MODIFIED STEFAN CONDITION IN STEFAN PROBLEM

Abstract

The two-phase one-dimensional Stefan problem (SP) with the boundary between the phases moving with time is considered. The position of the boundary is determined by the modified Stefan condition (MSC), which is obtained from the original nonlinear diffusion equation by integrating over a thin transition layer, and by tending its thickness to zero. Upon receipt of the MSC, the diffusion coefficient is represented by the sum of the Heaviside step functions. It is shown that the MSC differs from the standard one in that in the latter, the derivatives of the concentrations with respect to the phase coordinates are interchanged. An expression for the displacement of the interphase boundary is obtained, which, as in the standard SP, is proportional to the square root of time. The results of using the MSC are confirmed by experimental data on the displacement of the Cu/Sn interface during diffusion bonding during isothermal annealing.