= Viscous overturn of a dense crust
{title2=$\tau_s\sim[\mu_s/(\Delta\rho gA\sqrt\kappa)]^{2/3}$}
A dense viscous crust of thickness $a$ above lighter liquid can overturn on a <Rayleigh-Taylor instability> time $\mu_s/(\Delta\rho ga)$. If diffusive growth gives $a=A\sqrt{\kappa t}$, matching its age to that time gives $\tau_s\sim[\mu_s/(\Delta\rho gA\sqrt\kappa)]^{2/3}$. A renewed crust then supplies average solid-volume flux $J_s\sim(\Delta\rho g/\mu_s)^{1/3}(A^2\kappa)^{2/3}$. This scale assumes that heat supplied by the interior does not arrest the crust before instability.
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