Dynamics of vesicles in a wall-bounded shear flow

Tank treading of optically trapped red blood cells in shear flow

Tank-treading (TT) motion is established in optically trapped, live red blood cells (RBCs) held in shear flow and is systematically investigated under varying shear rates, temperature (affecting membrane viscosity), osmolarity (resulting in changes in RBC shape and cytoplasmic viscosity), and viscosity of the suspending medium. TT frequency is measured as a function of membrane and cytoplasmic viscosity, the former being four times more effective in altering TT frequency. TT frequency increases as membrane viscosity decreases, by as much as 10% over temperature changes of only 4°C at a shear rate of ∼43 s(-1). A threshold shear rate (1.5 ± 0.3 s(-1)) is observed below which the TT frequency drops to zero. TT motion is also observed in shape-engineered (spherical) RBCs and those with cholesterol-depleted membranes. The TT threshold is less evident in both cases but the TT frequency increases in the latter cells. Our findings indicate that TT motion is pervasive even in folded and deformed erythrocytes, conditions that occur when such erythrocytes flow through narrow capillaries.

Orientation and internal flow of a vesicle in tank-treading motion in shear flow

Deformation, orientation and internal flow of lipid bilayer vesicles in linear shear flows are investigated using phase contrast microscopy. We construct a rotating-cylinder apparatus, which can generate a linear shear flow with constant shear rates. Vesicles are prepared from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) by the gentle hydration method. When visualizing internal flows, polystyrene tracer particles are mixed with the hydration water solution. In our observation, vesicles deform to steady ellipsoidal shapes and show constant orientations given by θ(i), which is the angle between the major axis and the flow direction. The tracer particles inside a vesicle rotate around the center of the vesicle along ellipsoidal orbits, which are homothetic to the shape of the vesicle. It is shown that the relationship between θ(i) and the swelling ratio (volume/surface ratio) S(w) agrees quantitatively with the experimental result of Abkarian et al. [Biophys. J.89, 1055 (2005)], which was obtained with vesicles in wall-bounded shear flows. It also agrees with a theoretical analysis of Keller and Skalak [J. Fluid Mech.120, 27 (1982)] and other numerical simulations. It is also shown that angular velocities of the particles near the membrane change periodically and agree quantitatively with the experimental result for the motion of a particle adhering to the membrane of a tank-treading vesicle [Kantsler and Steinberg, Phys. Rev. Lett.95, 258101 (2005)]. A statistical analysis indicates that the velocity of the internal fluid close to the membrane is not constant along the circumference, which implies the possibility of a three-dimensional flow field of the lipid molecules or an apparent stretching motion of the membrane by the effect of hidden surface area due to thermal fluctuation.

Dynamic physical properties of dissociated tumor cells revealed by dielectrophoretic field-flow fractionation

Metastatic disease results from the shedding of cancer cells from a solid primary tumor, their transport through the cardiovascular system as circulating tumor cells (CTCs) and their engraftment and growth at distant sites. Little is known about the properties and fate of tumor cells as they leave their growth site and travel as single cells. We applied analytical dielectrophoretic field-flow fractionation (dFFF) to study the membrane capacitance, density and hydrodynamic properties together with the size and morphology of cultured tumor cells after they were harvested and placed into single cell suspensions. After detachment, the tumor cells exhibited biophysical properties that changed with time through a process of cytoplasmic shedding whereby membrane and cytoplasm were lost. This process appeared to be distinct from the cell death mechanisms of apoptosis, anoikis and necrosis and it may explain why multiple phenotypes are seen among CTCs isolated from patients and among the tumor cells obtained from ascitic fluid of patients. The implications of dynamic biophysical properties and cytoplasmic loss for CTC migration into small blood vessels in the circulatory system, survival and gene expression are discussed. Because the total capacitance of tumor cells remained higher than blood cells even after they had shed cytoplasm, dFFF offers a compelling, antibody-independent technology for isolating viable CTCs from blood even when they are no larger than peripheral blood mononuclear cells.

