Binary alloy Stefan similarity solution
= Binary alloy Stefan similarity solution
{title2=$a(t)=2\lambda\sqrt{D_lt}$}
A two-phase diffusion model with constant properties has <similarity solutions> built from the <complementary error function> in each half-line. Equilibrium gives $T_a=-mC_a$ 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 $\lambda=0$.