Pore-scale mushy layer modelling

Mushy layers are multicomponent porous media where the matrix and interstitial fluids can exchange both heat and mass. They are found in nature in sea-ice, magma chambers, possibly at Earth’s inner-core-outer-core boundary and during the early solidification of magma oceans. Passive (nonmushy) porous media exhibit a rich range of behaviour because of the different diffusion and advection rates of solute and heat. In mushy layers, the dynamics are made even more interesting by the coupling of solute concentration and temperature by freezing and melting. There has been a great deal of theoretical work on mushy layers using “ideal” mushy layer equations where the liquid and solid are assumed to be in perfect local thermodynamic equilibrium and are treated as a single continuum. In order for the liquid to remain in thermodynamic equilibrium with the matrix, there must be a separation of timescales between those for diffusion at the pore-scale and advective transport at the system scale. The range of validity of the ideal mushy layer equations has not previously been carefully examined. In passive porous media, pore scale modeling is now used to examine assumptions made in treating the solid and liquid as a single continuum. In this talk, I will first review the transport of heat and solute in passive porous layers and then show some interesting effects in mushy layers – such as the fact that the introduction of a hot fluid can induce freezing and a cold fluid can induce melting. I will then introduce a model of the simplest possible pore-scale mushy layer which consists of a cylindrical fluid region surrounded by a solid annulus where heat and mass can be exchanged at the pore wall. Using the pore-scale model, I will verify some predictions of ideal mushy layer theory regarding transport rates. I will additionally show that there is a threshold, appropriately defined, Peclet number below which ideal mushy layer theory remains valid. Applying this criterion to natural and laboratory analog systems shows that in some extreme cases, the mushy systems may have not been entirely ideal.