Temperature-driven flows in nanochannels: Theory and simulations

Area of Science:

• Fluid Dynamics
• Thermodynamics
• Statistical Mechanics

Background:

• Thermo-osmosis describes fluid motion driven by thermal gradients without external forces.
• The phenomenon arises from tangential pressure gradients near confining surfaces.
• Previous work elucidated its microscopic origins using linear response theory.

Purpose of the Study:

• To provide an explicit theoretical solution for thermo-osmotic fluid flow in slab geometry.
• To derive a simple expression for the pressure gradient using equilibrium properties.
• To validate theoretical predictions through extensive nonequilibrium molecular dynamics simulations.

Main Methods:

• Utilized conservation laws to solve stationary fluid flow equations.
• Expressed the thermo-osmotic coefficient as a mass-heat current correlation function.
• Performed 2D nonequilibrium molecular dynamics simulations with varying wall-particle interactions.

Main Results:

• Derived an explicit solution for the thermo-osmotic coefficient.
• Obtained a simple expression for the pressure gradient in terms of equilibrium properties.
• Simulations showed good agreement with theoretical predictions for pressure drop and velocity profiles in both liquid and gas regimes.

Conclusions:

• The theoretical framework accurately describes thermo-osmotic phenomena.
• The derived correlation function provides a microscopic link to macroscopic transport coefficients.
• Molecular dynamics simulations confirm the validity of the theoretical approach across different fluid states.