Some Exact Solutions for Solute Transport Through Soils Containing Large Cylindrical Macropores

Abstract

This paper presents several exact and approximate analytical solutions of the equations describing convective‐dispersive solute transport through large cylindrical macropores with simultaneous radial diffusion from the larger pores into the surrounding soil matrix. Adsorption effects were included through the introduction of linear isotherms for both the macropore region and the soil bulk matrix. In one formulation the macropores are surrounded by cylindrical soil mantles of finite thickness. Another formulation considers diffusion from a single cylindrical macropore into a radially infinite soil system. A relatively simple but very accurate approximate solution that ignores dispersion in the macropore region is also derived. The various analytical solutions in this paper can be used to calculate temporal and spatial concentration distributions in the macropore system. In addition, approximate solutions are presented for the radial concentration distribution within the adjacent soil matrix. By means of an example, it is demonstrated that at early times, little accuracy is lost when the radially finite soil mantle is replaced by an infinite system.