Approximate solutions to second-phase diffusion-controlled growth and dissolution in finite geometries

Abstract

The problem of diffusion-controlled growth and dissolution of a second phase which forms as a continuous layer on the grain boundaries of the parent phase and grows towards the grain interior is solved approximately. Three typical geometries of the second phase are considered: two infinite parallel plates, an infinitely long hollow cylinder and a hollow sphere. The heat balance integral method developed by Goodman is used, with a linear profile being employed in all cases. Such a method, though approximate, allows the treatment of soft impingement and yield simple solutions which allow the growth or dissolution rates to be estimated with little computing effort. It is believed that the solutions given here can be of considerable practical interest in the mathematical modelling of complex processes in which the phase transformation is but one step. In these circumstances, owing to the many approximations involved which normally require adjustable parameters, more accurate but substantially more time-consuming numerical methods are perhaps not always necessary.