Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations

Two-dimensional fluctuating vesicles in linear shear flow

The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the constraint of constant perimeter length. These equations are solved in the low-temperature limit and using a mean-field approach, in which the length constraint is satisfied only on average. The constraint imposes non-trivial correlations between the lowest deformation modes at low temperature. We also simulate a vesicle in a hydrodynamic solvent by using the multi-particle collision dynamics technique, both in the quasi-circular regime and for larger deformations, and compare the stationary deformation correlation functions and the time autocorrelation functions with theoretical predictions. Good agreement between theory and simulations is obtained.

Tank-treading, swinging, and tumbling of liquid-filled elastic capsules in shear flow

The dynamic motion of three-dimensional (3D) capsules in a shear flow is investigated by direct numerical simulation. The capsules are modeled as Newtonian liquid droplets enclosed by elastic membranes, with or without considering the membrane-area incompressibility. The internal liquid of the capsules is the same as that outside. The dynamic motion of capsules with initially spherical and oblate spheroidal unstressed shapes is studied under various shear rates. The results show that spherical capsules deform to stationary configurations and then the membranes rotate around the liquid inside (steady tank-treading motion). Such a steady mode is not observed for oblate spheroidal capsules. It is shown that with the shear rate decreasing, the motion of oblate spheroidal capsules changes from the swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to tumbling mode.

Dynamics of nearly spherical vesicles in an external flow

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.

Transient deformation of elastic capsules in shear flow: effect of membrane bending stiffness

The transient deformation of liquid capsules enclosed by elastic membranes with bending rigidity in shear flow has been studied numerically, using an improved immersed boundary-lattice Boltzmann method. The purpose of the present study is to investigate the effect of interfacial bending stiffness on the deformation of such capsules. Bending moments, accompanied by transverse shear tensions, usually develop due to a preferred membrane configuration or its nonzero thickness. The present model can simulate flow induced deformation of capsules with arbitrary resting shapes (concerning the in-plane tension) and arbitrary configurations at which the bending energy has a global minimum (minimum bending-energy configurations). The deformation of capsules with initially circular, elliptical, and biconcave resting shapes was studied; the capsules' minimum bending-energy configurations were considered as either uniform-curvature shapes (like circle or flat plate) or their initially resting shapes. The results show that for capsules with minimum bending-energy configurations having uniform curvature (circle or flat plate), the membrane carries out tank-treading motion, and the steady deformed shapes become more rounded if the bending stiffness is increased. For elliptical and biconcave capsules with resting shapes as minimum bending-energy configurations, it is quite interesting to find that with the bending stiffness increasing, the capsules' motion changes from tank-treading mode to flipping mode, and resembles Jeffery's flipping mode at large bending stiffness.

Swinging and tumbling of fluid vesicles in shear flow

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically triangulated surfaces, as well as a theoretical approach based on two variables: a shape parameter and the inclination angle, which has no adjustable parameters. We show that, between the well-known tank-treading and tumbling states, a new "swinging" state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.

Simulation of DNA motion in a microchannel using stochastic rotation dynamics

The authors propose a method to simulate the DNA motion in microchannels of complex geometry. It is based on stochastic rotation dynamics using a new scheme for the boundary condition. The method enables them to define a boundary wall of arbitrary shape and to describe a wall moving at an arbitrary velocity. As an application, they simulate the motion of DNA in Poiseuille flow between two parallel planes and show that DNA molecules tend to concentrate near the center of the channel in agreement with experimental results.

Shear-driven release of a bud from a multicomponent vesicle

The authors study the response of a multicomponent budded vesicle to an imposed shear flow using dissipative particle dynamics. Under certain circumstances, phase separation in the vesicle membrane leads to the formation of a minority domain which deforms into a nearly spherical bud in order to reduce its interfacial energy. The authors show that an imposed shear force has a varying effect on the vesicle, tending either to separate the bud from the vesicle or to stretch the bud open, depending on the vesicle orientation. The authors examine the interplay of membrane bending rigidity, line tension, and shear in determining the behavior of the vesicle. With the appropriate design, vesicles can be made to release buds in a controlled manner in response to shear. The authors outline a regime in which bud release is favorable.

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.

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.

Dynamic correlations in stochastic rotation dynamics

The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for stochastic rotation dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.

Hydrodynamic interactions and Brownian forces in colloidal suspensions: coarse-graining over time and length scales

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

Dynamic model and stationary shapes of fluid vesicles

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find stationary shapes of vesicles with different topologies and the dynamic evolution towards them. The results are in agreement with those found by minimization of the Canham-Helfrich free energy. This fact shows that our phase-field model could be applied to more complex problems of instabilities.

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.

Shape transitions of fluid vesicles and red blood cells in capillary flows

The dynamics of fluid vesicles and red blood cells (RBCs) in cylindrical capillary flow is studied by using a three-dimensional mesoscopic simulation approach. As flow velocity increases, a model RBC is found to transit from a nonaxisymmetric discocyteto an axisymmetric parachute shape (coaxial with the flow axis), while a fluid vesicle is found to transit from a discocyte to a prolate ellipsoid. Both shape transitions reduce the flow resistance. The critical velocities of the shape transitions are linearly dependent on the bending rigidity and on the shear modulus of the membrane. Slipper-like shapes of the RBC model are observed around the transition velocities. Our results are in good agreement with experiments on RBCs.