An initial value problem for the horizontal infiltration of water

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Abstract
An initial value problem for the horizontal infiltration of water is solved by means of a perturbation technique. The diffusivity is assumed to vary as a positive power of the normalized water content. Evolution of the profile is supposed to be taking place in two stages. In the first stage, moisture content at the origin increases steadily as some arbitrary power of dimensionless time until the maximum normalized value of unity is attained; thereafter, in the second stage, moisture content at the origin remains at the constant value of unity. The moisture distribution at the end of the first stage defines the initial values of moisture for the problem in the second stage. This paper derives the flow details for the second stage, and constructs moisture profiles as they evolve for times greater than unity.