Seminar Piotr Szymczak, University of Warsaw. In search of the ideal form: pattern formation in dissolving rocks

Dissolution of fractured and porous media introduces a positive feedback between fluid transport and chemical reactions at  mineral surfaces leading to the formation of pronounced wormhole-like channels. Using the combination of experimental, numerical and analytical techniques, we study the shapes of these channels as a function of the flow rate, reaction rate and initial geometry of the system. In particular, we are interested in finding stationary forms, which advance into the system with constant velocity and stationary shape. The most interesting result is the appearance of a morphological phase transition in the channel shapes as the flow rate is increased. At high flows, well-separated, cylindrical shafts are formed, of a nearly uniform diameter all along their lengths. They advance quickly into the matrix, with velocities several times larger than that of a unperturbed, planar dissolution front. On the other hand, for small flow rates, the channels are funnel-shaped with parabolic tips and their advancement velocity is of the same order as that of a planar front. The transition between the two  forms is abrupt, with no intermediate forms observed. We relate these results to the natural dissolution structures in karst landscapes.