Dynamics of red blood cells and vesicles in microchannels of oscillating width

We have studied the dynamics of red blood cells and fluid lipid vesicles in hydrodynamic flow fields created by microchannels with periodically varying channel width. For red blood cells we find a transition from a regime with oscillating tilt angle and fixed shape to a regime with oscillating shape with increasing flow velocity. We have determined the crossover to occur at a critical ratio L(y)/v(m) ≈ 2.2 × 10⁻³ s with channel width L(y) and red blood cell velocity v(m). These oscillations are superposed by shape transitions from a discocyte to a slipper shape at low velocities and a slipper to parachute transition at high flow velocities.

Micro-capsules in shear flow

This paper deals with flow-induced shape changes of elastic capsules. The state of the art concerning both theory and experiments is briefly reviewed starting with dynamically induced small deformation of initially spherical capsules and the formation of wrinkles on polymerized membranes. Initially non-spherical capsules show tumbling and tank-treading motion in shear flow. Theoretical descriptions of the transition between these two types of motion assuming a fixed shape are at odds with the full capsule dynamics obtained numerically. To resolve the discrepancy, we expand the exact equations of motion for small deformations and find that shape changes play a dominant role. We classify the dynamical phase transitions and obtain numerical and analytical results for the phase boundaries as a function of viscosity contrast, shear and elongational flow rate. We conclude with perspectives on time-dependent flow, on shear-induced unbinding from surfaces, on the role of thermal fluctuations and on applying the concepts of stochastic thermodynamics to these systems.

Deformability-based cell classification and enrichment using inertial microfluidics

The ability to detect and isolate rare target cells from heterogeneous samples is in high demand in cell biology research, immunology, tissue engineering and medicine. Techniques allowing label-free cell enrichment or detection are especially important to reduce the complexity and costs towards clinical applications. Single-cell deformability has recently been recognized as a unique label-free biomarker for cell phenotype with implications for assessment of cancer invasiveness. Using a unique combination of fluid dynamic effects in a microfluidic system, we demonstrate high-throughput continuous label-free cell classification and enrichment based on cell size and deformability. The system takes advantage of a balance between deformability-induced and inertial lift forces as cells travel in a microchannel flow. Particles and droplets with varied elasticity and viscosity were found to have separate lateral dynamic equilibrium positions due to this balance of forces. We applied this system to successfully classify various cell types using cell size and deformability as distinguishing markers. Furthermore, using differences in dynamic equilibrium positions, we adapted the system to conduct passive, label-free and continuous cell enrichment based on these markers, enabling off-chip sample collection without significant gene expression changes. The presented method has practical potential for high-throughput deformability measurements and cost-effective cell separation to obtain viable target cells of interest in cancer research, immunology, and regenerative medicine.

Dynamic modes of microcapsules in steady shear flow: effects of bending and shear elasticities

The dynamics of microcapsules in steady shear flow were studied using a theoretical approach based on three variables: the Taylor deformation parameter αD , the inclination angle θ , and the phase angle ϕ of the membrane rotation. It is found that the dynamic phase diagram shows a remarkable change with an increase in the ratio of the membrane shear and bending elasticities. A fluid vesicle (no shear elasticity) exhibits three dynamic modes: (i) tank treading at low viscosity ηin of internal fluid (αD and θ relaxes to constant values), (ii) tumbling (TB) at high ηin (θ rotates), and (iii) swinging (SW) at middle ηin and high shear rates γ (θ oscillates). All of three modes are accompanied by a membrane (ϕ) rotation. For microcapsules with low shear elasticity, the TB phase with no ϕ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of ϕ rotation. Synchronization of ϕ rotation with TB rotation or SW oscillation occurs with integer ratios of rotational frequencies. At high shear elasticity, where a saddle point in the energy potential disappears, intermediate phases vanish and either ϕ or θ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.

