Scale-Dependent Dispersion in Soils: An Overview

Abstract

Publisher Summary This chapter presents the differences between a scale-dependent dispersivity and time- or distance-dependent dispersivities. The scale-dependent dispersivity is identified based upon the estimated apparent dispersivities at different times or distances. However, in both cases, the obtained dispersivities are actually constant for time up to the point when the estimation is obtained, or for distance up to the place where the breakthrough curves are measured. Although stochastic theories explain why dispersivity tends to be time dependent, no development of a time-dependent dispersivity directly based upon the statistical properties of aquifers has been implemented. The birth of distance-dependent dispersivity can be attributed to the replacement of mean travel distance with distance in the time-dependent dispersivity functions. However, the use of a distance-dependent dispersivity lacks theoretical foundation. Nevertheless the generalized convection–dispersion equation (CDE) when incorporated with different forms of time-dependent or distance-dependent dispersivity functions has been solved analytically and numerically. According to analytical or numerical solutions of the generalized CDE with time- or distance-dependent dispersivities, the transport processes in these types of media express distinct differences from those in the media with constant dispersivities.