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I am working in an application where we pump a fluid in a water -filled tube, where the second fluid has a viscosity of 3-4 times the viscosity of water. We have laminar flow (Re around 20).

If the fluids were 100% compatible (e.g. colored water vs clear water) I have determined that if I pump say 100 µl (V), the edge of the second fluid (B) will be att 2V, and the amount of B at a certain cross section will be linearly increasing so at V there will be 50% of B and at 0 µl I will have 100% fluid 2.

For different viscosity I have found a shorter envelope of B in water. I can imagine why, but I don't seem to have the brains to compute how much.

Is there a way to describe the profile of B in water. Maybe there are more parameters needed like velocity, other material properties, ...

I don't need an exact answer. Rather a simple one if there is. Laminar theory works quite well for water/water and I don't seem to need to account for diffusion even though my tubing is 0.8 mm I.D.

Regards

Jens Cameron

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# Laminar flow with two fluids

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