Force stability of pore-scale fluid bridges and ganglia in axisymmetric and non-axisymmetric configurations

The force stability of isolated zero-gravity fluid bodies (bridges and ganglia) in porous media, both axisymmetric and nonaxisymmetric, is examined, with particular attention to the capillary repulsive force of Orr et al. [Orr, F.M., Scriven, L.E., Rivas, A.P., 1975a. Pendular rings between solids: meniscus properties and capillary force. J. Fluid Mech. 67 (4), 723-742.] and Rivas et al. [Rivas, A.P., Orr, F.M., Scriven, L.E., 1975. Capillary attraction and capillary repulsion. Lat. Am. J. Chem. Eng. Appl. Chem. 5 (1), 93-99.]. By consideration of the Young-Laplace solution set, force stability analyses and experiments, it is shown that fluid bridges and ganglia must adopt a geometry in which the net force exerted on their contacting solids is attractive or zero. Fluid bridges under repulsion - including axisymmetric (outer nodoid) and asymmetric (pseudo-nodoid) forms - are mechanically unstable and not physically realized. The role of wettability is critical: non-wetting fluids tend to cause capillary repulsion rather than attraction. Non-wetting fluid ganglia are therefore subject to a maximum volume condition, defined by the zero-force geometry; for axisymmetric and periodically symmetric (i.e. symmetric by rotation) configurations this constitutes the zone of a sphere. The analysis provides an explanation for the observed pseudo-spherical forms of non-wetting fluid ganglia. A modified Haines in-sphere method is presented for calculating the volumes of isolated spherical ganglia, including the effect of contact angle. The periodically symmetric solution set to the Young-Laplace equation is also examined, by analogy with the axisymmetric case.