Damköhler

The Damköhler number, Da, is a dimensionless group used to compare the rate of a chemical reaction with the rate of mass transport (such as diffusion or convection) in a system. It is named after the German chemist Gerhard Damköhler, who studied diffusion–reaction processes in porous media in the early 20th century. The concept is widely applied in chemical engineering, catalysis, combustion, and environmental modeling to judge whether a process is controlled by kinetics or by transport phenomena.

In interpretation, Da expresses the competition between reaction and transport. When Da is much greater than one, transport processes occur slowly relative to the reaction, and the overall rate is typically transport-limited. When Da is much less than one, the chemical kinetics are slow compared to transport, so the process is reaction-limited. Different systems use slightly different definitions of Da depending on geometry and governing transport mechanisms.

A common form arises in diffusion–reaction problems, where Da can be written as Da = k C0^(n−1) L^2 / D_eff. Here k is the rate constant, C0 a reference concentration, n the reaction order, L a characteristic length scale, and D_eff the effective diffusivity. This form compares the diffusion time scale (L^2 / D_eff) with the intrinsic chemical time scale (1 / (k C0^(n−1))). Other definitions exist for specific geometries, such as porous catalysts or gas–solid systems, but all share the same purpose: to quantify the relative speeds of reaction and transport.

See also concepts like the Thiele modulus and Peclet number, which relate to transport phenomena in reacting systems.