Hatta number

The Hatta number (Ha) was developed by Shirôji Hatta, who taught at Tohoku University. It is a dimensionless parameter that compares the rate of reaction in a liquid film to the rate of diffusion through the film. 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.

H a 2 = k 2 C A , i C B , b u l k δ L D A δ L   C A , i = k 2 C B , b u l k D A ( D A δ L ) 2 = k 2 C B , b u l k D A k L 2

For a reaction m^th order in A and n^th order in B:

H a = 2 m + 1 k m , n C A , i m − 1 C B , b u l k n D A k L

It is an important parameter used in Chemical Reaction Engineering.