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
where:
- k = kinetics 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:
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
where
- k_g is the global mass transport coefficient
- a is the interfacial area
