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

Abstract

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, d psi/dt = A+B cos(2 psi) (psi is the vesicle orientation angle in the shear flow), undergo a collapse upon increasing shear rate.

Tank-treading and tumbling frequencies of capsules and red blood cells

“…Such a fluid-to-solid transition has been observed for other soft-matter particulates, e.g., capsules [14][15][16][17][18][19] and vesicles [20][21][22][23][24][25][26][27][28][29][30][31], which are membrane-bound liquid drops and hence structurally similar to erythrocytes. The mechanical properties of the membranes are, however, different in the three cases; e.g., the membrane of erythrocytes * Corresponding author: pbagchi@jove.rutgers.edu is known to exhibit a resistance against shear deformation, area dilatation, and bending, whereas a vesicle membrane is incompressible, and it exhibits a bending resistance.…”

“…The experiments by Fischer et al [6], Tran-Son-Tay [8], and Fischer [10] did not consider the swinging erythrocytes. Very importantly, several recent studies have shown that a significant shape oscillation (vacillating breathing or trembling motion) may coexist during the swinging motion [22][23][24][25][26][27][28][29][30][31]. Hence, the shape and angular oscillations are highly coupled.…”

Vesicles and red blood cells in flow: From individual dynamics to rheology

“…Experiments have reported that VB exists for intermediate λ or capillary number [33]. Another measurable effect of increasing the capillary number on tumbling vesicles is a decrease of the tumbling frequency when approaching the transition to VB [12,40]. There is a consensus from theoretical studies that the phase diagram of the three regime (TT, VB and TB) has the shape shown in Fig.…”

Dynamics of Lipid Vesicles

“…Considerable knowledge about the individual dynamics of vesicles in different types of flow has been accumulated thanks to the intensive theoretical [23][24][25][26][27][29][30][31][32]74] and experimental [33][34][35][36][37][38][39]75] investigations performed so far. Recently, an important progress in this direction was made.…”

“…The theoretical background of the problem [23][24][25][26][27][28][29][30][31][32] and the experimental work performed so far [33][34][35][36][37][38][39] are reviewed and discussed. The theoretical background of the problem [23][24][25][26][27][28][29][30][31][32] and the experimental work performed so far [33][34][35][36][37][38][39] are reviewed and discussed.…”