Thermo-osmotic flows in closed channels

Thermal forces are an elusive phenomenon in the realm of out of equilibrium statistical physics. Fluids confined in nanochannels, pores, or membranes can be efficiently set into motion by thermal gradients. Confinement is essential to trigger this effect, known as thermo-osmosis, leading to a non-vanishing off-diagonal Onsager coefficient coupling mass flow and temperature gradients. Linear response theory allows us to explain this phenomenon from a microscopic standpoint. Specializing such an approach to a simple model, where the fluid is confined in a closed slab by frictionless walls, a solution respecting the symmetries of the system can be found. Enforcing conservation laws, several quantitative predictions have been obtained. In this study, we investigate, by nonequilibrium molecular dynamics simulations, the scaling of this solution with the width of the channel, showing that the analytical expressions reproduce very accurately both the pressure gradient and the velocity profiles observed in simulations in narrow channels. By increasing the pore width, non-linear effects in the energy transport must be taken into account, leading to a breakdown of linear response theory. However, for physically achievable thermal gradients, the analytical solution is shown to be consistent up to the mesoscopic regime.