The Hatta number (Ha) was developed by Shirôji Hatta (1895-1973 ) in 1932, who taught at

Tohoku University is a public research university in Sendai, Miyagi, Japan. It is colloquially referred to as or . Established in 1907 as the third of the Imperial Universities, after the University of Tokyo and Kyoto University, it initially focused on sc ...

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 The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale ( reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköh ...

, 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.

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