Evaporation-limited hemispherical imbibition ($R_{\ast }=(R_s+\sqrt{R_s^2+4k\Delta P{R}_s/(\mu F_e)})/2$)

When a hemispherical wetted front loses liquid at fixed volumetric flux per unit area $F_e$, equilibrium balances inlet flow with $2\pi R^2{F}_e$. The displayed radius exceeds $R_s$ and is stable because inlet flow decreases while evaporating area increases with radius. Porosity affects the adjustment time but cancels from the equilibrium radius.