Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.Comment: 20 pages, 7 figure

Micro-Capsules in Shear Flow

This paper deals with flow-induced shape transitions 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 variance 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 timedependent flow, on shear-induced unbinding from surfaces, on the role of thermal fluctuations, and on applying the concepts of stochastic thermodynamics to these systems.Comment: 34 pages, 15 figure

Micromechanical study of the flow of a deformable vesicle through a constriction

International audienc

Motion of a capsule through a constriction: a model for red blood cell filtration

International audienc

Flow of a capsule through a constriction

International audienc

Theoretical modelling of the motion and deformation of capsules in shear flows

International audienc

Flow of a capsule through a constriction: application to cell filtration

International audienc

Flow of a capsule through a constriction : application to cell filtration

The motion of a freely suspended capsule (liquid drop surrounded by a deformable membrane) forced to squeeze through an axisymmetric constriction smaller than its initial dimensions is studied by means of a numerical model based on boundary integrals. The flow is driven by a constant pressure difference. The suspending liquid and internal capsule viscosities are equal. It is found that the maximum energy loss is due to entrance effects rather than to the flow in the pore itself. The role of the membrane rigidity can be predicted

Passage d'une capsule dans une constriction: influence du comportement membranaire et de la géométrie initiale

International audienc