Mass Transfer at a Fluid-Fluid Interface: Film Theory

In the previous lectures, diffusion and mass transfer within fluids were considered.

Of greater interest in separation processes (absorption, distillation, extraction) is mass transfer across an interface between a gas and a liquid or between two liquids.

Several theoretical models have been developed to describe mass transfer between a fluid and a fluid-fluid interface where turbulence may persist.

Film Theory

Diffusion between fluids

Diffusion within fluids

Film theory

Molecular diffusion in stagnant fluids or fluids in laminar flow involves slow rate of diffusion.

If more rapid transfer is required, the fluid velocity is increased until turbulent mass transfer occurs.

To have a fluid in convective flow usually requires the fluid to be flowing past another immiscible fluid (a pure gas A diffuses into non-volatile liquid B) or a solid surface (e.g. a fluid flowing in a pipe).

In the turbulent region, particles in fluid no longer flow in the orderly manner found in the laminar sub-layer.

Relatively, large portions of the fluid called eddies or “chunks” of fluid moving rapidly in random fashion.

NOTE: Read pg. 53-54 of McCabe, Smith and Harriot for the profile of fluid flow (laminar & turbulent) and their relationship with Reynolds number, Re.

Film theory

Nernst proposed film theory in 1904 for turbulent mass transfer to or from a fluid phase boundary.

The entire resistance to mass transfer in a given turbulent phase is in a thin, stagnant region of that phase at the interface, called film.

The film is shown schematically in the above figure for the case of a gas-liquid interface, where the gas is pure component A, which diffuses into nonvolatile liquid B. A is absorbed into liquid B, without desorption of B into A.

Film theory

3 regions of mass transfer (MT) can be visualized:

Region Position Type of MT

1

Adjacent to the surface, a thin, viscous sublayer film is present.

Molecular diffusion, few or no eddies are present. Large concentration drop occurs across this film, slow rate of diffusion.

2

Transition/buffer region, adjacent to the first region.

Some eddies are present, MT is the sum of turbulent and molecular diffusion.

3

Adjacent to the buffer region (turbulent region).

Most of the transfer is by turbulent diffusion, with small amount by molecular diffusion. The concentration decrease is very small, eddies tend to keep the fluid concentration uniform

Film Theory

The concentration drop from cA1 adjacent to the surface is very close to the surface and then levels off. The average or mixed concentration cA is slightly greater than the minimum cA2. The film theory postulates that the concentration will follow the broken curve (Figure 3). The entire concentration difference (cA1 – cA2) is attributed to molecular diffusion within an “effective” film thickness, zT.

1 2 3

Figure 3: Concentration profile in turbulent MT from a surface to a fluid