Pervaporation chemical potential gradient

Pervaporation is a concentration-driven membrane process for liquid feeds. It is based on selective sorption of feed compounds into the membrane phase, as a result of differences in membrane-solvent compatibility, often referred to as solubility in the membrane matrix. The concentration difference (or, in fact, the difference in chemical potential) is obtained by applying a vacuum at the permeate side, so that transport through the membrane matrix occurs by diffusion in a transition from liquid to vapor conditions (Figure 3.1). Alternatively, a sweep gas can be used to obtain low vapor pressures at the permeate side with the same effect of a chemical potential gradient. 

Pervaporation (PV) is a membrane-based process used to separate the components of a liquid mixture. It requires dense membranes. The liquid feed is heated up and placed in contact with the active layer, whereas a vacuum or a sweep gas is applied downstream. The driving force is a chemical potential gradient through the membrane cross section. The separation phenomenon is explained according to the solution-diffusion model. The selective separation depends on the different dissolution of feed molecules into the membrane matrix and their diffusivity. 

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

Pervaporation is a separation process in which a multicomponent liquid is passed across a membrane that preferentially permeates one or more of the components. A partial vacuum is maintained on the permeate side of the membrane, so that the permeating components are removed as a vapor mixture. Transport through the membrane is induced by maintaining the vapor pressure of the gas on the permeate side of the membrane at a lower vapor pressure than the feed liquid. The gradients in chemical potential, pressure, and activity across the membrane are illustrated in Figure 2.12. 

Membrane operation is a specific, but not exotic, operation. In fact it is a hybrid of classical heat and mass transfer processes (Figure 4.1). Direct contact mass transfer operations tend to reach equilibrium due to a difference of chemical potential between two phases that are put into contact. In the same way, temperature equilibrium is aimed at during heat transfer operations, for which driving force is a temperature gradient. In contrast, for membrane operations, by using the specific properties of separation of the thin layer material that constitutes the membrane, under the particular driving force that is applied, it is possible to deviate from the equilibrium that prevails at fluid-to-fluid interphase with classical direct contact mass exchange systems and to reorientate the mass transfer properties. In particular, this is the case with classical operations such as microfiltration (MF), ultrafiltration (UF), reverse osmosis (RO), gas separation (GS), pervaporation (PV), dialysis (DI) or electrodialysis (ED), for which a few characteristics are recalled in Table 4.1. 

Under ideal conditions, a thermodynamic equilibrium will be reached when the chemical potential of the solute i is equal at the membrane surface and the feed phase adjacent to it. The sorption of these solutes at the membrane surface creates a solute concentration gradient across the membrane, resulting in a diffusive net flux of solute across the membrane polymer (Fig. 3.6-lOB). In vapor permea-tion/pervaporation, any solute that has diffused toward the membrane downstream surface is ideally instantaneously desorbed and subsequently removed from the downstream side of the membrane (Fig. 3.6-lOC). This can be achieved either by applying a vacuum (vacuum vapor permeation/pervaporation), or by passing an inert gas over the membrane downstream surface (sweeping-gas vapor permea-... 

Pervaporation, vapor permeation and gas permeation are very closely related processes. In aU three cases the driving force for the transport of matter through the membrane is a gradient in the chemical potential that can best be described by a gradient in partial vapor pressure of the components. The separation is governed by the physical-chemical affinity between the membrane material and the species to be passed through and thus by sorption and solubility phenomena. The transport through the membrane is affected by diffusion and the differences in the diffiisivities of the different components in the membrane can play an important role for the separation efficiency, too. All three processes are best described by the solution-diffusion mechanism , their main differences are determined by the phase state and the thermodynamic conditions of the feed mixture and the condensability of the permeate. 

In a pervaporation process the driving force is the gradient in the chemical potential which is defined as... 

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