Horizontal redistribution with capillary hysteresis

Exact and relatively simple analysis is possible for one hysteretic redistribution process, that in long horizontal columns with the two parts, x < 0 and x > 0, at different uniform moisture contents θ1 and θ2 (θ1 > θ2) at time t = 0. We formulate and solve this problem. The key to its simplicity is its similarity character, with moisture profile x(θ) proportional to t1/2. At the interface x = 0 there is, for t > 0, a permanent and constant moisture content jump θ3 to θ4 (θ3 > θ4). The operative moisture potential is the primary drying potential for x < 0, θ1 ≥ θ ≥ θ3 and the primary wetting potential for x > 0, θ4 ≥ θ ≥ θ2. The operative moisture diffusivity is the primary drying diffusivity for x < 0 and the primary wetting diffusivity for x > 0. The drying diffusivity is greater than the wetting diffusivity near θ = θ1 and less near θ = θ2 Solutions are found for illustrative examples corresponding to four values of H, the relative magnitude of the hysteresis loop. The resorptivity R, the total wet‐to‐dry exchange of water across x = 0 in reduced form, is analogous to the sorptivity S in absorption and infiltration. For the calculated examples, R is about one third of S for the corresponding absorption process and varies only mildly with H. Nonhysteretic calculations may thus give reasonable estimates of R for horizontal hysteretic redistribution, though they cannot give details such as the moisture jump at x = 0, Desorption moisture profiles for x < 0 are very gradual, with a large depth of penetration. Absorption profiles for x > 0 are relatively steep, and the penetration depth small. It follows that in experiments the initially wet section of the column should be made some 5–10 times longer than the initially dry sector.