Cross flow filtartion and non Newtonian fluid

[alifar]

Hi,

I am researching on cross flow filtration and the fluid is non Newtonian(Blood)and flow is pulstile too. I have a few questions:

1- For membrane, I am sure that Darcy's Eq. works but I am not sure about feeding line, with considering of pilsatile flow, Can I use Navier stokes formula for top of membrane(feed line)?

2- Which model works for blood? Casson model?

3- Can you introduce me a reference to cover my question or test?

In advance I appreciate for your consideration

Regards
Ali

 

[Latexman]

Navier-stokes will get very, very complex for non-Newtonian pulsing flow! There may be an easier way. It depends on how rigorous do you have to be? Is this for school? Can you use an empirical approach?

For pulsing flow in the feed line, a modified Darcy-Weisbach equation* can be used for frictional losses, but you will need to include an extra term to correct for "acceleration head loss"** due to pulsing flow.

There was a series of articles many years ago in Chemical Engineering magazine on non-Newtonian fluid flow design that may be helpful to you. I'm away from my files right now and a quick search of these fora did not reveal past references I have made to them. Maybe you have more time to search than me. Do a search for non-Newtonian flow, pressure drop, power law, etc. I'll reply again next week when I'm back in the office if you do not find it.

* I don't know much about blood rheology. Whatever rheology model you find is appropriate for blood, you will need the integrated form of the combination of that correlation and the differential force balance. This usually assumes steady flow (no pulsations and no acceleration losses), that's why you have to include the correction for acceleration losses as mentioned above.

** Google "acceleration head loss"

Good luck,
Latexman