Petia M. Vlahovska

Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease

We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.

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.

Vesicles in electric fields: Some novel aspects of membrane behavior†

This review focuses on the effects of electric fields on giant unilamellar vesicles, a cell-size membrane system. We describe various types of behavior of vesicles subjected to either alternating fields or strong direct current pulses, such as electrodeformation, -poration and -fusion. The vesicle response to alternating fields in various medium conditions is introduced and the underlying physical mechanisms are highlighted, supported by theoretical modeling. New aspects of the response of vesicles with charged or neutral membranes, in fluid or gel-phase, and embedded in different solutions, to strong direct current pulses are described including novel applications of vesicle electrofusion for nanoparticle synthesis.

Electrohydrodynamic Model of Vesicle Deformation in Alternating Electric Fields

We develop an analytical theory to explain the experimentally observed morphological transitions of quasispherical giant vesicles induced by alternating electric fields. The model treats the inner and suspending media as lossy dielectrics, and the membrane as an impermeable flexible incompressible-fluid sheet. The vesicle shape is obtained by balancing electric, hydrodynamic, bending, and tension stresses exerted on the membrane. Our approach, which is based on force balance, also allows us to describe the time evolution of the vesicle deformation, in contrast to earlier works based on energy minimization, which are able to predict only stationary shapes. Our theoretical predictions for vesicle deformation are consistent with experiment. If the inner fluid is more conducting than the suspending medium, the vesicle always adopts a prolate shape. In the opposite case, the vesicle undergoes a transition from a prolate to oblate ellipsoid at a critical frequency, which the theory identifies with the inverse membrane charging time. At frequencies higher than the inverse Maxwell-Wagner polarization time, the electrohydrodynamic stresses become too small to alter the vesicles quasispherical rest shape. The model can be used to rationalize the transient and steady deformation of biological cells in electric fields.

Vesicles in poiseuille flow

Blood microcirculation critically depends on the migration of red cells towards the flow centerline. We identify theoretically the ratio of the inner over the outer fluid viscosities lambda as a key parameter. At low lambda, the vesicle deforms into a tank-treading ellipsoid shape far away from the flow centerline. The migration is always towards the flow centerline, unlike drops. Above a critical lambda, the vesicle tumbles or breaths and migration is suppressed. A surprising coexistence of two types of shapes at the centerline, a bulletlike and a parachutelike shape, is predicted.

Electrohydrodynamics of drops in strong uniform dc electric fields

Drop deformation in an uniform dc electric field is a classic problem. The pioneering work of Taylor demonstrated that for weakly conducting media, the drop fluid undergoes a toroidal flow and the drop adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed a nonaxisymmetric rotational flow in strong fields, similar to the rotation of solid dielectric particles observed by Quincke in the 19th century. We present a systematic experimental study of this phenomenon, which highlights the importance of charge convection along the drop surface. The critical electric field, drop inclination angle, and rate of rotation are measured. We find that for small, high viscosity drops, the threshold field strength is well approximated by the Quincke rotation criterion. Reducing the viscosity ratio shifts the onset for rotation to stronger fields. The drop inclination angle increases with field strength. The rotation rate ...

Deformation of a surfactant-covered drop in a linear flow

We study the effect of adsorbed surfactant on drop deformation in linear flows by means of analytical solutions for small perturbations of the drop shape and surfactant distribution, and by numerical simulations for large distortions. We consider a drop with the same viscosity as the suspending fluid. Under these conditions, the problem simplifies because the disturbance flow field results solely from the interfacial stresses that oppose the distortion of shape and surfactant distribution induced by the incident flow. A general form of perturbation analysis valid for any flow is presented. The analysis can be carried out to arbitrary order given its recursive structure; a third-order perturbation solution is explicitly presented. The expansions are compared to results from boundary integral simulations for drops in axisymmetric extensional and simple shear flows. Our results indicate that under weak-flow conditions, deformation is enhanced by the presence of surfactant, but the leading-order perturbation of the drop shape is independent of the (nonzero) surfactant elasticity. In strong flows, drop deformation depends nonmonotonically on surfactant elasticity. The non-Newtonian rheology in a dilute emulsion that results from drop deformation and surfactant redistribution is predicted. Shear thinning is most pronounced for low values of the surfactant elasticity. In the weak-flow limit with finite surfactant elasticity, the emulsion behaves as a suspension of rigid spheres. In strong flows, the stresses can approach the behavior for surfactant-free drops.We study the effect of adsorbed surfactant on drop deformation in linear flows by means of analytical solutions for small perturbations of the drop shape and surfactant distribution, and by numerical simulations for large distortions. We consider a drop with the same viscosity as the suspending fluid. Under these conditions, the problem simplifies because the disturbance flow field results solely from the interfacial stresses that oppose the distortion of shape and surfactant distribution induced by the incident flow. A general form of perturbation analysis valid for any flow is presented. The analysis can be carried out to arbitrary order given its recursive structure; a third-order perturbation solution is explicitly presented. The expansions are compared to results from boundary integral simulations for drops in axisymmetric extensional and simple shear flows. Our results indicate that under weak-flow conditions, deformation is enhanced by the presence of surfactant, but the leading-order perturbation ...

Rheology of a dilute emulsion of surfactant-covered spherical drops

The rheology of a diluted emulsion of surfactant-covered spherical drops has been investigated. A diluted film of insoluble surfactant is assumed. A matrix formulation of the problem is derived and analyzed by perturbation expansions for low- and high-shear rates, and for high-viscosity drops; the high-viscosity expansion converges rapidly for a wide range of parameters. Our theory provides a quantitative description of shear thinning and normal stress differences that occur as a result of surfactant redistribution.

Small-deformation theory for a surfactant-covered drop in linear flows

A small-deformation perturbation analysis is developed to study the effect of surfactant on drop dynamics in viscous flows. The surfactant is assumed to be insoluble in the bulk-phase fluids; the viscosity ratio and surfactant elasticity parameters are arbitrary. Under small-deformation conditions, the drop dynamics are described by a system of ordinary differential equations; the governing equations are given explicitly for the case of axisymmetric and two-dimensional imposed flows. Analytical results accurate to third order in the flow-strength parameter (capillary number) are derived (i) for the stationary drop shape and surfactant distribution in simple shear and axisymmetric straining flows, and (ii) for the rheology of a dilute emulsion in shear flow which include a shear-thinning viscosity and non-zero normal stresses. For drops with clean interfaces, the small-deformation theory presented here improves the results of Barthes-Biesel & Acrivos ( J. Fluid Mech ., vol. 61, 1973, p. 1). Boundary integral simulations are used to test our theory and explore large-deformation conditions.

Surfactant-induced migration of a spherical drop in Stokes flow

In Stokes flows, symmetry considerations dictate that a neutrally buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small nonuniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts migration toward the flow centerline.