I What is the propagation speed of a diffusion

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Hello everybody!

For my water in nanoscaled-pores simulations with SPH I need a value for the characteristic velocity.
My planned approach is to estimate this value by attaining the propagation speed of a diffusion wave.
But I have problems with understanding this process since I find some sources talking about an infinite speed of sound as reference for the propagation speed, while others say that it is a finite value.

Could somebody please help me out of this? :)
 

Orodruin

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There is no such thing as a characteristic speed for diffusion if you do not somehow set a length or time scale. The reason for this is that diffusion is not a wave. It is described by the diffusion equation ##\partial_t u - D\nabla^2 u = \kappa##, where ##\kappa## represents a source term and ##D## is the diffusivity, which has units of length^2/time.
 
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There is no such thing as a characteristic speed for diffusion if you do not somehow set a length or time scale. The reason for this is that diffusion is not a wave. It is described by the diffusion equation ##\partial_t u - D\nabla^2 u = \kappa##, where ##\kappa## represents a source term and ##D## is the diffusivity, which has units of length^2/time.
ok thanks

but is there a general equation explaining with which speed a diffusion front propagates?
 
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There is no well-defined front, but if you look at a fixed concentration, you can determine where this is reached when. You'll find that its propagation slows down over time, so there is no characteristic speed either.
 

Henryk

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There is no such thing as 'diffusional wave'. Diffusion is the result of Brownian motion.
However, there is a formula to that is quite useful in estimating the range of the diffusion. Essentially, it is a solution of the diffusion equation; Gaussian function.
The (squared) width of the Gaussian is given by ##\sigma ^2 = 2 Dt##
It is quite useful in estimating the effects of the diffusion given the time and the dimensional scales.
 

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