流场环境下复杂囊泡的动力学行为

采用非平衡态分子动力学方法研究了二维复杂囊泡在剪切流中的动力学行为. 模拟发现了复杂囊泡经典的翻滚(tumbling)、摇摆(trembling)和坦克履(tank-treading)行为, 还观察到由坦克履行为向平动行为(translating)的转变. 囊泡的平动行为与剪切率大小、复杂囊泡的形状密切相关. 当大囊泡均匀嫁接较多数目的小囊泡后, 其平动方式消失. 该研究有益于加深对囊泡在剪切流场中复杂性行为的理解.     

Dynamics of a compound vesicle in shear flow

The dynamics of a compound vesicle (a lipid bilayer membrane enclosing a fluid with a suspended particle) in shear flow is investigated by using both numerical simulations and theoretical analysis. We find that the nonlinear hydrodynamic interaction between the inclusion and the confining membrane gives rise to new features of the vesicle dynamics: The transition from tank treading to tumbling can occur in the absence of any viscosity mismatch, and a vesicle can swing if the enclosed particle is nonspherical. Our results highlight the complex effects of internal cellular structures have on cell dynamics in microcirculatory flows. For example, parasites in malaria-infected erythrocytes increase cytoplasmic viscosity, which leads to increase in blood viscosity.     

Vacillating breathing and tumbling of vesicles under shear flow

The dynamics of vesicles under a shear flow are analyzed analytically in the small deformation regime. We derive two coupled nonlinear equations which describe the vesicle orientation in the flow and its shape evolution. A new type of motion is found, namely, a "vacillating-breathing" mode: the vesicle orientation undergoes an oscillation around the flow direction, while the shape executes breathing dynamics. This solution coexists with tumbling. Moreover, we provide an explicit expression for the tumbling threshold. A rheological law for a dilute vesicle suspension is outlined.     

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.     

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.     

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.     

An advected-field method for deformable entities under flow

We study dynamics of a deformable entity (such as a vesicles under hydrodynamical constraints). We show how the problem can be solved by means of Green's functions associated with the Stokes equations. A gauge-field invariant formulation makes the study of dynamics efficient. However, this procedure has its short-coming. For example, if the fluids are not Newtonian, then no Green's function is available in general. We introduce a new approach, the advected field one, which opens a new avenue of applications. For example, non-Newtonian entities can be handled without additional deal. In addition problems like budding, droplet break-up in suspensions, can naturally be treated without additional complication. We exemplify the method on vesicles filled by a fluid having a viscosity contrast with the external fluid, and submitted to a shear flow. We show that beyond a viscosity contrast (the internal fluid being more viscous), the vesicle undergoes a tumbling bifurcation, which has a saddle-node nature. This bifurcation is known for blood cells. Indeed red cells either align in a shear flow or tumble according to whether haematocrit concentration is high or low. Received 19 December 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: chaouqi.misbah@ujf-grenoble.fr     

On coupling between the orientation and the shape of a vesicle under a shear flow

A simple 2D model of deformable vesicles tumbling in a shear under flow is introduced in order to account for the main qualitative features observed experimentally as shear rates are increased. The simplicity of the model allows for a full analytical tractability while retaining the essential physical ingredients. The model reveals that the main axes of the vesicle undergo oscillations which are coupled to the vesicle orientation in the flow. The model reproduces and sheds light on the main novel features reported in recent experiments [M. Mader et al., Eur. Phys. J. E. 19, 389 (2006)], namely that both coefficients A and B that enter the Keller-Skalak equation, dψ/dt = A+Bcos(2 ψ) (ψ is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.     

Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear rates

We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent behaviour, have been identified using numerical methods. In this paper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions. Using this method, we find analytical expressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics is studied in more detail when the inverse shear rate is harmonically modulated around a constant mean value for which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency and phase, tumbling motion can be induced even if the mean shear rate corresponds to the swinging regime. We derive expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.     

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.     

Steady States of Sheared Active Nematics

A continuum hydrodynamic model has been used to characterize flowing active nematics. The behavior of such a system subjected to a weak steady shear is analyzed. We explore the director structures and flow behaviors of the system in flow-aligning and flow tumbling regimes. Combining asymptotic analysis and numerical simulations, we extend previous studies to give a complete characterization of the steady states for both contractile and extensile particles in flow-aligning and flow-tumbling regimes. Another key prediction of this work is the role of the system size on the steady states of an active nematic system: if the system size is small, the velocity and the director angle files for both flow-tumbling contractile and extensile systems are similar to those of passive nematics; if the system is big, the velocity and the director angle files for flow-aligning contractile systems and tumbling extensile systems are akin to sheared passive cholesterics while they are oscillatory for flow-aligning extensile and tumbling contractile systems.     

The large amplitude oscillatory strain response of aqueous foam: Strain localization and full stress Fourier spectrum

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.     

Rheology of a dilute suspension of vesicles

From the hydrodynamical equations of vesicle dynamics under shear flow, we extract a rheological law for a dilute suspension. This is made analytically in the small excess area limit. In contrast to droplets and capsules, the rheological law (written in the comoving frame) is nonlinear even to the first leading order. We exploit it by evaluating the effective viscosity eta(eff) and the normal stress differences N1 and N2. We make a link between rheology and microscopic dynamics. For example, eta(eff) is found to exhibit a cusp singularity at the tumbling threshold, while N(1,2) undergoes a collapse.     

