Continuum-statistical dynamics of colloidal suspensions under kinematic reversibility

TL;DR

This paper develops a linear response theory linking continuum mechanics to Onsager reciprocity in colloidal suspensions, applicable to multiple species and various boundary conditions, with implications for diffusiophoresis and dense suspensions.

Contribution

It introduces a unified framework deriving non-equilibrium colloidal diffusion from the Lorentz reciprocal theorem, applicable beyond boundary layer approximations and for multiple particle species.

Findings

Onsager reciprocity emerges from the Lorentz reciprocal theorem under kinematic reversibility.

The framework predicts colloids move towards higher solute concentrations unless excluded volume is comparable to particle size.

Numerical determination of transport coefficients in dense suspensions is enabled without microhydrodynamics explicitly resolved.

Abstract

We present a linear response theory that establishes the continuum-mechanical origin of Onsager reciprocity in colloidal motion. By decoupling hydrostatic and hydrodynamic stress, we show that Onsager reciprocal relations emerge from the Lorentz reciprocal theorem under kinematic reversibility, based on the auxiliary flow problem of colloidal sedimentation. Our framework applies to suspensions containing multiple species of microparticles and derives all non-equilibrium contributions to colloidal diffusion from a single application of the Lorentz reciprocal theorem, irrespective of whether a slip or no-slip hydrodynamic boundary condition is imposed at the colloidal surface. Furthermore, a boundary layer treatment is only assumed for microswimming, while the thermodynamic forces giving rise to phoretic motion are fully resolved beyond the boundary layer approximation. For the diffusiophoretic motion arising from volume exclusion of a solute, our results predict that a colloid is drawn towards regions of higher solute concentration, except when the excluded volume layer around it becomes comparable to its radius. Owing to its linear structure, the framework also enables numerical determination of transport coefficients in dense suspensions without explicitly resolving the underlying microhydrodynamics.