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Dynamic modes of quasispherical vesicles: Exact analytical solutions

M. Guedda^1,*, M. Abaidi¹, M. Benlahsen², and C. Misbah³

¹Université de Picardie Jules Verne, LAMFA CNRS UMR 7352, Amiens F-80039, France
²Université de Picardie Jules Verne, LPMC, Amiens F-80039, France
³Université Grenoble I, CNRS, Laboratoire Interdisciplinaire de Physique, UMR 5588, Grenoble F-38041, France

^*guedda@u-picardie.fr

Phys. Rev. E 86, 051915 – Published 26 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.051915

Abstract

In this paper we introduce a simple mathematical analysis to reexamine vesicle dynamics in the quasispherical limit (small deformation) under a shear flow. In this context, a recent paper [Misbah, Phys. Rev. Lett. 96, 028104 (2006)] revealed a dynamic referred to as the vacillating-breathing (VB) mode where the vesicle main axis oscillates about the flow direction and the shape undergoes a breathinglike motion, as well as the tank-treading and tumbling (TB) regimes. Our goal here is to identify these three modes by obtaining explicit analytical expressions of the vesicle inclination angle and the shape deformation. In particular, the VB regime is put in evidence and the transition dynamics is discussed. Not surprisingly, our finding confirms the Keller-Skalak solutions (for rigid particles) and shows that the VB and TB modes coexist, and whether one prevails over the other depends on the initial conditions. An interesting additional element in the discussion is the prediction of the TB and VB modes as functions of a control parameter $Γ,$ which can be identified as a TB-VB parameter.

Article Text

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