Diffusion-controlled solute gravity current
= Diffusion-controlled solute gravity current
{title2=$R\sim(\Delta\rho_0gV_0/\mu)^{1/3}D^{1/6}t^{1/2}$}
When vertical <diffusion equation> controls depth, $H\sim\sqrt{Dt}$, while conserved excess solute mass gives $\Delta\rho R^2H\sim\Delta\rho_0V_0$. Ambient viscous resistance then leads to a $t^{1/2}$ spreading law. The enriched-fluid volume grows, so the fixed-volume $t^{1/5}$ law does not apply.