Theories of Mass transfer

 Mass transfer

 The net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation.

Mass transfer theories

Film Theory

This is the oldest theory for gas-liquid mass transfer developed by Lewis and Whitman in 1924 . The theory postulates  The existence of a film of a thickness (δ) in both the gas and liquid phases separated by an interface. It is based on the following assumptions: 

(1) the mass transfer occurs by molecular diffusion through the film, beyond which the concentration (CAb) is homogeneous

 (2) the mass transfer through the film occurs under steady state conditions 

 (3) the flux is small and the mass transfer occurs at low concentration. Accordingly, for convective mass transfer, the concentration profile is linear

         fig 1.Schematic view of film theory

Penetration Theory

The “penetration theory” or “Higbie’s model” assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time, as schematically shown in Figure2. The basic assumptions of the theory are: 

(1) mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact

 (2) each of the liquid elements stays in contact with the gas for same time period

 (3) equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. 

fig 2. schematic view of penetration theory

Surface Renewel Theory

The surface renewal theory, developed by Danckwerts, applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film as shown in Figure 3. The basic assumptions of the theory are 

(1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk

 (2) at any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element

 (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions.

fig 3. Schematic view of Surface Renewel theory