= Phase-change volume source in a rigid mush
For constant phase <mass densities> $\rho_s,\rho_l$, a fixed solid framework has mixture density $\bar\rho=\rho_s\varphi+\rho_l(1-\varphi)$. <Mass conservation> gives
$$
\partial_t\bar\rho+\rho_l\nabla\cdot\mathbf u=0,\qquad \nabla\cdot\mathbf u=(1-r)\varphi_t,\qquad r=\rho_s/\rho_l,
$$
where $\mathbf u$ is <Darcy flux>. Equal phase densities give a divergence-free flux. Unequal densities require expansion or contraction flow during freezing or melting.
Back to article page
