Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations

TL;DR

This paper develops systematic reduction techniques for modeling the stochastic dynamics of elastic microstructures in fluids under thermal fluctuations, simplifying complex fluid-structure interactions in various limiting regimes.

Contribution

It introduces a singular perturbation analysis framework to derive effective equations for fluid-structure interactions with thermal noise, based on the Stochastic Eulerian Lagrangian Method.

Findings

Derived simplified models in strong coupling regimes

Established conditions for rapid hydrodynamic relaxation

Provided a continuum mechanics framework for stochastic fluid-structure interactions

Abstract

We investigate the dynamics of elastic microstructures within a fluid that are subjected to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum between the fluid and microstructures is strong, (ii) the mass of the microstructures is small relative to the displaced mass of the fluid, and (iii) the response to stresses results in hydrodynamics that relax rapidly to a quasi-steady-state relative to the motions of the microstructure. We derive effective equations using a singular perturbation analysis of the Backward Kolmogorov equations of the stochastic process. Our continuum mechanics description is based on the Stochastic Eulerian Lagrangian Method (SELM) which provides a framework for approximation of the fluid-structure interactions when subject to thermal fluctuations.