A Mathematical Model for Transport and Growth of Microbes in Unsaturated Porous Soil

Figure 1

Front propagation analytic solution for the time evolution of the concentration of microbes in water phase , plotted in relative units for several equidistantly separated depths . The solution is obtained by solving (15) for with given by the solution in (31), approximated zero, , and the constants of material conveniently chosen. In the inset, we present the corresponding solutions of (27) for several values for for comparison.