 Binary alloy Stefan similarity solution

A two-phase diffusion model with constant properties has similarity solutions built from the complementary error function in each half-line. Equilibrium gives $T_a=-m{C}_a$ and $C_s(a)=k_D{C}_a$. The Stefan condition and interfacial solute balance determine $\lambda$ and $C_a$; finite diffusion on both sides must be retained when constructing the narrow transition near $\lambda =0$.