Hamiltonian Transformation to Compute Thermo-osmotic Forces

Area of Science:

• Thermodynamics
• Fluid Dynamics
• Statistical Mechanics
• Materials Science

Background:

• A thermal gradient along a fluid-solid interface induces a thermo-osmotic force in the fluid.
• In steady-state conditions, this force is typically counterbalanced by the shear stress gradient.
• Existing microscopic methods lack a unique expression for calculating the thermo-osmotic force magnitude.

Purpose of the Study:

• To develop a novel method for directly computing the thermo-osmotic force at solid-fluid interfaces.
• To circumvent the need to balance the thermo-osmotic force with shear stress in simulations.
• To compare direct force measurements with traditional stress tensor gradient calculations.

Main Methods:

• Utilized nonequilibrium simulations to study fluid behavior under thermal gradients.
• Treated the mass (M) of fluid particles as a tensor within the Hamiltonian framework.
• Eliminated the balancing shear force in simulations to isolate and measure the thermo-osmotic force.

Main Results:

• Successfully computed the thermo-osmotic force directly at simple solid-fluid interfaces.
• Demonstrated that the directly measured thermo-osmotic force is inconsistent with common microscopic stress tensor definitions.
• Highlighted limitations of conventional stress tensor gradients for quantifying thermo-osmotic forces.

Conclusions:

• The tensor mass approach provides a viable method for direct thermo-osmotic force measurement.
• Standard microscopic definitions of the stress tensor may not accurately capture the thermo-osmotic force.
• This study offers a new perspective on understanding interfacial transport phenomena driven by thermal gradients.