors that grew in adherent cultures exhibited dielectric properties that were strikingly different from those of peripheral blood cell subpopulations while leukemia-derived lines that grew in non-adherent cultures exhibited dielectric properties that were closer to those of peripheral blood cell types. Our results suggest that DEP methods have wide applicability for the surface-marker independent isolation of viable CTCs from blood as well as for the concentration of leukemia cells from blood.

Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity

Rolling leukocytes deform and show a large area of contact with endothelium under physiological flow conditions. We studied the effect of cytoplasmic viscosity on leukocyte rolling using our three-dimensional numerical algorithm that treats leukocyte as a compound droplet in which the core phase (nucleus) and the shell phase (cytoplasm) are viscoelastic fluids. The algorithm includes the mechanical properties of the cell cortex by cortical tension and considers leukocyte microvilli that deform viscoelastically and form viscous tethers at supercritical force. Stochastic binding kinetics describes binding of adhesion molecules. The leukocyte cytoplasmic viscosity plays a critical role in leukocyte rolling on an adhesive substrate. High-viscosity cells are characterized by high mean rolling velocities, increased temporal fluctuations in the instantaneous velocity, and a high probability for detachment from the substrate. A decrease in the rolling velocity, drag, and torque with the formation of a large, flat contact area in low-viscosity cells leads to a dramatic decrease in the bond force and stable rolling. Using values of viscosity consistent with step aspiration studies of human neutrophils (5-30 Pa·s), our computational model predicts the velocities and shape changes of rolling leukocytes as observed in vitro and in vivo.

Flow loading induces oscillatory trajectories in a bloodstream parasite

The dynamics of isolated microswimmers are studied in bounded flow using the African trypanosome, a unicellular parasite, as the model organism. With the help of a microfluidics platform, cells are subjected to flow and found to follow an oscillatory path that is well fit by a sine wave. The frequency and amplitudes of the oscillatory trajectories are dependent on the flow velocity and cell orientation. When traveling in such a manner, trypanosomes orient upstream while downstream-facing cells tumble within the same streamline. A comparison with immotile trypanosomes demonstrates that self-propulsion is essential to the trajectories of trypanosomes even at flow velocities up to ∼40 times higher than their own swimming speed. These studies reveal important swimming dynamics that may be generally pertinent to the transport of microswimmers in flow and may be relevant to microbial pathogenesis.