Stochastic Eulerian-Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations and Shear Boundary Conditions

TL;DR

This paper introduces a comprehensive computational framework combining Eulerian and Lagrangian methods to simulate complex fluids with thermal fluctuations and shear boundary conditions, enabling detailed rheological studies.

Contribution

It presents a novel mixed Eulerian-Lagrangian formalism incorporating thermal fluctuations and shear boundary conditions for simulating complex fluid rheology.

Findings

Simulated shear responses of polymeric fluids, lipid vesicle fluids, and gel-like materials.

Validated the method's ability to capture thermal fluctuations and shear effects.

Demonstrated the approach's effectiveness in studying complex fluid rheology.

Abstract

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal fluctuations, and externally driven shear flows. A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical system. Microstructure configurations are represented in a Lagrangian reference frame. Conserved quantities, such as momentum of the fluid and microstructures, are represented in an Eulerian reference frame. The mathematical formalism couples these different descriptions using general operators subject to consistency conditions. Thermal fluctuations are taken into account in the formalism by stochastic driving fields introduced in accordance with the principles of statistical mechanics. To study the rheological responses of materials subject to shear, generalized periodic boundary conditions are developed where periodic images are shifted relative to the unit cell to induce shear. Stochastic numerical methods are developed for the formalism. As a demonstration of the methods, results are presented for the shear responses of a polymeric fluid, lipid vesicle fluid, and a gel-like material.