# Time Scale Problem: Solving Diffusion Time of Particles in 2D Space

• ishmandoo
In summary, the conversation discusses deriving the diffusion time for particles in a two-dimensional space with scatterers of a certain density and linear cross section. The person is having trouble understanding some of the concepts and asks for clarification. The summary provides explanations for the terms mentioned.
ishmandoo
I am having a lot of trouble starting the following problem. Any ideas? Thanks a lot for helping!

Derive from first principles, the diffusion time for particles traveling at speed v in a two dimensional (x,y) space to reach a distance R from their release point if the scatterers have a density n(m^-2) and linear cross section for scatter $$\sigma$$(m) Let each particle scatter with equal probability into the +/- x, +/-y directions.

I don't know what some of these things mean and they aren't explained well in my book or anywhere i look. What is the density it is referring to? What is the linear cross section for scatter? Again, thanks for any help.

Density n(m^-2) is number per square meter. The cross-section determines the probability of scatter - I am not sure how the normalization has been set up.

## 1. What is the "time scale problem" in relation to diffusion of particles in 2D space?

The "time scale problem" refers to the challenge of accurately predicting the time it takes for particles to diffuse or spread out in a 2D space. This problem arises because diffusion is a stochastic process, meaning it is affected by random factors that can make it difficult to predict the exact time it will take for particles to move from one point to another.

## 2. Why is solving the diffusion time of particles in 2D space important?

Solving the diffusion time of particles in 2D space is important for understanding and predicting various natural and industrial processes, such as the movement of pollutants in water or the diffusion of gases in a closed system. It can also help in designing and optimizing processes in fields such as material science and biophysics.

## 3. What factors affect the diffusion time of particles in 2D space?

The diffusion time of particles in 2D space is affected by several factors, including the concentration of particles, the size and shape of the space, and the properties of the particles themselves (such as their size and interaction with each other and the surrounding environment).

## 4. How is the diffusion time of particles in 2D space calculated?

The diffusion time of particles in 2D space can be calculated using mathematical models, such as the diffusion equation, which takes into account the factors mentioned above. These models can be solved using numerical methods or approximations to obtain an estimate of the diffusion time.

## 5. What are some challenges in solving the diffusion time of particles in 2D space?

One of the main challenges in solving the diffusion time of particles in 2D space is the complexity of the underlying mathematical models. These models often involve partial differential equations, which can be difficult to solve analytically. Another challenge is the need to accurately account for the random nature of diffusion, which can be challenging in certain scenarios.

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