Damköhlerzahl

The Damköhlerzahl, often abbreviated as Da, is a dimensionless number used in chemical engineering and reaction engineering to compare the relative timescales of chemical reactions and transport processes such as flow or diffusion. Named after the German chemist Gerhard Damköhler, the Damköhlerzahl provides insight into whether a reaction is limited by chemical kinetics or by mass transfer.

The Damköhlerzahl is typically defined as the ratio of the characteristic time for a flow or transport process to the characteristic time for a chemical reaction. In the context of reacting flows or reactors, it can be expressed as Da = (reaction rate) / (mass transport rate). For a specific reaction and flow system, the formulation varies depending on whether the focus is on surface reactions, gas-phase reactions, or other processes.

In a simple form for homogeneous reactions, Da can be calculated as the product of the reaction rate constant and a characteristic length or time. For instance, in continuous flow reactors, it is often expressed as Da = k * τ, where k is a rate constant and τ is a residence time.

The value of Damköhler number indicates the dominant process: a low Da (less than 1) suggests that transport processes are faster than reactions, and the system is reaction-limited. Conversely, a high Da (greater than 1) indicates that reactions proceed faster than mass transport, making the process transport-limited.

Understanding the Damköhler number helps engineers optimize reactor design, control reaction conditions, and improve efficiency by identifying whether to accelerate kinetics or enhance mixing and transport mechanisms. It is widely used in fields such as catalytic reactions, combustion, and environmental modeling.