Adsorption/desorption equilibrium constant dimensionless

Reactant equilibrium constants Kp and affect the forward kinetic rate constant, and all Ki s affect die adsorption terms in the denominator of the Hougen-Watson rate law via the 0, parameters defined on page 493. However, the forward kinetic rate constant does not appear explicitly in the dimensionless simulations because it is accounted for in Ihe numerator of the Damkohler number, and is chosen independently to initiate the calculations. Hence, simulations performed at larger adsorption/desorption equilibrium constants and the same intrapellet Damkohler number implicitly require that the forward kinetic rate constant must decrease to offset the increase in reactant equilibrium constants. The vacant-site fraction on the internal catalytic surface decreases when adsorption/desorption equilibrium constants increase. The forward rate of reaction for the triple-site reaction-controlled Langmuir-Hinshelwood mechanism described on page 491 is proportional to the third power of the vacant-site fraction. Consequently, larger T, s at lower temperature decrease the rate of reactant consumption and could produce reaction-controlled conditions. This is evident in Table 19-3, because the... 

The dimensionless adsorption/desorption equilibrium constants are 9i = KiCA,swf ceRT = 0.3 i = A2, B, C... 

The symbol in Equation 8 A.13 corresponds to the rate constant of adsorptive molecnles transferred from the subphase to the adsorption surface, and the symbol K, corresponds to rate constant for the desorption process. The ratio Ki K is nothing else than the dimensionless equilibrium constant of the adsorption, and the value Cs is the equilibrium adsorption constant that has... 

Note Since the model is linear for the special case considered, the same equation is also satisfied by the other three variables.) The following observations may be made from Eq. (98) that expresses the dimensionless dispersion coefficient A (i) The first term describes dispersion effects due to velocity gradients when adsorption equilibrium exists at the interface. We note that this expression was first derived by Golay (1958) for capillary chromatography with a retentive layer, (ii) The second term corresponds to dispersion effects due to finite rate of adsorption (since this term vanishes if we assume that adsorption and desorption are very fast so that equilibrium exists at the interface), (iii) The effective dispersion coefficient reduces to the Taylor limit when the adsorption rate constant or the adsorption capacity is zero, (iv) As is well known (Rhee et al., 1986), the effective solute velocity is reduced by a factor (1 + y). (v) For the case of irreversible adsorption (y — oo and Da —> oo), the dispersion coefficient is equal to 11 times the Taylor value. It is also equal to the reciprocal of the asymptotic Sherwood number for mass transfer in a circular... 

Although the assumptions of rapid adsorption and local equilibrium at the interface are justified in many situations of interest, sometimes the rates of adsorption and desorption must be considered. Equation 6.41 still applies, but the analysis must be modified. The terms adsorption barrier and desorption barrier are sometimes used when kinetic limitations exist for the respective processes. If a surface active solute diffuses between phases imder conditions where there is an appreciable desorption barrier, for example, interfacial concentration r will attain higher values than in the absence of the barrier, and interfacial tension will be lower. England and Berg (1971) and Rubin and Radke (1980) have studied such situations. Figure 6.11 shows an example of predicted interfacial tension as a fimction of time for various values of a dimensionless rate constant. The low transient interfacial tension is evident. 

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