# Particle motion driven by non-uniform thermodynamic forces

## TL;DR

This paper develops a comprehensive framework for understanding particle motion in multi-component fluids driven by non-uniform thermodynamic forces, extending classical non-equilibrium transport theories to complex colloidal systems.

## Contribution

It introduces a reciprocal description that relates particle flux to thermodynamic force distributions, incorporating interfacial properties and hydrodynamics for the first time.

## Key findings

- Describes diffusion and sedimentation accurately.
- Predicts force-free phoretic motion under non-uniform gradients.
- Derives hydrodynamic form of phoretic force validated by classical functions.

## Abstract

We present a complete reciprocal description of particle motion inside multi-component fluids that extends the conventional Onsager formulation of non-equilibrium transport to systems where the thermodynamic forces are non-uniform on the colloidal scale. Based on the dynamic length and time scale separation in suspensions, the particle flux is shown to be related to the volume-averaged coupling between the Stokes flow tensor and the thermodynamic force density acting on the fluid. The flux is then expressed in terms of thermodynamic quantities that can be computed from the interfacial properties and equation of state of the colloids. Our results correctly describe diffusion and sedimentation, and suggest that force-free phoretic motion can occur even in the absence of interfacial interactions, provided that the thermodynamic gradients are non-uniform at the colloidal surface. In particular, we derive an explicit hydrodynamic form for the phoretic force resulting from these non-uniform gradients. The form is validated by the recovery of the Henry function for electrophoresis and the Ruckenstein term for thermophoresis.