Two-Dimensional Fluctuating Vesicles in Linear Shear Flow

TL;DR

This paper investigates the stochastic behavior of two-dimensional vesicles in shear flow, deriving nonlinear Langevin equations, solving them at low temperature, and validating results through simulations, revealing complex mode correlations.

Contribution

It introduces a mean field approach to analyze vesicle deformation under shear flow, accounting for the perimeter constraint and comparing theoretical predictions with simulations.

Findings

Good agreement between theory and simulations.

Non-trivial correlations between deformation modes.

Validation of Langevin equations in low temperature regime.

Abstract

The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the constraint of constant perimeter length. These equations are solved in the low temperature limit and using a mean field approach, in which the length constraint is satisfied only on average. The constraint imposes non-trivial correlations between the lowest deformation modes at low temperature. We also simulate a vesicle in a hydrodynamic solvent by using the multi-particle collision dynamics technique, both in the quasi-circular regime and for larger deformations, and compare the stationary deformation correlation functions and the time autocorrelation functions with theoretical predictions. Good agreement between theory and simulations is obtained.