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in the second order differential equation are also negligible, resulting in a solution of the form with R = rsep + (1 − rsep) c′′ rsep = 1 dn∗ dc∗ c2 =−B2exp 1− dc∗ ∗0 (4.22) c∗0 c∗0 − n∗|c∗0 B1 and B2 are constants of integration which are evaluated to center the adsorbed-phase transition at ζ = 0 as seen in Figure 4.1. For the adsorbed-phase transition to be centered stoichiometrically at ζ = 0 the area of the two shaded regions must be equal, as illustrated by Coppola and LeVan4 and Rodrigues et al.8 Thus, we have with Example 1 ξn∗dξ ∗0 0 −∞ 0 (1 − n∗) dζ = n∗dζ (4.23) (4.24) n = 1ξdξ 0 +∞ The solution above pertains to any fixed-bed adsorber exhibiting constant pattern behavior with an axisymmetric piecewise continuous velocity profile and a slightly favorable isotherm. As an example of the application of the more general results, we evaluate the solution for a Langmuir isotherm, written in the dimensionless constant separation factor form ∗ c∗ n = R+(1−R)c∗ where R is the separation factor given by LeVan and Carta.6 c′ (4.25) (4.26) (4.27) R = 1 gives a linear isotherm, and R = 0 corresponds to the rectangular (or irre- versible) isotherm. Our solution applies to R slightly less than unity. 56 1+Kc′′PDF Image | TEMPERATURE SWING ADSORPTION COMPRESSION AND MEMBRANE SEPARATIONS
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