Hi, PF! In the study of mass transfer involving chemical reactions, I have seen the use of two different non-dimensional parameters which apparently quantify the same ratio. These are the second Damköhler number and the Thiele modulus, which are defined as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\textrm{Da}^{\textrm{II}} = \frac{\textrm{reaction rate}}{\textrm{diffusion rate}} = \frac{\textrm{diffusion time}}{\textrm{reaction time}}[/tex]

[tex]\phi = \frac{\textrm{reaction rate}}{\textrm{diffusion rate}} = \frac{\textrm{diffusion time}}{\textrm{reaction time}}[/tex]

I would like to know why is a distinction made between both parameters, i.e. why do we need both dimensionless numbers if they quantify the same physical ratio. Right now, the only difference I found between the two is that Da^{II}is used only for heterogeneous reactions, whereas the Thiele modulus is used for both homogeneous and heterogeneous reactions.

My guess right now is that, even if they physically represent the same, the physical quantities needed to define each of them appear in different kinds of systems and equations. So in one system, the Damköhler number may appear when scaling its governing equation, and in a different one, the Thiele modulus appears when scaling the equation. But I would like to think there's more to it than that.

Thanks in advance for any input!

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# Difference between Thiele modulus and Damköhler number

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