Some thermodynamic and stability properties of a fluid with gradient dependent free energy

Abstract

A thermodynamic theory for a fluid continuum whose free energy depends on the density gradient is developed. Such a theory is, perhaps, the simplest approximation to a nonlocal theory, necessary to account for the dynamics of the liquid–vapor transition. Relations between the thermodynamic quantities and an expression for the entropy production are found. It is shown that asymptotic dynamic stability of the equilibrium, in the sense of Lyapunov, is equivalent to classical thermostatic stability. The theory predicts that homogeneous equilibrium solutions of negative compressibility may be stable if the fluid is enclosed in a sufficiently small constant volume container.