Vesicles In Shear Flow Research Articles

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.

Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method

We consider numerical algorithms for the simulation of hydrodynamics of two-dimensional vesicles suspended in a viscous Stokesian fluid. The motion of vesicles is governed by the interplay between hydrodynamic and elastic forces. Continuum models of vesicles use a two-phase fluid system with interfacial forces that include tension (to maintain local “surface” inextensibility) and bending. Vesicle flows are challenging to simulate. On the one hand, explicit time-stepping schemes suffer from a severe stability constraint due to the stiffness related to high-order spatial derivatives in the bending term. On the other hand, implicit time-stepping schemes can be expensive because they require the solution of a set of nonlinear equations at each time step. Our method is an extension of the work of Veerapaneni et al. [S.K. Veerapaneni, D. Gueyffier, D. Zorin, G. Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334–2353], in which a semi-implicit time-marching scheme based on a boundary integral formulation of the Stokes problem for vesicles in an unbounded medium was proposed. In this paper, we consider two important generalizations: (i) confined flows within arbitrary-shaped stationary/moving geometries; and (ii) flows in which the interior (to the vesicle) and exterior fluids have different viscosity. In the rest of the paper, we will refer to this as the “ viscosity contrast”. These two problems require solving additional integral equations and cause nontrivial modifications to the previous numerical scheme. Our method does not have severe time-step stability constraints and its computational cost-per-time-step is comparable to that of an explicit scheme. The discretization is pseudo-spectral in space, and multistep BDF in time. We conduct numerical experiments to investigate the stability, accuracy and the computational cost of the algorithm. Overall, our method achieves several orders of magnitude speed-up compared to standard explicit schemes. As a preliminary validation of our scheme, we study the dependence of the inclination angle of a single vesicle in shear flow on the viscosity contrast and the reduced area of the vesicle, the lateral migration of vesicles in shear flow, the dispersion of two vesicles, and the effective viscosity of a dilute suspension of vesicles.

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.

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.

D211 Immersed-Boundary法によるせん断流中におけるベシクルの流動解析

In shear flows, vesicles like a red blood cell(RBC) change their shape in response to the local flow conditions. In the present work, a numerical simulation of vesicles in shear flows was conducted. The immersed-boundary method was used to simulate the deformation of vesicles. At first, the motion of a liposome in a simple shear flow was studied. In a simple shear flow, a liposome showed tank-treading motion. Our results were quantitatively in good agreement with the numerical results obtained by Kraus et al. and experimental results obtained by Hatakenaka et al. Then, numerical simulation of red blood cells in a cylindrical channel was conducted. In a cylindrical channel, red blood cells deformed their shapes to parachute-like shapes.

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.

Orientation and Dynamics of a Vesicle in Tank-Treading Motion in Shear Flow

Experimental results on mean inclination angle and its fluctuation due to thermal noise in tank-treading motion of a vesicle in shear flow as a function of vesicle excess area, normalized shear rate, viscosity, and viscosity contrast between inner and outer fluids, , are presented. Good quantitative agreement with theory made for was found. At the dependence is altered significantly. Dependence of the vesicle shape on shear rate is consistent with theory. A tank-treading velocity of the vesicle membrane is found to be a periodic function close to that predicted by theory.

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

The dynamical behavior of vesicles is investigated in simple shear flow. A simulation technique is presented that combines a three-dimensional particle-based mesoscopic model (multiparticle collision dynamics) for the solvent with a dynamically triangulated surface model for the membrane. In this model, thermal fluctuations of the solvent and of the membrane are consistently taken into account. The membrane viscosity can be varied by changing the bond-flip rate of the dynamically triangulated surface. Vesicles are found to transit from steady tank-treading to unsteady tumbling motion with increasing membrane viscosity. At small reduced volumes, the shear induces a transformation from a discocyte to a prolate shape at low membrane viscosity. On the other hand, at high membrane viscosity, the shear induces a transformation from prolate to discocyte, or tumbling motion accompanied by shape oscillations between these two states. Thermal fluctuations induce intermittent tumbling and smooth out the transitions. This effect can be understood from a simplified stochastic model.

Fluid Vesicles with Viscous Membranes in Shear Flow

The effect of membrane viscosity on the dynamics of vesicles in shear flow is studied. We present a new simulation technique, which combines three-dimensional multiparticle collision dynamics for the solvent with a dynamically triangulated membrane model. Vesicles are found to transit from steady tank treading to unsteady tumbling motion with increasing membrane viscosity. Depending on the reduced volume and membrane viscosity, shear can induce both discocyte-to-prolate and prolate-to-discocyte transformations. This behavior can be understood from a simplified model.

Tank Treading and Unbinding of Deformable Vesicles in Shear Flow: Determination of the Lift Force

Deformation and tank-treading motion of flaccid vesicles in a linear shear flow close to a wall are quantitatively studied by light microscopy. Velocities of bounded vesicles obey Goldman's law established for rigid spheres. A progressive tilt and a transition of unbinding of vesicles are evidenced upon increasing the shear rate, gamma;. These observations disclose the existence of a viscous lift force, F(l), depending on the viscosity eta of the fluid, the radius R of the vesicle, its distance h from the substrate, and a monotonous decreasing function f(1-v) of the reduced volume v, in the following manner: F(l) = eta(gamma)(R(3)/h)f(1-v). This relation is valid for vesicles both close to and farther from the substrate.

Rotation of giant phospholipid vesicles in an uniform shear flow.

Rotation of giant "point attached" phospholipid (POPC) vesicles in a shear flow was studied. The dependence of the angular velocity on the flow gradient was measured and the experimental results were compared to the predictions of a theoretical model. A good linear correlation between the angular velocity of the vesicle and the flow gradient, as predicted, was observed.

Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipiticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed.

Large Deformations of Giant Floppy Vesicles in Shear Flow

The flow deformation and rheology of vesicles of a soluble surfactant are studied. Direct observation under shear flow reveals that the vesicles become strongly elongated to form an entangled structure of connected bilayer tubes. The large deformation is due to the permeability of the membrane and the large solubility of the surfactant. The formation of the entangled structure is observed in the rheology as a strong increase of the viscosity with time.

Deformation of giant lipid bilayer vesicles in shear flow

We describe experimental studies of the deformation of giant lipid bilayer vesicles in shear flow. The experiments are carried out with a counterrotating Couette apparatus. The deformation depends on the mechanical properties of the lipid bilayer, the vesicle radius, and the viscosity of the surrounding Newtonian liquid. We show that the relevant mechanical parameter is the bending rigidity. A simple model has been developed that describes the deformation of a vesicle. This model takes thermal undulations of the bilayer into account. We have obtained a value for the bending rigidity of dimyristoyl-phosphatidylcholine bilayers and its value has been compared with literature data and with results from micropipette aspiration experiments. From the measurements we are able to discriminate between unilamellar and multilamellar vesicles.