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The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate chemical reaction timescale to other phenomena occurring in a system.
There are several Damköhler numbers, and their definition varies according to the system under consideration.
For a general chemical reaction A → B of n-th order, the Damköhler number is defined as
<math>Da = k C_0^{\ n-1} t<math>
where:
- k = kinetics reaction rate constant
- C0 = initial concentration
- n = reaction order
- t = time
and it represents a dimensionless reaction time.
In continuous or semibatch chemical processes, the general definition of the Damköhler number is defined as:
- reaction rate / mass transport rate or characteristic time/reaction time
For example, in a continuous reactor, the Damköhler number is:
<math>Da = \frac{k_cC_0^n}{C_0/\tau} = k_cC_0^{(n-1)}\tau<math>
where τ is the mean residence time.
In reacting systems that include also interphase mass transport, the second Damköhler number (DaII) is defined as the ratio of the chemical rate to the mass transfer rate
<math>DaII = \frac{k C_0^{n-1}}{k_g a}<math>
where
- k_g is the global mass transport coefficient
- a is the interfacial areasv:Damköhler tal