In this paper first it is shown for several geometries that classical similarity solutions for particle growth exist if and only if the Stefan problem is well-posed in the sense of being mass conserving. The extension of the similarity solutions to multicomponent alloys, which makes the problem nonlinear, is illustrated by the application to a hypothetic alloy with realistic input values. The similarity solutions are based on the assumption of local equilibrium at the interface. In the second part, the assumption of local equilibrium is relaxed using a first-order interface reaction. The influence of the interface reaction on the movement of the interface and on the interface concentrations is evaluated using Finite Difference calculations. A Newton scheme is used to solve the nonlinear problem.