The origin of underground cave systems, such as those at Mammoth Mountain, Kentucky (right) has been investigated for over 100 years. Sir Charles Lyell realized that subterranean caverns were the result of dissolution by weakly acidic solutions of atmospheric CO2. However, models for the dissolution process suggest that water flowing through limestone formations is very quickly saturated with calcium ions, over distances of the order of centimetres. Nevertheless, limestone caverns extend for kilometers; Mammoth cave in Kentucky has nearly 400 miles of passages. So how does the dissolution get so deep? The answer until recently has been described in terms of changes in chemical kinetics; in natural calcite the reaction rate decreases by orders of magnitude near saturation.
Paradoxically this promotes dissolution since the undersaturated solution can penetrate deeper into the fractured rock. Although this is an appealing and widely accepted resolution of the cave formation paradox, it turns out to be an incomplete explanation. About 15 years ago, Hanna and Rajaram  showed by computer simulation that a fracture does not necessarily open uniformly across its width, but develops localized regions of dissolution. This insight was subsequently confirmed by laboratory experiments . Recently, Piotr Szymczak and I realized that there is a universal instability in the equations for fracture dissolution, so that a dissolution front is always unstable . This can provide a more effective means to promote dissolution than changes in chemical kinetics and has a profound effect on how long it takes for breakthrough (when the fracture opens along its whole length) to occur. A popular account of this work appeared in the January 2011 issue of Science News and as an Editor's Choice in Science.
An understanding of the non-linear dynamics of the dissolution process is important in predicting the long-term integrity of underground storage systems, and in particular those being proposed as part of the Department of Energy Carbon Sequestration Program. We have an ongoing research program in collaboration with Piotr Szymczak (University of Warsaw) to model the evolution of permeability in dissolving fractures using theoretical and numerical methods [4-6].