Energy Considerations for Multiphase Fluids with Variable Density and Surface Tension

Abstract

We examine the energy budget associated with a multiphase fluid system in the presence of a fluid-fluid interface with variable surface tension. Such an interface is found in thermo-capillary systems and also describes solutions of miscible liquids separated from a third fluid by an interface. We incorporate local density variations and derive an energy budget from the Navier-Stokes and advection-diffusion equations. In addition to the usual potential, kinetic, surface, and dissipated energy, three additional terms are found which correspond to transfers from thermodynamic internal energy to surface, potential, or kinetic energy, respectively. Energy transfers from internal energy to surface energy are found to be comparable to viscously dissipated energy in thermo-capillary systems. Taking into account such transfers is essential to assessing the validity of numerical simulations of such systems.