Interfacial mass transfer rates

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. 

In a similar manner as for the volume averaging method in sect 3.4.1, the stress terms are normally rewritten introducing interfacial mean quantities weighted by the interfacial mass transfer rate (i.e., in the volume averaging method the interfacial area averaged stresses are not weighted by the mass transfer rate). The interfacial mean pressure weighted by the interfacial mass transfer rate per unit surface area becomes ... 

Using the mean value theorem the interfacial mass transfer rate due to phase change (3.144) becomes [61, 72, 12] ... 

For gas-liquid interfaces the interfacial mass transfer rate through each of the two films, is used to approximate (3.144), as expressed by ... 

In summary, one of the weakest links in modeling reactive systems operated in bubble columns is the fluid dynamic part considering multi-phase turbulence modeling, interfacial closures, and especially the impact and descriptions of bubble size and shape distributions. For reactive systems the estimates of the contact areas and thus the interfacial mass transfer rates are likely to contain large uncertainties. 

The particles can change their mass if sublimation, condensation or evaporation occurs, or if mass is lost or gained due to interfacial mass transfer (mass diffusion). The interfacial mass transfer rate can be represented by use of the simple film model and expressed in terms of a mass transfer coefficient ... 

Calculate interfacial mass-transfer rates in terms of the local mass-transfer coefficients for each phase. 

N,j are the interfacial mass-transfer rates the product of the molar fluxes and the net interfacial area. The overall molar balances are obtained by summing Eqs. (9.8) and (9.9) over the total number (c) of components in the mixture. At the vapor-U-quid interface we have the continuity equations... 

Pulsed columns, depicted in Fig. 6.3-2, are frequently used in solvent extraction. The design of pulsed packed colunms is identical with the design of static packed columns. Just the two-phase liquid hold-up is periodically vertically moved with the frequency /. Typically, the pulsation height is about 0.8-1.2 cm. Very common is a pulsation intensity of a / 1-2.5 cm/s. The pulsation effects a decrease of droplet size and, in turn, an increase of interfacial mass transfer rates. 

The mechanisms depicted in Fig. 6.4-12 dominate the operation of solvent extractors. Hence, solvent extractors should not be operated in a mode with mass transfer directed out of the dispersed phase (see Sect. 6.3.2) since drop size and interfacial area are small and not sufficient for a good interfacial mass transfer rate. 

Used for fluid-fluid systems and signifies whether the reaction takes place in the bulk or near the interface (of reaction phase). It is ratio of reaction rate to interfacial mass transfer rate... 

PAk is the area averaged interfacial mass transfer rate defined by ... 

For catalytic solid surfaces the interfacial mass transfer rate is defined by (3.149) as ... 

The bubble size distribution is among the important factors controlling the interfacial mass transfer rate in gas liquid stirred tank reactors. This distribution is determined by a balance of coalescence and breakage rates. For this reason the trailing vortices play an important role in the gas dispersion processes in gas-liquid stirred tanks. This role stems from the vortex s ability to capture gas bubbles in the vicinity of the impeller, accumulate them inside the vortex and disperse them as small bubbles in the vortex tail. This ability is related to the high vorticity associated with the rotation of the vortex. Sudiyo [86] investigated bubble coalescence in a 2.6 L stirred tank. 

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