Hatta number

The Hatta number ( Ha ) is a dimensionless parameter in the field of chemical macrokinetics. It describes the interaction of mass transfer phenomena and pure reaction kinetics ( microkinetics ) for liquid-liquid or gas -liquid systems. The counterpart to the Hatta number of Heterogeneous Catalysis ( gas-solid or liquid-solid ) is the Thiele modulus.

In general we define the Hatta number as

.

In the literature one often finds the following definition:

Or in more detail:

With

For a simple 1st order reaction, the Hatta number is simplified to the form often used, shortened:

,

  • Thickness of the boundary layer,
  • Rate constant of the reaction,
  • Rate of mass transfer of component A
  • Concentration of the component A in the phase interface
  • Reaction order of component A
  • Reaction order of component B
  • Diffusion coefficient of component A in the fluid phase ( instructions below in the text).

Classification of multiphase reactions

With the help of the Hatta number can be reactions to which mass transport processes are upstream or coupled with mass transfer properties, classify. Examples are the chemical absorption or multiphase reactions.

First considering an interface between two phases ( liquid-liquid or gas-liquid ). The concentration profile of the diffusing component can be described ( by Lewis and Whitman ) with the two-film model.

Hatta, the number is then the ratio of the rate of reaction in the reaction phase to the rate of mass transfer by the phase boundary in the reaction phase.

We distinguish several cases:

  • Slow response

This case applies to a value of the Hatta number was less than 0.3.

The reaction is much slower than the mass transfer. The reaction takes place only in the reaction phase. The reaction does not exercise any interaction with the material transfer.

  • Mean reaction

This case applies to a value of the Hatta number between 0.3 and 3

The reaction is about as fast as the mass transfer. A portion of the diffusing component reacts in the boundary layer.

  • Quick response

This case applies to a value of the Hatta number is greater than 3

The reaction is faster than the mass transfer. The diffusing component reacts in the boundary layer. This means that the reaction is continuously removed via the continuous component from the barrier film. The concentration profile in the film is not straight but curved. This leads to acceleration of mass transfer with respect to the non-reactive mass transfer.

The corresponding acceleration factor, called gain factor has a value of

  • Currently reaction

This is the case in Ha >> 3

The reaction is much faster than the mass transfer. The diffused component reacts shortly after entry into the boundary layer within a plane parallel to the surface. The maximum possible rate of reaction is limited by the diffusion of the liquid reactant to the reaction plane. In the vicinity of this plane, the reactant concentrations are low, the product concentrations are high.

Reaction rate constant
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