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 Damkhler number is defined as

where:

  • k = kinetic 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