Interfacial Mass Transfer

INTERFACIAL MASS TRANSFER

So far, only diffusion in the boundary layers of a single phase has been dis-cussed. In practice, however, two phases are normally present and mass transfer across the interface must occur. On a macroscopic scale, the interface can be regarded as a discrete boundary. On the molecular scale, however, the change from one phase to another takes place over several molecular diameters. Because of the movement of molecules, this region is in a state of violent change, the entire surface layer changing many times a second. Transfer of molecules at the actual interface is, therefore, virtually instantaneous, and the two phases are, at this point, in equilibrium.

Since the interface offers no resistance, mass transfer between phases can be regarded as the transfer of a component from one bulk phase to another through two films in contact, each characterized by a mass transfer coefficient. This is the two-film theory and is the simplest of the theories of interfacial mass transfer. For the transfer of a component from a gas to a liquid, the theory is described in Figure 4.3. Across the gas film, the concentration, expressed as partial pressure, falls from a bulk concentration P_Ag to an interfacial concentration P_Ai. In the liquid, the concentration falls from an interfacial value C_Ai to a bulk value C_Al.

At the interface, equilibrium conditions exist. The break in the curve is due to the different affinities of component A for the two phases and the different units expressing concentration. The bulk phases are not, of course, at equilib-rium, and it is the degree of displacement from equilibrium conditions that provides the driving force for mass transfer. If these conditions are known, an overall mass transfer coefficient can be calculated and used to estimate the rate of mass transfer.

Transfer of a component from one mixed phase to another, as described above, occurs in several processes. Liquid-liquid extraction, leaching, gas absorption, and distillation are examples. In other processes, such as drying, crystallization, and dissolution, one phase may consist of only one component. Concentration gradients are set up in one phase only, with the concentration at the interface given by the relevant equilibrium conditions. In drying, for

FIGURE 4.3 Interfacial mass transfer.

example, a layer of air in equilibrium, that is, saturated, with the liquid is postulated at the liquid surface and mass transfer to a turbulent airstream will be described by equation (4.5). The interfacial partial pressure will be the vapor pressure of the liquid at the temperature of the surface. Similarly, dissolution is described by equation (4.6), the interfacial concentration being the saturation concentration. The rate of solution is determined by the difference between this concentration, the concentration in the bulk solution, and the mass transfer coefficient.