Title:

Microscopic forces and flows due to temperature gradients

Nanoscale fluid flow is unlike transport on the macroscale. 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 nanoscale. At a microscopic level, flows induced by thermal gradients are caused by forces that act on atoms or molecules near an interface. These thermoosmotic 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 steadystate, the average force per particle vanishes, as the thermoosmotic 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 thermoosmotic force to the gradient of the microscopic pressure tensor. Yet, because the pressure is not uniquely defined, we arrive at multiple answers for the thermoosmotic force, where at most one can be correct. To resolve the latter puzzle, we develop a direct, nonequilibrium simulation protocol to measure the thermoosmotic 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 wellknown microscopic pressure expressions. We, therefore, derive a thermodynamic expression that gets close. In this work, we report the first, direct calculation of the thermoosmotic force while simultaneously showing that standard microscopic pressure expressions fail to predict pressure gradients.
