Liquid-phase permeability, pressure independence

Table 2.2 Pressure-Independence for Liquid-Phase Permeability and Selectivity...

Two cases arise. The simpler case is one in which we imagine that the liquid is confined in a piston-and-cylinder arrangement with a rigid membrane that is permeable to the vapor but not to the liquid, as indicated in Figure 10.1. Pressure may then be exerted on the liquid independently of the pressure of the vapor. The temperatures of the two phases are equal and are held constant. The Gibbs-Duhem equation for the vapor phase is... 

A similar example of a promising application of solar heat for intensified process systems is pervaporation. In pervaporation, a selective membrane is used as barrier between two phases, the liquid feed and the vapour permeate. The process depends on the sorption equilibrium and the mobility of the components through the membrane and is rather independent of the vapour liquid equilibrium. The desired component, which is in liquid form in the feed, permeates through the membrane and evaporates while passing the membrane, because the partial pressure of the permeating component is kept lower than the equilibrium vapour pressure [21]. Permeabilities depend on the solubility and diffusion rates through the membrane. 

If gas is used as non-reactive fluid, at low gas pressures the mean free path of gas molecules gets the order of the pore dimensions. Then gas molecules have a finite velocity at the pore wall, but for liquids, a zero velocity at the wall is assumed. The gas slippage effect increases the flow rate and causes an overestimated permeability. Klinkenberg correction uses measurements at different pressures and an extrapolation for a (theoretical) infinite pressure (Cosentino, 2001). It results in the Klinkenberg corrected permeability , which is independent of the type of gas, and approximately the same as for a single phase liquid. Forchheimer effect ... 

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