Diffusion of linearly distributed gas particles

boks

Joined Oct 10, 2008
218
If the gas particles in a box are uniformly distributed in the y and z directions, and linearly distributed in the x direction, is it true that the concentration won't change with time, according to the diffusion equation? I find this very unintuitive.

KL7AJ

Joined Nov 4, 2008
2,225
If the gas particles in a box are uniformly distributed in the y and z directions, and linearly distributed in the x direction, is it true that the concentration won't change with time, according to the diffusion equation? I find this very unintuitive.
This is an interesting one. I don't know if you could actually DO this physically. Under longitudinal pressure waves, you could solve this along the X axis using the one dimensional wave equation...but that would involve a SINUSOIDAL, not a LINEAR density distribution. Once the disturbing force that CREATED this distribution is gone, equilibrium would tend to set in, once the initial oscillation is damped.

eric

studiot

Joined Nov 9, 2007
4,998
Presumably you are studying Ficks law, which states:

'The rate of change of concentration is proportional to the second derivative of concentration with respect to distance.'

The second derivative of any linear function is zero so the rate of change of concentration is zero.
And of course the second derivatives in the directions of constant concentration are also zero.

KL7AJ

Joined Nov 4, 2008
2,225
Presumably you are studying Ficks law, which states:

'The rate of change of concentration is proportional to the second derivative of concentration with respect to distance.'

The second derivative of any linear function is zero so the rate of change of concentration is zero.
And of course the second derivatives in the directions of constant concentration are also zero.

The operative phrase here is "with respect to distance". However, this is an unstable condition with respect to TIME.

eric