Normalized Permeate Flow equation

Normalized permeate flow (NPF) is a function of the average applied transmembrane pressure, the osmotic pressures of the feed and permeate, and temperature, as shown in Equation 11.1. Factors that cause an increase or decrease in the NPF are discussed below. 

Equation (1) gives the rate of permeation, in the steady state of flow, through unit area of any medium, in terms of the concentration gradient across the medium, and a constant called the diffusion constant D. The second equation refers to the accumulation of matter at a given point in a medium as a function of time. That is, it refers to a non-stationary state of flow. This second equation may be derived from the first, by considering diffusion in the -f x direction of a cylinder of unit cross-section. The accumulation of matter within an element of volume dx bounded by two planes, i and 2, normal... 

Terms other than permeability (Equation 12.6), such as permeant transmission rate, permeance, and thickness normalized flow, can be used to describe the steady-state permeation of molecules through the polymer films [2]. Permeant transmission rate is the amount of permeant passing through a plane of unit area normal to the direction of the flow during unit time (Equation 12.8). The term permeance is used when differences in partial pressure between both sides of the material are also taken into account (Equation 12.9), whereas thickness normalized flow considers material thickness but not difference in partial pressure (Equation 12.10). 

The equations derived in the previous section represent permeation rates and flux, and examples 18.1 and 18.2 are applications to a specific model. The model assnmes the fluid on each side of the membrane to have a constant composition parallel to the membrane. The compositions normal to the membrane are also assumed constant, with the possible exception of composition gradients in the Aims adjacent to the membrane. The bulk phase compositions on both sides of the membrane had to be given since no material balances were considered. The flow pattern implied in this model is that of perfect mixing (if the film resistances next to the membrane are neglected). Other flow patterns include cross flow, countercurrent flow, and cocurrent flow. 

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