An explicit derivation of an exponential dependence of the hydraulic conductivity on relative saturation

It is shown how to derive explicitly an exponential dependence of the unsaturated hydraulic conductivity, K, on relative saturation, S, and under what conditions such a relationship holds. An earlier derivation of the same result was so restrictive, that it appeared that realistic realizations were not possible, but the present derivation demonstrates the contrary. From existing results, the implication is that the steady-state unsaturated hydraulic conductivity will be log-normally distributed. The log-normal distribution, as well as an exponential dependence on moisture content, have been reported from the same experiment on the same field.