Kayaking and wagging of rods in shear flow

For the first time, we have simulated the periodic collective orientational motions performed by rigid liquid-crystalline polymers with large aspect ratio in the nematic state in shear flow. In order to be able to do so, we developed a new, event-driven Brownian dynamics technique. We present the results of simulations of rods with aspect ratios L/d ranging from 20 to 60 at volume fractions phi given by Lphi/d = 3.5 and 4.5. By studying the path of the director, i.e., the average direction of the rods, we observe kayaking, wagging, flow aligning, and log-rolling type of orbits, depending on the parameters of the simulation and the initial orientation. We find that the tumbling periods depend on Lphi/d and the shear rate but not on the type of motion. Our simulation results qualitatively confirm theoretical predictions and are in good agreement with the experimental measurements of tumbling times of fd viruses.     

Semiflexible polymers in shear flow

The dynamics of semiflexible polymers under the influence of shear flow is studied analytically. Power laws are derived for various conformational and dynamical quantities which are in agreement with experimental findings. In particular, the tumbling motion is analyzed and expressions are provided for the probability distributions of the orientation angles and the tumbling time. The calculations explain the similarities in the behavior of flexible and semiflexible polymers as well as free-draining and nondraining systems.     

Analysis of membrane tank-tread of nonspherical capsules and red blood cells

We present an analysis of membrane motion of deformable capsules and red blood cells suspended in a linear shear flow and undergoing swinging and tumbling motions using three-dimensional numerical simulations. This study is motivated by the theory of the shape-preserving cells which predicts that the direction of the membrane rotation depends on the cell orientation and reverses at every 45° inclination angle of the cell major axis with respect to the external flow direction. By considering large deformation of capsules and red blood cells, here we investigate how the shape oscillation affects the time dependence and the direction reversal of the membrane rotation. We find that the membrane tank-tread is highly time-dependent in nature and synchronized with the time-dependent deformation. The maximum and minimum of the tank-tread velocity occur at and near the minimum and maximum deformation, respectively. For the swinging capsules and red blood cells, the direction of the membrane rotation is always along the direction of the external fluid rotation; however, a direction reversal occurs during the tumbling motion in which case the membrane rotates in the direction of the external fluid rotation when the major axis is mostly in the extensional quadrant of the shear flow, and in the opposite direction when it is mostly in the compressional quadrant. Unlike the theory which predicts the direction reversal at every 45° inclination angle irrespective of the control parameters, namely, the capillary number, viscosity ratio, and asphericity, we find that the angle at which the direction reversal occurs depends on these parameters. In particular, if the tumbling motion occurs by decreasing the capillary number, the membrane rotation is in the direction of the external flow rotation in the entire extensional quadrant, but in the opposite direction in the compressional quadrant, irrespective of the specific values of the capillary number. If the tumbling motion occurs by increasing the viscosity ratio and asphericity, the angle at which the direction reversal occurs depends on the specific values of these two parameters. The spatial variation of the tank-tread velocity also is analyzed and attributed to the straining motion of the external flow.      

Effects of oscillatory shear flow on chain-like cluster dynamics in ferrofluids without magnetic fields

Brownian dynamics simulations of interacting magnetic particles in a quasi-two-dimensional ferrofluid system are performed at zero temperature, under the influence of oscillatory shear flow in the absence of external magnetic fields. Starting from chain-like clusters of the particles, we study the time-dependent behavior of both magnetization and microstructures of the ferrofluid by changing values of two parameters, the shear rate strength and frequency of oscillatory shear flow. Simulation results show that there are three different dynamical regimes for the chain clusters dynamics, depending on these two parameters. Scaling behavior of the asymptotic magnetization is also observed for a certain range of parameters.     

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.     

Vesicles in haptotaxis with hydrodynamical dissipation

We analyze the problem of vesicle migration in haptotaxis (a motion directed by an adhesion gradient), though most of the reasoning applies to chemotaxis as well as to a variety of driving forces. A brief account has been published on this topic [#!Cantat99a!#]. We present an extensive analysis of this problem and provide a basic discussion of most of the relevant processes of migration. The problem allows for an arbitrary shape evolution which is compatible with the full hydrodynamical flow in the Stokes limit. The problem is solved within the boundary integral formulation based on the Oseen tensor. For the sake of simplicity we confine ourselves to 2D flows in the numerical analysis. There are basically two regimes (i) the tense regime where the vesicle behaves as a “droplet” with an effective contact angle. In that case the migration velocity is given by the Stokes law. (ii) The flask regime where the vesicle has a significant (on the scale of the vesicle size) contact curvature. In that case we obtain a new migration law which substantially differs from the Stokes law. We develop general arguments in order to extract analytical laws of migration. These are in good agreement with the full numerical analysis. Finally we mention several important future issues and open questions. Received 24 June 2002 and Received in final form 4 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: isabelle.cantat@univ-rennes1.fr     

A front-tracking method with Catmull–Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow

This paper presents a front-tracking method for studying the large deformation of a liquid capsule enclosed by a thin shell in a shear flow. The interaction between the fluid and the shell body is accomplished through an implicit immersed boundary method. An improved thin-shell model for computing the forces acting on the shell middle surface during the deformation is described in surface curvilinear coordinates and within the framework of the principle of virtual displacements. This thin-shell model takes full account of in-plane tensions and bending moments developing due to the shell thickness and a preferred three-dimensional membrane structure. The approximation of the shell middle surface is performed through the use of the Catmull–Clark subdivision surfaces. The resulting limit surface is C²-continuous everywhere except at a small number of extraordinary nodes where it retains C¹ continuity. The smoothness of the limit surface significantly improves the ability of our method in simulating capsules enclosed by hyperelastic thin shells with different shapes and physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, ellipsoidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, swinging, tumbling and transition from tumbling to swinging have been studied over a range of shear rates, viscosity ratios and bending modulus.