The dynamics of a vesicle in simple shear flow

Author:

ZHAO HONG,SHAQFEH ERIC S. G.

Abstract

We have performed direct numerical simulation (DNS) of a lipid vesicle under Stokes flow conditions in simple shear flow. The lipid membrane is modelled as a two-dimensional incompressible fluid with Helfrich surface energy in response to bending deformation. A high-fidelity spectral boundary integral method is used to solve the flow and membrane interaction system; the spectral resolution and convergence of the numerical scheme are demonstrated. The critical viscosity ratios for the transition from tank-treading (TT) to ‘trembling’ (TR, also called VB, i.e. vacillating-breathing, or swinging) and eventually ‘tumbling’ (TU) motions are calculated by linear stability analysis based on this spectral method, and are in good agreement with perturbation theories. The effective shear rheology of a dilute suspension of these vesicles is also calculated over a wide parameter regime. Finally, our DNS reveals a family of time-periodic and off-the-shear-plane motion patterns where the vesicle's configuration follows orbits that resemble but are fundamentally different from the classical Jeffery orbits of rigid particles due to the vesicle's deformability.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

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