Diffusive Scaling - How does it work

[jbunten]

I am reading that diffusive scaling in one dimension means that "increasing the size of a cell by a factor of 20 increases average diffusion time by a factor of 400". I can't find anything on diffusive scaling. Can anyone give me an explanation of this?

Thanks

 

[mathman]

I am reading that diffusive scaling in one dimension means that "increasing the size of a cell by a factor of 20 increases average diffusion time by a factor of 400". I can't find anything on diffusive scaling. Can anyone give me an explanation of this?

Thanks

The mathematical theory of diffusion (Brownian motion) has particles spreading out randomly with a normal distribution, where the variance is proportional to time. This means the distance spreading (square root of variance) is proportional to the square root of time, or time is proportional to the square of the distance spread. In your example 400 (time) is proportional to to the square of distance (20).

You can google "Brownian motion" or "diffusion" to get more details.

 

[jbunten]

Thanks for your excellent reply mathman.