Eur. Phys. J. B 29, 311-316 (2002)
https://doi.org/10.1140/epjb/e2002-00307-6

An advected-field method for deformable entities under flow

Groupe de Recherche sur les phénomènes hors équilibre, Laboratoire de spectrometrie physique, Université Joseph Fourier, BP87 38402 Saint Martin d'Hères Cedex, France

Corresponding author: ^a chaouqi.misbah@ujf-grenoble.fr

Received: 19 December 2001
Revised: 31 May 2002
Published online: 2 October 2002

Abstract

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.