On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines

Abstract

1. The omission of the tension in the air-water interface has introduced an erroneous factor into Haines’ formulae; certain additional factors have also crept into his expressions for average stress.2. With these corrections, the stress due to moisture varies comparatively little with changing water content, though falling slightly throughout the range. The energy needed to cause rupture rises continuously in a manner not unlike Haines’ measurements, and should more probably be associated with them than should the tensile stress.3. The geometrical approximation used by Haines gives a close geometrical representation of the figure, but a mechanical approximation which is less satisfactory. Since neither the formulae connected with the true curve, nor the tables needed to use them, are readily, accessible, sufficiently exact numerical data have been here put on record.

Calculations of the Equilibrium Vapor Pressure of Water over Adhering 50–200-nm Spheres

“…Depending on their interests, they looked at the solutions of the problem in terms of liquid volumes (i.e., liquid contents), meniscal areas, meniscal curvatures, or forces exerted on the solid surfaces by the pendular ring. For instance, volumes were of concern in calculations of water saturation in soils (Haines, 1925;Fisher, 1926); curvatures were crucial to the study of capillary condensation or evaporation in porous materials (Melrose, 1966); forces were of special interest in liquid-phase sintering (Heady and Cahn, 1970), or in the study of deformation of moist soils (Haines, 1925) or in the depen-dence of the bulk mechanical properties of powders upon humidity (Coughlin et al, 1982).…”

“…The solutions are then surfaces with constant mean curvature. Fisher (1926), was the first to evaluate volumes and forces for pendular rings between identical spheres with zero contact angle. Melrose (1966) developed expressions for the curvature, the confined volume, and the surface area of the liquid-vapor interface in terms of elliptic integrals in the case of identical spheres, but he solved the Laplace-Young equation only for negative curvatures, missing some interesting features.…”

A Theoretical and Wind Tunnel Investigation of the Effect of Capillary Water on the Entrainment of Sediment by Wind

“…F,:2r R2T + r R.rz T,n -*j, (4) where R1 is the radius of the air-water interface and R2 is the radius of the "waist" of the water wedge (Fig. 1) Haines (1925) and Fisher (1926) for spheres predict a sharp drop in capillary force with increasing moisture content up to l0% by mass. …”

Percolation study for the capillary ascent of a liquid through a granular soil

“…If S < 2λ, a capillary bridge may eventually established for some V; otherwise, there is no possible path between the grains for the water to rise. This limit can be estimated through the toroidal approximation method [19] (Fig. 2) or by numerical simulations.…”