Chaotic dynamics of red blood cells in a sinusoidal flow

We show that the motion of individual red blood cells in an oscillating moderate shear flow is described by a nonlinear system of three coupled oscillators. Our experiments reveal that the cell tank treads and tumbles either in a stable way with synchronized cell inclination, membrane rotation and hydrodynamic oscillations, or in an irregular way, very sensitively to initial conditions. By adapting our model described previously, we determine the theoretical diagram for the red cell motion in a sinusoidal flow close to physiological shear stresses and flow variation frequencies and reveal large domains of chaotic motions. Finally, fitting our observations allows a characterization of cell viscosity and membrane elasticity.

A passive microfluidic device for plasma extraction from whole human blood

Promising microfluidic devices are proposed herein to continuously and passively extract plasma from whole human blood. These designs are based on the red cells lateral migration and the resulting cell-free layer locally expanded by geometric singularities, such as an abrupt enlargement of the channel or a cavity adjacent to the channel. After an explanation of flow patterns, devices are experimentally and biologically validated for plasma extraction. They are also successively optimized with extraction yields up to 17.8% for a 1:20 blood injected at 100 microL/min.

Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Near-Wall Region of a Shear Flow

Our research focused on the polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC) and the subsequent melanoma cell emboli formation in a shear flow, an important process of tumor cell extravasation from the circulation during metastasis. We applied population balance model based on Smoluchowski coagulation equation to study the heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber, which simulates in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. To the best of our knowledge, a multiscale near-wall aggregation model was developed, for the first time, which incorporated the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, are discussed. Several parameter identification approaches are proposed and validated which, in turn, demonstrate the importance of the reaction coefficient and the critical bond number on the aggregation process.

Dielectrophoretic-field flow fractionation analysis of dielectric, density, and deformability characteristics of cells and particles

Dielectrophoretic field-flow fractionation (DEP-FFF) has been used to discriminate between particles and cells based on their dielectric and density properties. However, hydrodynamic lift forces (HDLF) at flow rates needed for rapid separations were not accounted for in the previous theoretical treatment of the approach. Furthermore, no method was developed to isolate particle or cell physical characteristics directly from DEP-FFF elution data. An extended theory of DEP-FFF is presented that accounts for HDLF. With the use of DS19 erythroleukemia cells as model particles with frequency-dependent dielectric properties, it is shown that the revised theory accounts for DEP-FFF elution behavior over a wide range of conditions and is consistent with sedimentation-FFF when the DEP force is zero. Conducting four elution runs under specified conditions, the theory allows for the derivation of the cell density distribution and provides good estimates of the distributions of the dielectric properties of the cells and their deformability characteristics that affect HDLF. The approach allows for rapid profiling of the biophysical properties of cells, the identification and characterization of subpopulations, and the design of optimal DEP-FFF separation conditions. The extended DEP-FFF theory is widely applicable, and the parameter measurement methods may be adapted easily to other types of particles.

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities etain and etaout inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast etain/etaout. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance ycm of the vesicle center of mass from the wall is well described by an effective power law ycm(-2) for intermediate distances 0.8Rp< approximately ycm< approximately 3Rp with vesicle radius Rp. The boundary-integral calculation indicates that the lift force decays asymptotically as 1/[ycm ln(ycm)] far from the wall.

Flow-induced clustering and alignment of vesicles and red blood cells in microcapillaries

The recent development of microfluidic devices allows the investigation and manipulation of individual liquid microdroplets, capsules, and cells. The collective behavior of several red blood cells (RBCs) or microcapsules in narrow capillaries determines their flow-induced morphology, arrangement, and effective viscosity. Of fundamental interest here is the relation between the flow behavior and the elasticity and deformability of these objects, their long-range hydrodynamic interactions in microchannels, and thermal membrane undulations. We study these mechanisms in an in silico model, which combines a particle-based mesoscale simulation technique for the fluid hydrodynamics with a triangulated-membrane model. The 2 essential control parameters are the volume fraction of RBCs (the tube hematocrit, H(T)), and the flow velocity. Our simulations show that already at very low H(T), the deformability of RBCs implies a flow-induced cluster formation above a threshold flow velocity. At higher H(T) values, we predict 3 distinct phases: one consisting of disordered biconcave-disk-shaped RBCs, another with parachute-shaped RBCs aligned in a single file, and a third with slipper-shaped RBCs arranged as 2 parallel interdigitated rows. The deformation-mediated clustering and the arrangements of RBCs and microcapsules are relevant for many potential applications in physics, biology, and medicine, such as blood diagnosis and cell sorting in microfluidic devices.

