Hatta number
The Hatta number was developed by Shirôji Hatta in 1932, who taught at Tohoku University from 1925 to 1958. It is a dimensionless parameter that compares the rate of reaction in a liquid film to the rate of diffusion through the film. It is related to one of the many Damköhler numbers, Hatta being the square root of such a Damköhler number of the second type. Conceptually the Hatta number bears strong resemblance to the Thiele modulus for diffusion limitations in porous catalysts, which also is the square root of a Damköhler number. For a second order reaction Hatta is defined via:
For a reaction order in and order in :
For gas-liquid absorption with chemical reactions, a high Hatta number indicates the reaction is much faster than diffusion, usually referred to as the "fast reaction" or "chemically enhanced" regime. In this case, the reaction occurs within a thin film, and the surface area and the Hatta number itself limit the overall rate.
For Ha>2, with a large excess of B, the maximum rate of reaction assumes that the liquid film is saturated with gas at the interfacial and that the bulk concentration of A remains zero; the flux and hence the rate of reaction becomes proportional to the mass transfer coefficient and the Hatta number:.
Conversely, a Hatta number smaller than unity suggests the reaction is the limiting factor, and the reaction takes place in the bulk fluid; the concentration of A needs to be calculated taking the mass transfer limitation - without enhancement - into account.