Onsager's Variational Principle for the Dynamics of a Vesicle in a Poiseuille Flow

TL;DR

This paper develops a systematic model using Onsager's variational principle to analyze vesicle migration in Poiseuille flow, capturing different steady states and their transitions through a combined phase field and hydrodynamics approach.

Contribution

The paper introduces a novel formulation combining phase field theory and hydrodynamics based on Onsager's principle for vesicle dynamics in flow.

Findings

Identified three steady states: bullet, snaking, and slipper shapes.

Transitions among steady states are explained by dissipation contributions, especially friction.

Model successfully reproduces observed vesicle behaviors in simulations.

Abstract

We propose a systematic formulation of the migration behaviors of a vesicle in a Poiseuille flow based on Onsager's variational principle. Our model is described by a combination of the phase field theory for the vesicle and the hydrodynamics for the flow field. The time evolution equations for the phase field of the vesicle and the flow field are derived based on the Onsager's principle, where the dissipation functional is composed of viscous dissipation of the flow field, bending energy of the vesicle and the friction between the vesicle and the flow field. We performed a series of simulations on 2-dimensional systems by changing the bending elasticity of the membrane, and observed 3 types of steady states, i.e. those with bullet, snaking, and slipper shapes. We show that the transitions among these steady states can be quantitatively explained with use of the Onsager's principle, where the dissipation functional is dominated by the contribution from the friction between the vesicle and the flow field.