Variational derivation for higher gradient Van der Waals fluids equilibria and bifurcating phenomena

The equilibrium equations for a higher gradient van der Waals fluid is obtained in this paper from a variationally consistent formulation. An initial instability analysis for a fluid in a cubic-shaped hard device with sliding walls is then performed. In particular, the uniform contraction of a cubic block of fluid governed by the van der Waals free energy is analyzed. A finite perturbation about a homogeneous state is considered and a consistent linearization of such perturbation is shown to yield the possibility of bifurcation. This happens whenever the local volume ratio lies within the spinodal region of the energy and in the presence of sufficiently small capillarity.