Stability of Multi-Phase Systems Evolving on an Equilibrium Manifold

Abstract The paper extends Gibbs tangent plane theory for equilibrium (infinite time) systems to a limited class of non-equilibrium (finite time) systems. The class of systems we consider have dynamics constrained to an equilibrium manifold defined by contact between the entropy and its supporting hyper-plane. It is established that points on the manifold are stabilized provided the degrees of freedom (boundary conditions) are chosen appropriately. The result is applied to the multi-component flash. The adiabatic flash with fixed feed conditions, constant molar hold-up and pressure has a unique and stable steady state. However, a flash with fixed product composition and fixed pressure may have multiple steady states.