The geometry and motion of sharp fronts within geochemical transport problems
Peter Grindrod · Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences · 1995
Abstract We consider some reactive geochemical transport problems in groundwater systems. When incoming fluid is in disequilibrium with the mineralogy, sharp transition fronts may develop. We show that this is a generic property for a class of systems where the time scales associated with reaction and diffusion phenomena are much shorter than those associated with advective transport. Such multiple timescale problems are relevant to a variety of processes in natural systems: mathematically, methods of singular perturbation theory reduce the dimension of the problems to be solved locally. Furthermore, we consider how spatial heterogeneous mineralogy can make an impact upon the propagation of sharp geochemical fronts. We develop an asymptotic approach in which we solve equations for the evolving geometry of the front and indicate how the non-smooth perturbations, due to natural heterogeneity of the mineralogy on underlying groundwater flow field, are balanced against the smoothing effect of diffusion-dispersive processes. Fronts are curvature damped, and the results here indicate the generic nature of separate front propagation within both model (idealized) and natural (heterogeneous) geochemical systems.