The first Damköhler number and its importance for characterizing the influence of mixing on competitive chemical reactions. (16th January 2021) - Rehage, Hendrik; Kind, Matthias
Highlights: Dimensional analytic investigation of the Da number definition for three examples. τ c o n v characterizes more than only "convection time scales" in Reynolds similar flows. D a m e c h and D a e b should be distinguished since both enable different application scenarios. A physically meaningful definition of τ m i c r o is unnecessary for D a m e c h definitions. D a e b definition for real stirred-tank reactors is given by Da e b = k c ∞ n - 1 N - 1 . Abstract: The first Damköhler number, Da I, is a widely-used Π group for characterizing the influence of mixing on competitive chemical reactions (CCRs). Although numerous different definitions of Da I are present in literature, there has been little discussion on how these definitions vary in terms of application areas. In this work, we overcome this issue by deriving Da I for three examples of different complexity. We find that defining Da I by physical meaningful time scales has no advantage over a definition by characteristic time scales only. Furthermore, we identify that several issues regarding Da I usage are due that two different types of Da I numbers should be discriminated: The "equation-based" D a e b and the "mechanistic" D a m e c h . D a e b is part of a Π group series with the Reynolds number and enables the scale-up of geometrically similar reactors. Alternatively, D a m e c h enables to transfer results between differently shaped micro-mixing reactors but is limited to micro mixing dominated reactors.