Fluid-particle interactions and fluctuation-dissipation relations I -- General linear theory and basic fluctuational patterns

TL;DR

This paper develops a comprehensive linear theory for fluid-particle interactions, deriving fluctuation-dissipation relations that incorporate hydrodynamic effects and memory kernels, applicable to both unconfined and confined geometries.

Contribution

It provides a unified solution to fluctuation-dissipation relations in particle hydrodynamics, including arbitrary memory effects and fluid inertia, extending previous models to confined geometries.

Findings

Derived fluctuation-dissipation relations with memory kernels

Expressed memory kernels as superpositions of exponential modes

Extended theory to confined geometries with fluid inertia effects

Abstract

The article provides a unitary and complete solution to the fluctuation-dissipation relations for particle hydromechanics in a generic fluid, accounting for the hydrodynamic fluid-particle interactions (including arbitrary memory kernels in the description of dissipative and fluid inertial effects) in linear hydrodynamic regimes, via the concepts of fluctuational patterns. This is achieved by expressing the memory kernels as a linear superposition of exponentially decaying modes. Given the structure of the interaction with the internal degrees of freedom, and assuming the representation of the thermal force as a superposition of modal contributions, the fluctuation-dissipation relation follows simply from the moment analysis of the corresponding Fokker-Planck equation, imposing the condition that at equilibrium all the internal degrees of freedom are uncorrelated with particle velocity. Moreover, the functional structure of the resulting equation of motion corresponds to the principle of complete decoupling amongst the internal degrees of freedom. The theory is extended to the case of confined geometries, by generalizing previous results including the effect of fluid inertia.