# Fluid dynamics and particulate diffusion question

1. Dec 5, 2013

### ArriFerrari

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. Dec 6, 2013

### Andy Resnick

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

3. Dec 6, 2013

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 90-degree bend and the fact that you assume there is some flow going on as well.

4. Dec 6, 2013

### Andy Resnick

That's a fair point; I assumed the smaller tube was initially full of (incompressible) solvent devoid of solute.

5. Dec 11, 2013

### ArriFerrari

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 non-constant flow. We can still assume that the laminar, non-compressible 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.

6. Dec 11, 2013