A physical model for liquid capillary bridges between adsorptive solid spheres: The nodoid of plateau

A physical model is proposed for the equilibrium profile of a liquid bridge between spherical particles, in cases where gravitational distortion of the liquid profile may be neglected. The effects of contact angle and particle separation are taken into account. The model is based on thermodynamical equilibrium considerations on a closed system, where the total free energy is minimized, considering a constant liquid volume as a constraint with respect to extremization. A second-order differential equation (Euler equation) for the extrenal profile is found, containing a preliminary unknown Lagrange multiplier. The extremal profile, as well as the value of the multiplier, is obtained by numerical integration of the Euler equation. Calculation of different profiles for a given liquid volume and increasing particle separation lead to accurate information about inherent stability requirements of the liquid profile. This model is of fundamental interest in adsorption thermodynamics, the study of adhesion and their applications.