Generalized Stokes laws for active colloids and their applications

TL;DR

This paper develops generalized Stokes laws for active colloids with surface slip, enabling precise calculation of forces, torques, and stress in active suspensions, and explores their implications for phase behavior and dynamics.

Contribution

It introduces the generalized Stokes laws for active colloids, linking surface slip to force distributions and many-body interactions, advancing microscopic modeling of active suspensions.

Findings

Active forces and torques are long-ranged and many-body in nature.

Derived equations for Brownian active suspensions incorporating momentum conservation.

Showed how active interactions can lead to phase separation and synchronization.

Abstract

The force per unit area on the surface of a colloidal particle is a fundamental dynamical quantity in the mechanics and statistical mechanics of colloidal suspensions. Here we compute it in the limit of slow viscous flow for a suspension of $N$ spherical active colloids in which activity is represented by surface slip. Our result is best expressed as a set of linear relations, the "generalized Stokes laws", between the coefficients of a tensorial spherical harmonic expansion of the force per unit area and the surface slip. The generalized friction tensors in these laws are many-body functions of the colloidal configuration and can be obtained to any desired accuracy by solving a system of linear equations. Quantities derived from the force per unit area - forces, torques and stresslets on the colloids and flow, pressure and entropy production in the fluid - have succinct expressions in terms of the generalized Stokes laws. Most notably, the active forces and torques have a dissipative, long-ranged, many-body character that can cause phase separation, crystallization, synchronization and a variety of other effects observed in active suspensions. We use the results above to derive the Langevin and Smoluchowski equations for Brownian active suspensions, to compute active contributions to the suspension stress and fluid pressure, and to relate the synchrony in a lattice of harmonically trapped active colloids to entropy production. Our results provide the basis for a microscopic theory of active Brownian suspensions that consistently accounts for momentum conservation in the bulk fluid and at fluid-solid boundaries