Precipitation/dissolution reactions coupled with solute transport are modelled as a cellular automaton in which solute molecules perform a random walk on a regular lattice and react according to a local probabilistic rule. Stationary solid particles dissolve with a certain probability and, provided solid is already present or the solution is saturated, solute particles have a probability to precipitate. In our simulation of the dissolution of a solid block inside uniformly flowing water we obtain solid precipitation downstream from the original solid edge, in contrast to the standard reaction-transport equations. The observed effect is the result of fluctuations in solute density and diminishes when we average over a larger ensemble. The additional precipitation of solid is accompanied by a substantial reduction in the relatively small solute concentration. The model is appropriate for the study of the r^ole of intrinsic fluctuations in the presence of reaction thresholds and can be employed to investigate porosity changes associated with the carbonation of cement.
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