From local to hydrodynamic friction in Brownian motion: A multiparticle collision dynamics simulation study

TL;DR

This study uses multiparticle collision dynamics simulations to explore how boundary conditions and angular momentum conservation affect hydrodynamic friction and diffusion in colloidal particles, revealing deviations from classical theories.

Contribution

It provides new insights into the impact of slip/no-slip boundaries and angular momentum conservation on colloidal hydrodynamics through detailed simulation analysis.

Findings

Hydrodynamic friction follows Stokes law for no-slip boundaries.

Slip boundary conditions reduce hydrodynamic friction when angular momentum is not conserved.

Simulation results challenge the additivity assumption of local and hydrodynamic diffusion coefficients.

Abstract

The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modelled by multiparticle collision dynamics (MPC) with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.