Hamiltonian transformation to compute Thermo-osmotic Forces

TL;DR

This paper introduces a Hamiltonian-based method to directly compute thermo-osmotic forces at solid-fluid interfaces, revealing discrepancies with traditional stress tensor approaches.

Contribution

It proposes a novel Hamiltonian transformation treating fluid particle mass as a tensor to measure thermo-osmotic forces directly in non-equilibrium simulations.

Findings

Thermo-osmotic force cannot be derived from common stress tensor definitions.

The Hamiltonian approach effectively isolates the thermo-osmotic force.

Traditional stress-based estimates do not match direct measurements.

Abstract

If a thermal gradient is applied along a fluid-solid interface, the fluid experiences a thermo-osmotic force. In steady state this force is balanced by the gradient of the shear stress. Surprisingly, there appears to be no unique microscopic expression that can be used for computing the magnitude of the thermo-osmotic force. Here we report how, by treating the mass $M$ of the fluid particles as a tensor in the Hamiltonian, we can eliminate the balancing shear force in a non-equilibrium simulation and therefore compute the thermo-osmotic force at simple solid-fluid interfaces. We compare the non-equilibrium force measurement with estimates of the thermo-osmotic force based on computing gradients of the stress tensor. We find that the thermo-osmotic force as measured in our simulations cannot be derived from the most common microscopic definitions of the stress tensor.