Growth of ${\mathrm{He}}^3$ Layers from Surfaces of Nearly Saturated Solutions of ${\mathrm{He}}^3$ in Superfluid ${\mathrm{He}}^4$

The problem of the growth of the ${\mathrm{He}}^3$ phase from a free surface of a nearly saturated solution of ${\mathrm{He}}^3$ in superfluid ${\mathrm{He}}^4$ at zero temperature is considered. Using a Fermi-liquid theory modified to account for the finite thickness of the ${\mathrm{He}}^3$ phase by introducing a distortion of the Fermi surface, we find that the number of ${\mathrm{He}}^3$ layers $N_L$ in the ${\mathrm{He}}^3$ phase increases as the ${\mathrm{He}}^3$ chemical potential ${\mu }_3$ approaches its bulk value ${\mu }_0^3$ as $N_L\sim {({\mu }_3^0-{\mu }_3)}^{-\frac{1}{2}}$. This prediction is in agreement with recent experimental results of Guo, Edwards, Sarwinski, and Tough.