What is the differential equation for steady state molecular diffusion of fluid in a laminar flow?

Question

I need the equation in differential form for steady state molecular diffusion of a fluid in a laminar flow. I am looking for an equation that will work for Reynold's Number 35. Also is it possible to derive it from Ficks law of mass transfer?

Answer 1

Of course you can use Fick's law! Since it is dependent upon the molecular average velocity anyway, so your variable will be included, anyway; your equation is:
JA= -DAB(dCA/dCB); where JA is the diffusion flux for component A, which is proportional to the concentration gradient dCA/dCB,
DAB is the diffusivity of component A in its mixture with B.

Now how we come up with that and in regard to velocities;
the molal flux of a mixture is NM=rMuo, where rM is the average MOLAR denisty of the mixture and uo is the average velocity, then, by substituting rM with more measurable variable which is the molar concentration, we obtain
-for a molecule of A crossing a stationary plane with a linear velocity the following:
NA=cAuA; so JA=cAuA-cAuo which equlas to JA=-DAB(dcA/dB), note here that DAB has the units of meter sqare/seconds "time", since we are measuring the flux.
Hope that helped!

Answer 2

Try to explore the site below:
http://www.rpgroup.caltech.edu/~natsirt/aph162/diffusion.pdf

For Physics Related Topics:
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html