Can the Peclet Number Control Diffusion in Nanoscale Laminar Flow Experiments?

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The discussion centers on using the Peclet number to control diffusion in nanoscale laminar flow experiments involving water and dye solvents. The Peclet number, which represents the ratio of convection to diffusion, is proposed as a tool to maintain diffusion below a critical threshold. However, participants express skepticism about its effectiveness at the nanoscale, where the continuum approximation fails, particularly when maintaining variations in the vertical direction below 5nm over a distance of 50nm.

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ponjavic
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I am going to run an experiment where I have a laminar flow of water with a dye solvent.

It is necessary that the velocity of the dye particles is mostly in the horisontal directions. Naturally particles will diffuse but my questions is how I can ascertain that this is kept below some prerequisite.

I assume there should be some dimensional number telling me for example the ratio of convection/diffusion (thinking Peclet?) and using this I can choose my flow rate and channel dimension to keep diffusion below the required number. However, will this work in practice?

I am looking at particles at a nanoscopic scale where variations in y must be kept below ~5nm over a distance of ~50nm.
 
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I think you are going to have a problem because the continuum approximation breaks down at those scales. You can try to use (for example) the Peclet number, but I don't think it will work that well.
 

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