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

[ponjavic]

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.

 

[Andy Resnick]

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.

 

[charng]

Thank you for sharing your experiment plan. Neglecting Brownian diffusion is a valid approach for laminar flow experiments, as it assumes that the particles are moving in a straight line without any random motion. However, it is important to consider the diffusion effects, especially at the nanoscale.

To ensure that the diffusion is kept below the desired level, it is necessary to calculate the Peclet number, which is the ratio of convection to diffusion. This number can be used to determine the appropriate flow rate and channel dimensions to achieve the desired level of diffusion. It is a useful tool for predicting the behavior of particles in a flow and can be used to optimize experimental conditions.

However, it is important to note that the Peclet number is a theoretical calculation and may not always accurately reflect the actual behavior of particles in a flow. There may be other factors such as interactions between particles and the channel walls that can affect diffusion. Therefore, it is recommended to also perform experimental validation of the chosen flow rate and channel dimensions.

In addition, at the nanoscale, it is important to consider the effects of thermal fluctuations on particle motion. These can also contribute to diffusion and should be taken into account in your experimental design.

Overall, using the Peclet number as a guide can be a useful approach to keep diffusion below a certain level in your experiment. However, it is important to also consider other factors and validate your results experimentally. I wish you success in your research.