Minimum Capillary Rise in an Ideal Uniform Soil

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Abstract
The rise, into an ideal uniform soil, of liquid, under the action of capillary forces, differs from the steady flow across the soil. The steady transmission of fluids takes place through the continuous capillaries extending across the soil; the rise, under capillary forces, of liquid is from cell to cell. The hexagonal scheme of grains spaced at a distance (2r+d), where d is a function of porosity, is used as a statistical representation of the soil; and the problem discussed from the standpoint of this packing. The fluid, in its passage through the long capillaries, flows through a cyclic capillary showing definite maxima and minima in each element; and likewise, the rise, from cell to cell, under capillary forces, is through a channel with definite maxima and minima. The minimum opening, of a cell, is the section defined by the plane of centers; the greatest is the section defined by the plane, parallel to the plane of centers, tangent to the grains of the cell immediately over the first cell. The greatest rise, occurs when the minimum opening holds the meniscus and is observed by allowing the liquid to fall through the soil; the least rise should occur when the maximum opening holds the meniscus and should be observed by allowing the liquid to rise through the soil. Wetting phenomena introduce, however, complications affecting the minimum rise. Rings of liquid form, just above the meniscus, around the point of contact of each pair of grains, and carry the rising liquid higher until it attains a position where it is no longer able to reach the rings so formed; equilibrium then prevails at a rise intermediate to the two extremes just defined. The exact conditions controlling the rise phenomena are determined; the approximation, developed for the capillary equation, in an earlier paper, is then used, with these conditions, to calculate the minimum rise. The results are compared with the data given in the earlier paper; good agreement, within the experimental error, is obtained.

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