## Ji kvp [cl C

where kiov, p', QL, Qv are the overall mass transfer rate constant, molar density of feed, bulk liquid phase concentration (mole fraction), and bulk vapor phase concentration, respectively, for component i. The most commonly used selectivity parameter is the separation factor shown in Equation 3.20. Sometimes, however, the enrichment factor, Pi, is used as an indication of the separation selectivity for component i (Equation 3.32):

As the concentration of component i is reduced, the concentration of component j will approach 1. The separation factor will therefore be close to the value of the enrichment factor, Pi, for dilute solutions (Equation 3.33):

Pervaporative transport process follows the solution-diffusion model that is also the transport mechanism of RO and NF, which consists of the following steps:

1. Diffusion through the liquid boundary layer next to the feed side of the membrane

2. Selective partitioning of molecules of components into the membrane

3. Selective transport (diffusion) through the membrane matrix

4. Desorption into vapor phase on the permeate side

5. Diffusion away from the membrane and into the vapor boundary layer on the permeate side of the membrane

Often, each step can be modeled with different approaches and fundamental assumptions; however, as with all mass transfer operations, the slowest step in this sequence will limit the overall rate of mass transfer and will be the center of research focus. Naturally, these steps are conveniently expressed in the form of the resistance-in-series model, which is expressed with mathematical symbols as the following (Equation 3.34):

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