Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

Abstract

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibility. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation functions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.