Relation between Mass Transfer Coefficient and Diffusivity

Film Theory:
Film theory is one of the most widely used models to describe mass transfer between two phases. According to this theory, a stationary film of fluid is formed around the surface of the solid, which is in contact with the fluid. The movement of solute molecules in this film is considered to be the rate-controlling step of mass transfer.

Mass Transfer Coefficient (K):
Mass transfer coefficient (K) represents the rate of mass transfer between two phases. It is defined as the amount of solute transferred per unit area per unit time per unit concentration difference between the two phases.

Diffusivity (D):
Diffusivity (D) is a measure of the ability of a substance to move from one place to another due to concentration gradients. It is defined as the rate of diffusion of a substance through a unit area per unit concentration gradient.

Relation between K and D:
According to film theory, the rate of mass transfer is directly proportional to the diffusivity of the solute. Therefore, the relation between mass transfer coefficient and diffusivity can be expressed as:

K ∝ D

This means that the mass transfer coefficient is directly proportional to the diffusivity of the solute. If the diffusivity of the solute increases, the mass transfer coefficient also increases.

Conclusion:
In summary, the film theory model suggests that the mass transfer coefficient is directly proportional to the diffusivity of the solute. This relationship is important for understanding the rate of mass transfer between two phases and for designing efficient mass transfer processes.