Vesicles and red blood cells in shear flow

We describe the similarities and the specificities of the behaviour of individual soft particles, namely, drops, lipid vesicles and red blood cells subjected to a shear flow. We highlight that their motion depends in a non-trivial way on the particle mechanical properties. We detail the effect of the presence of a wall with or without wall-particle attractive interaction from a biological perspective.

Responsive viscoelastic giant lipid vesicles filled with a poly(N-isopropylacrylamide) artificial cytoskeleton

Responsive giant lipid vesicles filled with aqueous PolyNipam sol (SFV) or gel (GFV) were prepared by ultra-violet polymerisation performed in situ. Upon crossing the lower critical transition temperature of PolyNipam, SFVs and GFVs undergo a significant change of their structural and mechanical properties or a drastic volume transition, respectively. Rheometric and micropipette experiments show that both internal viscosity of SFVs and internal shear modulus of GFVs are tunable over several orders of magnitude and lie in the range observed for living cells. Moreover, the vesicle membrane is strongly bound to the internal polymer medium, making these systems interesting for mimicking the basic mechanical behaviour of passive living cells.

Modeling the interactions between compliant microcapsules and pillars in microchannels

Using a computational model, we investigate the motion of microcapsules inside a microchannel that encompasses a narrow constriction. The microcapsules are composed of a compliant, elastic shell and an encapsulated fluid; these fluid-filled shells model synthetic polymeric microcapsules or biological cells (e.g., leukocytes). Driven by an imposed flow, the capsules are propelled along the microchannel and through the constricted region, which is formed by two pillars that lie in registry, extending from the top and bottom walls of the channels. The tops of these pillars (facing into the microchannel) are modified to exhibit either a neutral or an attractive interaction with the microcapsules. The pillars (and constriction) model topological features that can be introduced into microfluidic devices or the physical and chemical heterogeneities that are inherently present in biological vessels. To simulate the behavior of this complex system, we employ a hybrid method that integrates the lattice Boltzmann model (LBM) for fluid dynamics and the lattice spring model (LSM) for the micromechanics of elastic solids. Through this LBM/LSM technique, we probe how the capsule's stiffness and interaction with the pillars affect its passage through the chambers. The results yield guidelines for regulating the movement of microcarriers in microfluidic systems and provide insight into the flow properties of biological cells in capillaries.

Adhesion induced non-planar and asynchronous flow of a giant vesicle membrane in an external shear flow

We show the existence of a flow at the surface of strongly adhering giant lipid vesicles submitted to an external shear flow. The surface flow is divided into two symmetric quadrants and presents two stagnation points (SP) on each side of the vesicle meridian plane. The position of these stagnation points depends strongly on the adhesion strength, characterized by the ratio of the contact zone diameter to the vesicle diameter. Contrary to the case of non-adhesive vesicles, streamlines do not lie in the shear plane. By avoiding the motionless contact zone, streamlines result in three-dimensional paths, strongly asymmetric away from the SP. Additional shearing dissipation may occur on the membrane surface as we observed that the mean rotational velocity of the membrane increases towards the vesicle SP, and is mainly determined by the adhesion induced vesicle shape.

Swinging of red blood cells under shear flow

We reveal that under moderate shear stress (etagamma[over ] approximately 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tank treading (TT) motion. A model based on a fluid ellipsoid surrounded by a viscoelastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing etagamma[over ], a etagamma[over ]-triggered transition toward a narrow etagamma[over ] range intermittent regime of successive swinging and tumbling, and a pure tumbling at low etagamma[over ] values.

