Expansions in time for the solution of one-dimensional stefan problems of crystal growth

Abstract

A new method is presented for the solution of mass transport Stefan problems in one dimension and in semi-infinite regions. It relies on expansions of the concentration distribution and growth rate in powers of t 1 2. Field conditions at the moving boundary are not necessarily constant; they can be arbitrary. Such conditions often lead to non-similar solutions. Although these problems are nonlinear, the expansion coefficients satisfy linear recurrence relations. These coefficients result from simple algebraic manipulations of functions closely related to the iterated error functions. The method is applied to several examples of crystal growth from supersaturated solutions. The first two examples assume isothermal conditions; they illustrate the difference between surface equilibrium and finite surface kinetics. The third example demonstrates effects due to homogeneous cooling. © 1980.