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