# Estimating Surface Reactions - Liquid, Turbulent Flow

So, I need a method of estimating the influence of a surface (rate constant would do for a start), the idea is to estimate just Reactant + Surface -> Product in a turbulent liquid flow.

Now I am aware of the book "The properties of gases and liquids" by Poling and Prausnitz which gives me two terms for estimating diffusion in a liquid, one general formula from 1975 and a formula specific to hydrocarbons (applicable in my case) from 1982, namely:

Tyn and Calus, 1975:

$$D(AB) = \frac{7.4\,10^{-4} (\phi M(B))^{1/2}T}{\eta(B) V(A)^{0.6}}$$

Hayduk and Minhas, 1982:

$$D(AB) = \frac{13.3\,10^{-8}T^{1.47} \eta(B)^{\epsilon}}{V(A)^{0.71}}$$ where $\epsilon = \frac{10.2}{V(A)}-0.791$

The other variables are

• $M(B)$ = molecular weight of solvent B
• $T$ = temperature
• $\eta(B)$ = viscosity of solvent B
• $V(A)$ = molar volume of solute A
• $\phi$ = association factor of solvent B (1 if unassociated)

Given that in my special case I am looking at a liquid in a turbulent flow, I can use the kinetic theory of gases to estimate a surface collision rate - and include surface efficiency using the work on Baldwin and Howarth from 1982.

For a cylindrical pipe with the solute tending to zero, an upper limit for my rate constant for a surface reaction would be: $k(s) = \frac{8D}{r^2}$

Now there is one big problem with this: The diffusion estimate is not for a turbulent flow (I might be able to get get a diffusion term from Fluent to get a more accurate estimate).

Secondly, at best this would give me an upper limit.

So my question is, do you know of any better more accurate methods of estimating (at least limits) a rate constant for surface reactions? (Or at least the collision rate with the surface.)

• Hi DetlevCM, welcome to chemistry.se. I have edited your post to include Mathjax for your equations. Please take a look at the edit to see how it works. – Michiel May 20 '13 at 12:50
• On the content of your question: I don't exactly understand why you are so interested in a diffusion coefficient. If you have a turbulent flow I would think that species transport is convection dominated, not diffusion dominated – Michiel May 20 '13 at 12:55
• @michielm You are possibly right - diffusion is not the dominant factor in a turbulent flow. It is just that I would need a "diffusion-like" description to allow me to link back to kinetic theory. (Which is the best I have short of trying to go down the long route of setting up a CFD simulation for this aspect of the problem I have.) – DetlevCM May 20 '13 at 13:37