Embryonic nodal flow and the dynamics of nodal vesicular parcels

We address with fluid-dynamical simulations using direct numerical techniques three important and fundamental questions with respect to fluid flow within the mouse node and left-right development. First, we consider the differences between what is experimentally observed when assessing cilium-induced fluid flow in the mouse node in vitro and what is to be expected in vivo. The distinction is that in vivo, the leftward fluid flow across the mouse node takes place within a closed system and is consequently confined, while this is no longer the case on removing the covering membrane and immersing the embryo in a fluid-filled volume to perform in vitro experiments. Although there is a central leftward flow in both instances, we elucidate some important distinctions about the closed in vivo situation. Second, we model the movement of the newly discovered nodal vesicular parcels (NVPs) across the node and demonstrate that the flow should indeed cause them to accumulate on the left side of the node, as required for symmetry breaking. Third, we discuss the rupture of NVPs. Based on the biophysical properties of these vesicles, we argue that the morphogens they contain are likely not delivered to the surrounding cells by their mechanical rupture either by the cilia or the flow, and rupture must instead be induced by an as yet undiscovered biochemical mechanism.

Dynamics of a viscous vesicle in linear flows

An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility, and resistance to bending. The constraint for a fixed total area leads to a nonlinear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank-treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow.

A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy

Research on giant vesicles is becoming increasingly popular. Giant vesicles provide model biomembrane systems for systematic measurements of mechanical and rheological properties of bilayers as a function of membrane composition and temperature, as well as hydrodynamic interactions. Membrane response to external factors (for example electric fields, ions and amphiphilic molecules) can be directly visualized under the microscope. In this paper we review our current understanding of lipid bilayers as obtained from studies on giant unilamellar vesicles. Because research on giant vesicles increasingly attracts the interest of scientists from various backgrounds, we also try to provide a concise introduction for newcomers in the field. Finally, we summarize some recent developments on curvature effects induced by polymers, domain formation in membranes and shape transitions induced by electric fields.

Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

We describe here a new procedure for the simultaneous investigation of sedimentation and diffusion of a colloidal particle in close proximity to a solid, planar wall. The measurements were made using the optical technique of total internal reflection microscopy, coupled with optical radiation pressure, for dimensionless separation distances (gap width/radius of particle) ranging from 0.01 to 0.05. In this region, the hydrodynamic mobility and diffusion coefficient are substantially reduced below bulk values. The procedure involved measuring the mean and the variance of vertical displacements of a Brownian particle settling under gravity toward the plate. The spatially varying diffusion coefficient was calculated from the displacements at small times (where diffusive motion was dominant). The mobility relationship for motion normal to a flat plate was tested by measuring the average distance of travel versus time as the particle settled under the constant force of gravity. For the simple Newtonian fluid used here (aqueous salt solution), the magnitude of the diffusion coefficient and mobility, plus their dependence on separation distance, showed excellent agreement with predictions. This new technique could be of great value in measuring the mobility and diffusion coefficient for near-contact motion in more complex fluids for which the hydrodynamic correction factors are not known a priori, such as shear-thinning fluids.

Dynamics of viscous vesicles in shear flow

The dynamics of giant lipid vesicles under shear flow is experimentally investigated. Consistent with previous theoretical and numerical studies, two flow regimes are identified depending on the viscosity ratio between the interior and the exterior of the vesicle, and its reduced volume or excess surface. At low viscosity ratios, a tank-treading motion of the membrane takes place, the vesicle assuming a constant orientation with respect to the flow direction. At higher viscosity ratios, a tumbling motion is observed in which the whole vesicle rotates with a periodically modulated velocity. When the shear rate increases, this tumbling motion becomes increasingly sensitive to vesicle deformation due to the elongational component of the flow and significant deviations from simpler models are observed. A good characterization of these various flow regimes is essential for the validation of analytical and numerical models, and to relate microscopic dynamics to macroscopic rheology of suspensions of deformable particles, such as blood.

Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow

Experimental results on the tank-treading-tumbling transition in the dynamics of a vesicle subjected to a shear flow as a function of a vesicle excess area, viscosity contrast, and the normalized shear rate are presented. Good agreement on the transition curve and scaling behavior with theory and numerical simulations was found. A new type of unsteady motion at a large degree of vesicle deformability was discovered and described as follows: a vesicle trembles around the flow direction, while the vesicle shape strongly oscillates.