# Hatta number

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 (rA = k2CBCA), the maximum rate of reaction assumes that the liquid film is saturated with gas at the interfacial concentration (CA,i); thus, the maximum rate of reaction is k2CB,bulkCA,iδL.

$Ha^2 = {{k_{2} C_{A,i} C_{B,bulk} \delta_L} \over {\frac{D_A}{\delta_L}\ C_{A,i}}} = {{k_2 C_{B,bulk} D_A} \over ({\frac{D_A}{\delta_L}}) ^2} = {{k_2 C_{B,bulk} D_A} \over {{k_L} ^2}}$

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

$Ha = {{ \sqrt{{\frac{2}{{m} + 1}}k_{m,n} {C_{A,i}}^{m - 1} C_{B,bulk}^n {D}_A}} \over {{k}_L}}$

It is an important parameter used in Chemical Reaction Engineering.

## References

1. ^ S. Hatta, Technological Reports of Tôhoku University, 10, 613-622 (1932).
2. ^ R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed. John Wiley & Sons, 2002