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A New Approximate Solution for Diffusional Growth and Dissolution of Spherical Precipitates

A new approximate solution for diffusional growth and dissolution of spherical precipitates has been proposed. The exact analytical solutions of the time-dependent diffusion equation with the flux balance at the interface is often difficult to obtain. The approximate solutions are useful even when the exact solutions are obtainable. The present approximation is the modified version of the conventional linearized gradient approximations, which are tractable for the spherical precipitates growth but does not agree accurately with the exact solution. It is shown that the present model is better than the conventional approximations. The present model is also applicable to the spherical precipitates dissolution, which has no exact solution. The present model gives an ordinary differential equation for dissolution, which can be solved numerically. [doi:10.2320/matertrans.MT-M2020310]