A single source-cylindrical soil domain model for studying simultaneous controlled release and mixing processes

Favorable application of controlled-release agrochemicals requires an understanding of the two simultaneous processes of release from the controlled-release sources into the surrounding soil, and the subsequent spread, uptake, and degradation in the soil profile. In previous research the release process was conceptually approximated by artificial decoupling of the diffusional release and vertical, convective-dispersive transport of the released material. The present article describes a new physical model that avoids this decoupling approximation and conceptualizes the complete three-dimensional, axisymmetric problem of diffusional controlled release and convective-dispersive vertical transport of the agrochemical in the soil. A numerical finite-element scheme was coded for solving the model equations, and it was employed to investigate the effects of the various quantifiers of the controlled-release source and the soil on the release process and, in particular, to study the interplay between the processes of release into the cylindrical soil domain and the convective-dispersive spread in the soil. The actual computations refer to the three-dimensional water velocity filed around an impermeable capsule and the resulting spreading mechanisms, but for the sake of brevity, the outline of the model equations refers to vertical water velocities throughout the cylindrical domain, disregarding radial water fluxes and the resulting vertical dispersive fluxes of the released material. In general, the release rate is expected to increase with increasing membrane conductance, capsule radius, capsule inner concentration, water flux, and the soil longitudinal and, especially, transverse dispersivities. A dimensional analysis of the problem provided a deeper understanding of the dependence of the release rates on these factors, and provided a distinction between the two extremes of slow capsule-controlled release and fast soil-controlled release.