Capillary Flow Through an Ideal Uniform Soil

Abstract

An ideal soil is an assemblage of spheres packed to a definite porosity, and for statistical purposes may be represented by grains placed in hexagonal array, with adjacent grain centers equidistant and at a distance (2r+d), where r is the grain radius and d a spacing constant adjusted to suit the observed porosity. Three sets of capillaries, found to extend continuously throughout the packing, furnish the channels through which fluid crosses the soil body. The velocity through the mean capillary is calculated by a method essentially due to Slichter; and from this quantity, the sectional area of the mean capillary, and the number of capillaries per cm², the quantity of fluid per sec., f, crossing a soil of section area s and length L, is found to be $${\text{f=0.00809\hspace{0.17em}(1−P)}}^{\text{2/3}}{\text{{0.9850/(1−P)}}^{\text{2/3}}{\text{−1}}}^2{\mathrm{\Delta pD}}^2\mathrm{s/\eta L}$$ P is the porosity, D the diameter of the grains, η the viscosity of the fluid, and Δp the pressure difference under which the flow occurs. Intrinsic permeabilities computed from this equation are compared with values for carefully sized glass spheres and quartz sands observed experimentally by Green and Ampt. A further comparison with corresponding values calculated from Slichter's equation is given.