Hatta number

Template:Short description The Hatta number (Ha) was developed by Shirôji Hatta (1895-1973 ) in 1932, who taught at Tohoku University from 1925 to 1958. 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 (Template:Math), the maximum rate of reaction assumes that the liquid film is saturated with gas at the interfacial concentration Template:Math; thus, the maximum rate of reaction is Template:Math.

$H{a}^2=\frac{k_2{C}_{A,i}{C}_{B,bulk}{\delta }_L}{\frac{D_A}{{\delta }_L}{C}_{A,i}}=\frac{k_2{C}_{B,bulk}{D}_A}{(\frac{D_A}{{\delta }_L}{)}^2}=\frac{k_2{C}_{B,bulk}{D}_A}{{k_L}^2}$

For a reaction Template:Math order in Template:Math and Template:Math order in Template:Math:

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

For gas-liquid absorption with chemical reactions, a high Hatta number indicates the reaction is much faster than diffusion. In this case, the reaction occurs within a thin film, and the surface area limits the overall rate. Conversely, a Hatta number smaller than unity suggests the reaction is the limiting factor, and the reaction takes place in the bulk fluid, requiring larger volumes.

See also

• Dimensionless quantity
• Dimensional analysis

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