Temperature-driven flows in nanochannels: Theory and Simulations

TL;DR

This paper develops a theoretical framework for thermo-osmotic flows in nanochannels, deriving explicit formulas and validating them through molecular dynamics simulations in different regimes.

Contribution

It provides an explicit solution for thermo-osmotic flow equations and relates the pressure gradient to equilibrium properties, supported by simulation validation.

Findings

Theoretical predictions match simulation results for pressure drop and velocity profiles.

Derived pressure gradient expression depends on equilibrium properties.

Validated the theory in both liquid and gas regimes.

Abstract

The motion of a fluid induced by thermal gradients in the absence of driving forces is known as thermo-osmosis. The physical explanation of this phenomenon stems from the emergence of gradients in the tangential pressure due to the presence of a confining surface. The microscopic origin of the effect was recently elucidated in the framework of linear response theory. Here, by use of conservation laws, we provide an explicit solution of the equations governing the fluid flow at stationarity in slab geometry, expressing the thermo-osmotic coefficient as the integrated mass current-heat current correlation function (which vanishes in the bulk). A very simple expression for the pressure gradient in terms of equilibrium properties is also derived. To test the theoretical predictions in a controlled setting, we performed extensive nonequilibrium molecular dynamics simulations in two dimensions. Few simple models of wall-particle interactions are examined and the resulting pressure drop and velocity profile are compared with the theoretical predictions both in the liquid and in the gas regime.