Microscopic Forces and Flows due to Temperature Gradients

Nano-scale fluid flow is unlike transport on the macro-scale. Pressure gradients typically dominate effects on a large scale while thermal gradients contribute negligibly to the motion of fluid. The situation entirely reverses on the nano-scale. At a microscopic level, flows induced by thermal gradients are caused by forces that act on atoms or molecules near an interface. These thermo-osmotic forces cannot, at present, be derived analytically or measured experimentally. Clearly, it would be useful to calculate these forces via molecular simulations, but direct approaches fail because in the steady-state, the average force per particle vanishes, as the thermo-osmotic force is balanced by a gradient in shear stress. In our journey to indirectly calculate the osmotic force, we met another unknown in the field of molecular theory at interfaces: the microscopic pressure tensor. The latter is an open problem since the microscopic pressure near an interface is not uniquely defined. Using local thermodynamics theories, we relate the thermo-osmotic force to the gradient of the microscopic pressure tensor. Yet, because the pressure is not uniquely defined, we arrive at multiple answers for the thermo-osmotic force, where at most one can be correct. To resolve the latter puzzle, we develop a direct, non-equilibrium simulation protocol to measure the thermo-osmotic force, whereby a thermal gradient is imposed and the osmotic force is measured by eliminating the shear force. Surprisingly, we find that the osmotic force cannot be derived from the gradient of well-known microscopic pressure expressions. We, therefore, derive a thermodynamic expression that gets close. In this work, we report the first, direct calculation of the thermo-osmotic force while simultaneously showing that standard microscopic pressure expressions fail to predict pressure gradients.Raymond and Beverly Sackler Fund for the Physics of Medicin