Abstract
Heat and mass transport through porous media is governed by the advection-dispersion equation. Near the forward moving mixing front the longitudinal and transversal dispersion lengths are non-zero; only dispersion by molecular diffusion remains. The present paper presents mathematical-physical arguments why in steady transport the dispersion lengths are equal to zero. In conventional models the dispersion lengths are generally assumed to be process-independent. To interpolate between the relatively large dispersion lengths near time-dependent moving front and the steady transport conditions far away from the front, a mathematical model is proposed to describe the process-dependent time-evolution of the dispersion lengths. In this model, the dispersion lengths near the forward moving front are equal to the well-established conventional dispersion lengths that correctly represent the mixing near the front. However, further behind the moving front, where the mass transport has become (almost) steady, the process-dependent model results in vanishing dispersion lengths and, consequently, in a substantially smaller transversal mixing zone.