We are interested in the derivation of a two-phase flow model that incorporates surface tension effects using Hamilton’s principle of stationary action. The Lagrangian functional, which defines the action, consists of kinetic energy—accounting for interface characteristics—and potential energy.
A key feature of the model is the assumption that the interface separating the two phases possesses...
We present a class of hyperbolic systems modeling two-phase, two-velocity flows that can be obtained from Hamilton's principle of stationary action. The hyperbolicity is guaranteed for small relative velocities by the presence of turbulence through a Reynolds stress tensor. Various forms of the turbulent term are proposed, and the ones leading to a hyperbolic system of equations are...
Developing a variational formulation for multiphase flows immediately raises the challenge of handling multiple reference frames and their relative noninertial motion. This talk discusses the associated theoretical issues encountered in the pursuit of a consistent continuous mixture theory.
In this talk, we show that the solutions of the Kapila system, generated by initial data close to equilibrium, are obtained in the pressure-relaxation limit from solutions of a one-velocity Baer-Nunziato (BN) model.
Besides the fact that the quasilinear part of (BN) cannot be written inconservative form, its natural associated entropy is only positive semi-definite such that the entropic...
By generalizing the theory of convection to any type of thermal and compositional source terms (diabatic processes), we show that thermohaline convection in Earth oceans, fingering convection in stellar atmospheres, and moist convection in Earth atmosphere are deriving from the same general diabatic convective instability. We show also that "radiative convection" triggered by CO/CH4 transition...
Liquid foam exhibits surprisingly high viscosity, higher than each of its phases. This dissipation enhancement has been rationalized by invoking either a geometrical confinement of the shear in the liquid phase, or the influence of the interface viscosity. However, a precise localization of the dissipation, and its mechanism at the bubble scale, is still lacking. To this aim, we...
In this work we develop a liquid/gas model for magmatic flow that describes the physical processes from the microscopic and macroscopic scales. The resulting two-phase model considers an incompressible liquid phase and a compressible gas phase that exchange mass. It also preserves the conservation of mass and momentum, and a dissipative energy balance under appropriate temperature equations...
