Hatta number

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The Hatta number (Ha) was developed by Shirôji Hatta, who taught at Tohoku University.^[1] It is a dimensionless parameter that compares the rate of reaction in a liquid film to the rate of diffusion through the film.^[2] For a second order reaction (r_A = k₂C_BC_A), the maximum rate of reaction assumes that the liquid film is saturated with gas at the interfacial concentration (C_A,i); thus, the maximum rate of reaction is k₂C_B,bulkC_A,iδ_L.

\( {\displaystyle Ha^{2}={{k_{2}C_{A,i}C_{B,bulk}\delta _{L}} \over {{\frac {D_{A}}{\delta _{L}}}\ C_{A,i}}}={{k_{2}C_{B,bulk}D_{A}} \over ({\frac {D_{A}}{\delta _{L}}})^{2}}={{k_{2}C_{B,bulk}D_{A}} \over {{k_{L}}^{2}}}} \)

For a reaction mth order in A and nth order in B:

\( {\displaystyle Ha={{\sqrt {{\frac {2}{{m}+1}}k_{m,n}{C_{A,i}}^{m-1}C_{B,bulk}^{n}{D}_{A}}} \over {{k}_{L}}}} \)

It is an important parameter used in Chemical Reaction Engineering.
References

S. Hatta, Technological Reports of Tôhoku University, 10, 613-622 (1932).

R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed. John Wiley & Sons, 2002