Dispersion-induced chromatographic waves

Motivated by field and laboratory observations of unusual wave propagation, we investigate the behavior of simple model problems involving transport, with competitive adsorption of H+ and a metal cation. In the absence of dif fusion/dispersion, the model problem yields two shocks with the velocities expected from classical theory. In the presence of diffusion/dispersion, th e solution exhibits an additional feature, a pulse of metal ion concentrati on that moves rapidly and independently of the metal ion shock. This "fast wave" is associated with the pH shock in the simplest model problem studied here. Theoretical analysis of this problem yields a jump condition which n umerical experiments confirm. Diffusion/dispersion is prerequisite for this phenomenon: it causes a flux of metal cation through the pH shock while th e two fronts are near each other. One practical implication of this finding is the importance of accurate handling of diffusion and dispersion in nume rical simulation of reactive transport problems. Another is that estimates of species migration based on simple theory, such as retardation factors, m ay fail to capture important features of the actual behavior.