Permeation rate curve

MATHEMATICAL MODEL, 68 Calculation of Permeation Rate Curve, 69 Calculation of Sorption and Desorption Rate Curves, 70... 

Numerical solutions were applied to the dual-mode sorption and transport model for gas permeation, sorption, and desorption rate curves allowing for mobility of the Langmuir component. Satisfactory agreement is obtained between integral diffusion coefficient from sorption and desorption rate curves and apparent diffusion coefficient from permeation rate curves (time-lag method). These rate curves were also compared to the curves predicted by Fickian-type diffusion equations. 

On the other hand, the apparent diffusion coefficient Dj, is calculated from the time-lag method of permeation rate curve. 

Figure 6 shows the pressure dependence of diffusion coefficients calculated from permeation, sorption, and desorption rate curves for CO2 in PI2080. The average values of diffusion coefficients from sorption and desorption rate curves D y are in fair agreement with that from permeation rate curve D. The solid line in Figure 6 was computed from Equation 14... 

Srinivasan and Tien (18) have made an analytical study on the mass-transfer characteristics of reverse osmosis in curved tubular membranes. The increase in mass-transfer due to secondary flow resulted in a substantial reduction in the wall concentration (the polarization modulus) for Np =100 and a/R=0.01 (see Figure 39). Further, the production capacity (permeation rate) was markedly increased (see Figure 40). 

Controlled centrifugal instabilities (called Dean vortices), resulting from flow around a curved channel, were used by MaUubhotla and Belfort [74] to reduce both concentration polarization and the tendency toward membrane fouling. These vortices enhanced back-migration through convective flow away from the membrane-solution interface and allowed for increased membrane permeation rates. 

Permeation Properties. The data shown in Figure 2 are the toluene permeation rates of the fluorinated and untreated containers g. toluene/container per day are plotted vs. the time of toluene exposure on a logarithmic scale. These cumulative permeation rates were calculated based on the cumulative weight loss over the time of toluene exposure, as opposed to the differential permeation rates based on the differential weight loss over each time interval. The room temperature permeation rates for the in-situ fluorinated containers were less than 0.01 g./day and, hence, have been rounded up to 0.01 g./day for illustrative purposes. In Figure 2, the,flat portion of the curves for the untreated containers yielded the steady state permeation rates. From these values, the permeability coefficients (P) for the untreated containers were calculated using Equation 1. 

The flux also depends on the physical make-up of the membrane and the pore size. The pure water flux vs. hydrauhc pressure difference curve is linear. Liquid flux for membrane processes is shown in F ure 1.5. The data show how the permeation rate varies with the size of the species and pore size (implicit in type of membrane). The ordinate represents the flux of water per unit pressure gradient. Since the pore radius of an RO membrane is 0.6 nm, water molecules whose radius is about 0.1 nm can pass through the membrane freely while dissolved ions and organic solutes (e.g., sucrose) cannot. These solutes are either rejected at the membrane surface, or are more strongly attracted to the solvent water phase than to the membrane surface. The preferential sorption of water molecules at the solvent—membrane interface, which is caused by the interaction force working between the membrane, solvent, and solute responsible for the separation [8]. As the pore size decreases and tends toward a non-porous skin structure, the transport mecharusm changes from convective flow through pores to SD in the membrane polymer. The latter is the transport mechanism in GS and PV. 

NUMERICAL SOLUTION OF THE PERMEATION, SORPTION, AND DESORPTION RATE CURVES INCORPORATING THE DUAL-MODE SORPTION AND TRANSPORT MODEL... 

Numerical Solution of the Permeation, Sorption, and Desorption Rate Curves 71 For desorption,... 

Figure 6. Pressure dependence of diffusion coefficients calcuiated from permeation ( -), sorption ((,)) and desorption (A) rate curves for CO2 in PI2080. 9 is average vaiue of diffusion coefficients from sorption and desorption rate curves at same pressure. The soiid iine is caicuiated from Equation 14 using parameters 0 in Tabie 1. The dotted line is calculated from Equation 15 using parameters in Table 1.

Seleciivity and permeation rate as a function of the etching time with PES hollow fibers. Dashed line 1 untreated fibers Curve 2 etched fibers [31]. 

When gases (He, Hg, Ar, Ng, Og) diffuse through silica glass, one sometimes gets a continual change in slope of log (permeation rate) l/r curves at low temperatures ((57,58,59) see also Table 23 and Chap. Ill), thought to be due to grainboundary diffusion. 

Some data giving permeability constants and permeation rates at different temperatures are presented in Tables 113 and 114, for systems with high temperature coefficients, and ilegli ble coefficients respectively. For a number of resin, and rubber, membranes the curves of log P (P permeability constant) against l/T are linear, and from the slopes one may evaluate E in the equation P = Some of these values... 

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