NONEQUILIBRIUM SWELLING-PRESSURE AND CAPILLARY-PRESSURE RELATIONS FOR COLLOIDAL SYSTEMS

In a previous article (Achanta et al., Int. J. Eng. Sci., in press) the authors developed a constitutive theory for a multiphase, multicomponent mixture with interfaces. Here that theory is exploited for both equilibrium and nonequilibrium situations to develop functional forms for swelling pressure (or disjoining pressure) and capillary pressure in colloidal systems. The swelling pressure is found to be the pressure difference between the interfacial and bulk phases only at equilibrium. For the general nonequilibrium case, using a linear theory, an extra term in the material derivative of volume fraction is found in the swelling relationship. This nonequilibrium relationship is consistent with the intuitive postulate of Thomas and Windle (Polymer 23, 529, 1982), who used a similar relationship to explain viscous swelling of polymers under osmotic stresses. The equilibrium swelling pressure is shown to reduce to the exponential form of Low (Langmuir 3, 18, 1987) under special conditions. A similar relation is developed for capillary pressure, which is consistent with an earlier derivation of Hassanizadeh and Gray (Water Resour. Res. 29, 3389, 1993). (C) 1994 Academic Press, Inc.