Hatta Number

The Hatta number (Ha) was developed by Shirôji Hatta (1895-1973 ) in 1932, who taught at Tohoku University from 1925 to 1958.S. Hatta, Technological Reports of Tôhoku University, 10, 613-622 (1932). It is a dimensionless parameter that compares the rate of reaction in a liquid film to the rate of diffusion through the film. R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed. John Wiley & Sons, 2002 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:

$Ha^2 = = =$

For a reaction order in and order in :

$Ha =$

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 (hypothetical) 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.

References

See also

*Dimensionless quantity
* Dimensional analysis

Catalysis
Dimensionless numbers of chemistry
Transport phenomena

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