The beauty of dissolution shapes: from cylindrical shafts to fractal trees

Dissolution of porous media introduces a positive feedback between fluid flow and reactant transport triggering hydrochemical instabilities. This leads to the spontaneous appearance of a variety of dissolution shapes, both at macroscale (caves, karst conduits and pinnacles) and at the pore scale. We study the dissolution-induced pattern formation experimentally using two different setups. The first is a microfluidic chip with a gypsum block inserted in between two polycarbonate plates, which is the simplest model of a fracture. The second is a high-pressure flow cell, which we place inside a microCT to observe the formation of the dissolution conduits in real rock samples. 

The microfluidic experiments show that, with time, the dissolution conduits attain a stationary form,  advancing into the system  with a constant velocity and shape. The most interesting result is the appearance of a morphological phase transition in the conduit 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 an unperturbed, planar dissolution front. On the other hand, for small flow rates, the conduits 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. 

We then show the transition between the smooth forms and fractal trees, which takes place as the heterogeneity of the system is increased and relate the ramified structures observed in the microfluidic experiments in this regime to the fractal wormholes formed during the dissolution of real rocks.  Finally, we discuss the shapes of pinnacles - the objects which remain after most of the rock matrix has dissolved.