Thermodynamic stability of single-phase fluids and fluid mixtures under the influence of gravity

The equilibrium state attained by a single-phase fluid or fluid mixture when under the influence of gravity and subject to given external constraints differs, as is well known, from its gravity-free counterpart. The thermodynamic stability of single-phase fluids and their mixtures, however, is shown to be uninfluenced by the presence of gravity. Single-phase fluids and their mixtures are thermodynamically stable when under the influence of gravity if, and only if, the gravity-free stability criteria are satisfied everywhere throughout the fluid volume. Gravitational fields, therefore, introduce no additional mechanism whereby spontaneous fluctuations can destabilize an equilibrium state.