= Pressure-limited spherical freezing in a porous medium
{title2=$\Lambda=k\gamma\mu\epsilon/(\Pi\rho_sL)$}
A growing ice-filled sphere expels liquid because ice is less dense than water. With <porosity> $\phi$, $\epsilon=1-\rho_s/\rho$, and pressure-induced <freezing-point depression> $T_i=T_m-\gamma p_i$, the <Darcy velocity> gives $p_i=\mu\phi\epsilon a\dot a/\Pi$. Quasi-steady spherical <thermal conduction> gives $\phi\rho_sLa\dot a=k(T_i-T_\infty)$. Hence $a\dot a=k(T_m-T_\infty)/[\phi\rho_sL(1+\Lambda)]$, where $\Lambda=k\gamma\mu\epsilon/(\Pi\rho_sL)$. The interface approaches the far-field temperature at low <permeability of a porous medium>, while its pressure tends to a finite equilibrium value.
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