Dynamics and rheology of a dilute suspension of vesicles: higher order theory

TL;DR

This paper develops a higher order theoretical framework to analyze vesicle dynamics under shear flow, revealing bifurcation behaviors and rheological properties that differ from previous models.

Contribution

It introduces a consistent higher order theory for vesicle dynamics, capturing bifurcations and rheology more accurately than prior leading order models.

Findings

Direct bifurcation from tank-treading to tumbling at low capillary number

Presence of vacillating-breathing mode at higher capillary numbers

Effective viscosity shows minima at bifurcation points

Abstract

Vesicles under shear flow exhibit various dynamics: tank-treading ($tt$), tumbling ($tb$) and vacillating-breathing ($vb$). A consistent higher order theory reveals a direct bifurcation from $tt$ to $tb$ if $C_a\equiv \tau \dot\gamma $ is small enough ($\tau$= vesicle relaxation time towards equilibrium shape, $\dot\gamma$=shear rate). At larger $C_a$ the $tb$ is preceded by the $vb$ mode. For $C_a\gg 1$ we recover the leading order original calculation, where the $vb$ mode coexists with $tb$. The consistent calculation reveals several quantitative discrepancies with recent works, and points to new features. We analyse rheology and find that the effective viscosity exhibits a minimum at $tt-tb$ and $tt-vb$ bifurcation points.