I What is the propagation speed of a diffusion

SirVuk

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.

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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.

SirVuk

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?

mfb

Mentor
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

Gold Member
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.

"What is the propagation speed of a diffusion"

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