# Neglecting brownian diffusion

• ponjavic
In summary, the conversation discusses an experiment involving a laminar flow of water with a dye solvent, where it is important to keep the velocity of the dye particles mostly in the horizontal direction to prevent diffusion. The speaker suggests using a dimensional number, such as the Peclet number, to choose the flow rate and channel dimension to keep diffusion below a certain threshold. However, it is noted that at a nanoscopic scale, this approach may not be effective due to the breakdown of the continuum approximation.
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.

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.

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.

## What is brownian diffusion?

Brownian diffusion is the random movement of particles suspended in a fluid due to collisions with surrounding molecules. This phenomenon was first observed by scientist Robert Brown in the 19th century.

## Why is brownian diffusion important?

Brownian diffusion plays a crucial role in many natural and industrial processes, such as the dispersion of pollutants in the atmosphere, the spread of diseases, and the mixing of substances in chemical reactions.

## How does brownian diffusion relate to neglecting?

Neglecting brownian diffusion refers to the assumption that the random movement of particles has a negligible impact on their overall behavior. In some cases, this assumption is valid and simplifies mathematical calculations, but in others, it can lead to inaccurate results.

## What factors can affect the extent of brownian diffusion?

The extent of brownian diffusion can be influenced by several factors, including particle size, fluid viscosity, temperature, and concentration of particles. These factors can either increase or decrease the rate of diffusion.

## What are the limitations of neglecting brownian diffusion?

Neglecting brownian diffusion can lead to inaccurate predictions in systems where the random movement of particles plays a significant role. This limitation is especially important in small-scale systems, where brownian motion can have a more significant impact on particle behavior.

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