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On the Dissolution—growth Process of a Grain:: Large Time Behavior and Special Solutions

We study here the large time behavior of the radius R(t) of a spherical grain in a dilute solution of the same substance. The evolution in time of the grain is governed by a reaction-diffusion process in the licluid phase and by a dissolution/accretion process located at the interface which determines the interface kinetics. When there is no reaction, the order of R(t) is rather independent of the interface kinetics; we prove that R(t) = O(&) and construct special solutions with R(t) = P& for the interface liinetics of interest. In the situation with nontrivial chemistry, we obtain a general upper bound R(t) = O(t3I2); for the particular kinetics there is an easy linear upper bound R(t) = O(t) and we obtain a complementary linear lower bound for R(t), clearly distinguishing this from the situation without reaction.