Convective hindrance factor

UF and RO models may all apply to some extent to NF. Charge, however, appears to play a more important role than for other pressure driven membrane processes. The Extended-Nemst Planck Equation (equation (3.28)) is a means of describing NF behaviour. The extended Nernst Planck equation, proposed by Deen et al. (1980), includes the Donnan expression, which describes the partitioning of solutes between solution and membrane. The model can be used to calculate an effective pore size (which does not necessarily mean that pores exist), and to determine thickness and effective charge of the membrane. This information can then be used to predict the separation of mixtures (Bowen and Mukhtar (1996)). No assumptions regarding membrane morphology ate required (Peeters (1997)). The terms represent transport due to diffusion, electric field gradient and convection respectively. Jsi is the flux of an ion i, Di,i> is the ion diffusivity in the membane, R the gas constant, F the Faraday constant, y the electrical potential and Ki,c the convective hindrance factor in the membrane. 

Here, is the local fluid velocity in the pore and Gc is a factor by which the solute velocity is reduced from the fluid velocity (Anderson and Quinn, 1974). One can also average this flux expression over the whole pore cross section in the manner of expression (3.1.112g). The quantity Gc is called the convective hindrance factor a pore-average value of this may be developed as in expression (3.1.112i). The treatment provided assumes that there are no solute-pore wall interactions via adsorption or electrical potential effects. 

Here, is the concentration of solute i averaged over a pore cross section, G is a convective hindrance factor, accounting for the ratio between the velocity of solute molecules and the averaged pore velocity of the solvent Vz (usually less than 1), and Dip is the diffusion coefficient of solute molecules of species i in the pore (Anderson and Quinn, 1974). We have seen earlier from (3.1.113) that... 

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