Thermohydrodynamics for a van der Waals fluid

Following a cell method of van Kampen for the calculation of a coarse-grain ed free-energy functional for the van der Waals gas, we compute a correspon ding entropy functional from microscopic principles. This entropy functiona l is one of the building blocks of the recently developed GENERIC framework [H. C. Ottinger and M. Grmela, Phys. Rev. E 56, 6633 (1997)]. This framewo rk allows us to obtain, in a thermodynamically consistent way, the continuu m hydrodynamic equations for a fluid able to display liquid-vapor coexisten ce. Surface tension appears naturally and the resulting model describes int erfaces as diffuse regions, much in the same spirit as the gradient theory for equilibrium situations. We suggest that using interfacial forces in the integral form obtained in the microscopic derivation instead of third orde r derivatives of the density field might represent an advantage from a comp utational point of view. (C) 2001 American Institute of Physics.