Fluid dynamics and particulate diffusion question

[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?

 

[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).

 

[boneh3ad]

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.

 

[Andy Resnick]

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

 

[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.

 

[boneh3ad]

How exactly do you have a steady flow if one end is capped off? That would seem to be impossible. Is the second tube connected so as to form a T with the first tube and allow a constant flow through the first tube or is it an L as you originally described?