Hatta number
Template:Short description The Hatta number (Ha) was developed by Shirôji Hatta (1895-1973 [1]) in 1932,[2][3] who taught at Tohoku University from 1925 to 1958.[1][2] It is a dimensionless parameter that compares the rate of reaction in a liquid film to the rate of diffusion through the film.[4] 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 (Template:Math) Hatta is defined via:
For a reaction Template:Math order in Template:Math and Template:Math order in Template:Math:
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.[5]
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 Template:Math and that the bulk concentration of A remains zero; the flux and hence the rate of reaction becomes proportional to the mass transfer coefficient Template:Math and the Hatta number: Template:Math.
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.[5]
References
See also
- ↑ 1.0 1.1 Template:Cite book
- ↑ 2.0 2.1 S. Hatta, Technological Reports of Tôhoku University, 10, 613-622 (1932).
- ↑ Template:Cite book
- ↑ R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed. John Wiley & Sons, 2002
- ↑ 5.0 5.1 Template:Cite book