Mesoporous membranes: thermo-osmotic and isothermal flows with and without capillary condensation

Flow equations in differential and integral forms have been developed via the thermodynamics of irreversible processes for steady-state transport of a sorbable single chemical species through mesoporous membranes under conditions where capillary condensate and inhomogeneous fluid, which includes the Gibbs excess, co-exist in gradients of temperature and pressure. Criteria for the thermo-osmotic steady state of zero flow are considered and relationships are given between heats of transport of gas phase, inhomogeneous fluid and capillary condensate. Numerical values are tabulated for heats of transport of the inert gases, alkanes and other gases using carbon compacts of two different kinds. The heats are given and considered as functions of temperature (both differential and integral values), and as functions of the initial pressure prior to establishing the thermoosmotic steady state of zero flow (the integral heats). Also considered is the determination of phenomenological coefficients, factors determining steady-state concentration profiles of inhomogeneous fluid and co-existing capillary condensate within the membrane, and the role of capillary pressure in augmenting flow, especially for pervaporation.