Laboratoire Matière et Systèmes Complexes

Bistability in Rayleigh-Bénard convection with a melting boundary

Laurent Duchemin Professeur au laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH, UMR 7636) à l’ESPCI, Paris

Monday March 2nd, room 454 A 11:30

Flow-phase-change interactions are studied in a simple configuration where a pure and incompressible material is bounded by a top cold plate and a bottom hot plate at fixed temperatures. A solid-liquid interface is present inside the domain such that its temperature is in between the two imposed ones. Both melting and solidification can occur depending on the initial conditions. In some cases, stationary states are achieved where the liquid can no longer be solidified and the solid cannot be further melted.

Two-dimensional simulations are performed by solving the Navier-Stokes equations coupled with a phase-field method. The system allows two types of equilibrium : diffusive or convective. In the latter case, a Rayleigh-Benard convection is observed in the liquid layer which shapes the interface accordingly. Depending on the control parameters, we show that the equilibrium states and the equilibrium heights can be predicted analytically and show good approximation with the simulations. We also show that, for some parameter regimes, this system is sensitive to the initial conditions and can lead to multiple equilibria coexisting. The existence of this bi-stable regime is investigated both numerically and analytically.