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Fluid dynamics and particulate diffusion questionby ArriFerrari
Tags: diffusion, dynamics, experimental design, fluid, fluid dynamics, particulate, question 
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#1
Dec513, 08:20 PM

P: 2

I have two cylindrical tubes connected at a 90 degree junction. One tube has a constant flow of a laminar fluid going through it and the fluid is saturated by a soluble particulate with a known concentration. The other tube has a much smaller radius, initially has no particles and is closed at the unconnected end.
How do I find the number of particulates that enter the smaller, closed tube? What equations would be most suitable for this situation? 


#2
Dec613, 08:35 AM

Sci Advisor
P: 5,539

Interesting problem. I would model the smaller tube as a constantpressure system with a fixed highconcentration source of particles at one end, perhaps similar to thermal diffusion (constant heat source at one end).



#3
Dec613, 09:56 AM

PF Gold
P: 1,503

Were this one straight tube split by some diaphragm with a high concentration on one side and zero on the other and the diaphragm were suddenly removed, this would be easily solved analytically using the diffusion equation. However, I imagine there is no analytical solution here on account of the 90degree bend and the fact that you assume there is some flow going on as well.



#4
Dec613, 01:20 PM

Sci Advisor
P: 5,539

Fluid dynamics and particulate diffusion question
That's a fair point; I assumed the smaller tube was initially full of (incompressible) solvent devoid of solute.



#5
Dec1113, 01:36 PM

P: 2

That is a fair assumption. In the experiment, it is. The only reason I can't use a simple diffusion equation is that constant flow. This is actually only a first step though, I need to find how much of the solute gets in the smaller tube when there is a nonconstant flow. We can still assume that the laminar, noncompressible fluid is going straight down the larger tube, like water in a pipe. But it is driven by a rhythmic pressure fluctuation (like a heartbeat). I have access to COMSOL, but very little experience setting up this sort of thing.



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