It is named after German chemist Gerhard Damköhler, who worked in chemical engineering, thermodynamics, and fluid dynamics.
In its most commonly used form, the first Damköhler number (DaI) relates particles' characteristic residence time scale in a fluid region to the reaction timescale.
For a general chemical reaction A → B following the Power law kinetics of n-th order, the Damköhler number for a convective flow system is defined as: where: On the other hand, the second Damköhler number (DaII) is defined in general as: It compares the process energy of a thermochemical reaction (such as the energy involved in a nonequilibrium gas process) with a related enthalpy difference (driving force).
[1] In terms of reaction rates: where The value of Da provides a quick estimate of the degree of conversion that can be achieved.
In addition, for a single reaction a conversion may be defined in terms of the limiting reactant, for the simple decomposition that is species
Alternatively, one can graph the expressions and see where they intersect with the line given by the inverse Damköhler number to see the solution for conversion.