There are several theories dealing with mass transfer among phases like the penetration theory, the surface renewal theory, and the two-film theory. Mass transfer in multiphase systems is one of the most critical processes occurring in petrochemical, biological engineering applications, and chemical engineering.

## Penetration Theory

Higbie’s Penetration theory assumes that each liquid element at the gas interface is exposed to the gas for a short time. In the absorption of gases from bubbles or absorption by wetted-wall columns, the mass transfer surface is formed spontaneously and diffusion of the material takes place. The basic assumption of penetration theory are:

Once the gas and the liquid are in contact then the mass transfer from the gas into a liquid element occurs under unsteady-state conditions.

Each of the liquid elements stays in contact with the gas for the same period.

Equilibrium exists at the gas-liquid interface.

The penetration theory expresses the liquid–side mass transfer coefficient (Θ) in terms of contact time and the molecular diffusivity of the gas in the liquid.

kL = 2(DAB / πΘ)0.5

## Surface Renewal Theory

Higbie’s penetration theory was modified by Danckwert in the year 1951, for the mass transfer in a liquid phase. Higbie applies the mathematics of the penetration theory to a more believable situation, where the liquid is pictured as two regions, an interfacial region, and a well-mixed bulk region. Higbie’s proposed the following assumptions:

At any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element.

Liquid elements at the interface are being randomly swapped by fresh elements from the bulk.

Mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions. Hence, instead of using a constant contact time (Θ), the differential liquid volume at the gas-liquid interface is renewed due to the turbulence around the interface, referred to as the surface renewal frequency (s).

kL = (DABs )0.5

The mathematical description of the surface renewal theory depends on the length of time that small fluid elements spend in the interfacial region. The model assumes that the absorption strategy would depend on the time the element is on the surface, and then it needs a time distribution function of elements in the surface, Ѱ (t). The product Ѱ (t) it represents the fluid fraction that remains in the surface a time between ‘t’ and ‘t + data, and so:

⌠Ѱ (t) . dt = 1

## Surface Renewal Theories PDF

The Surface Renewal Theory (SRT) is one of the most unfamiliar models to characterize fluid-fluid and fluid-fluid-solid reactions, which are of considerable industrial and academic importance. In turbulent environments, theories like boundary-layer, surface renewal, and the stagnant film have been contemplated as the main component of the science of heat transfer. The stagnant-film theory is regarded as too unfeasible, but on the other hand, this theory is very popular because of its clarity.

### Conclusion

This is to conclude that there are several theories dealing with mass transfer among phases like the penetration theory, the surface renewal theory, and the two-film theory. Mass transfer in multiphase systems is one of the most critical processes occurring in petrochemical, biological engineering applications, and chemical engineering.