Diffusion between phases

Your objectives in studying this section are to be able to  

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

Define and use, where appropriate, overall mass-transfer coefficients. 

Having established that departure from equilibrium provides the driving force for diffusion, we can now study the rates of diffusion in terms of the driving forces. Many of the mass-transfer operations are carried out in steady-flow fashion, with continuous and invariant flow of the contacted phases and under circumstances such that concentrations at any position in the equipment used do not change with time. It will be convenient at this point to use one of these operations as an example with which to establish the principles and to generalize with respect to other operations later. 

For this purpose, let us consider the absorption of a soluble gas such as ammonia (substance A) from a mixture with air, by liquid water, in a wetted-wall tower. The ammonia-air mixture may enter at the bottom of the tower and flow upward, while the water flows downward around the inside of the pipe. The ammonia concentration in the gas mixture diminishes as it flows upward, while the water absorbs the ammonia as it flows downward and leaves at the bottom as an aqueous ammonia solution. Under steady-state conditions, the concentrations at any point in the apparatus do not change with the passage of time. 

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For (1) dilute solutions or (2) equal molar diffusion between phases (e.g., distillation)... 

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. 

The mathematics of mass diffusion within a single phase has thus been well estab-Ushed. Diffusion between phases such as air and water was not fully understood until 1923 when Whitman proposed the two-film theory in which transfer is expressed using two mass transfer coefficients in series, one for each phase (Whitman, 1923). This concept has been rediscovered in pharmacology and probably in other areas and is now more correctly termed the two-resistance theory. ... 

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