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 theta 1 and theta 2, (theta 1 > theta 2) at time t = 0. We formulate and solve this problem. The key to its simplicity is its similarity character, with moisture profile x(theta) proportional to t 1/2. At the interface x = 0 there is, for t > 0, a permanent and constant moisture content jump theta 3 to theta 4 (theta 3 > theta 4). The operative moisture potential is the primary drying potential for x < 0, theta 1 greater than or equal to theta greater than or equal to theta 3 and the primary wetting potential for x > 0, theta 4 greater than or equal to theta greater than or equal to theta 2. 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 theta = theta 1 and less near theta = theta 2. 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.