Capillary pressure of a liquid in a layer of close-packed uniform spheres

The capillary pressure in liquid partially filling the pore space in a layer of equidimensional close-packed spheres has been calculated numerically and studied experimentally. The case of square packing when the centers of the spheres are in the same plane and lie at the corners of a square receives primary consideration for zero gravity. In the absence of gravity, the menisci shapes of a liquid that occupies some fraction of the pore space are constructed using the Surface Evolver code. The mean curvature (and, hence, the capillary pressure) of the liquid surface is calculated. The dependence of capillary pressure on the liquid volume is obtained for selected contact angles in the range 0 ⩽ θ ⩽ π . The evolution of the shape of the liquid’s free surface and the capillary pressure under quasistatic infiltration and drainage can be deduced from these results. The maximum pressure difference between liquid and gas required for a meniscus passing through a pore is calculated and compared with that for hexagonal packing and with an approximate solution given by Mason and Morrow. The lower and upper critical liquid volumes that determine the stability limits for the equilibrium of a capillary liquid in contact with spheres in a square packed array are tabulated for a set of contact angles. To assess the applicability of the obtained results to multiple layers, the possibility that the constructed menisci intersect spheres from adjacent layers has been analyzed. The effect of gravity has also been examined. For square packing the dependence of capillary pressure on liquid volume is constructed for selected contact angles and Bond numbers, Bo , and compared with the case of zero gravity ( Bo = 0 ) . Maximum capillary pressures are calculated for a set of contact angles and Bo = 5 in the limiting cases of square packing and hexagonal packing. Experiments were performed for a layer of square-packed spheres to compare with numerical predictions.