- #1
Dario56
- 289
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- TL;DR
- How can concentration gradient field come into existence immediately at all points in non-stationary diffusion?
Suppose there is a non-stationary diffusion process in 2D rectangular plane. Component diffuses from the outside through all four faces of the plane.
When I think about the simulations of the non-stationary diffusion in Matlab for example (finite difference numerical solution), I remember how time change in concentration happens simultaneously at all points and concentration gradient also decreases continuously. Diffusion profile becomes flater and flater.
However, when I think about the process in the head, I think about it as the component diffusing from the edge inwards (1st paragraph). It's a process happening in series not parallel where component diffuses from point to point following the concentration gradient and time change in concentration doesn't happen simultaneously at all points. Mole flux and concentration gradient are vectors and therefore defined at the point. Component only knows what is happening at the point and follows the vector field of molar flux from point to point. As the time goes, diffusion progresses deeper and deeper into the sample (diffusion length goes up).
It seems that this picture is incorrect and process actually happens in parallel, simultaneously at all points. What isn't intuitive to me is how can concentration gradient field come into existence immediately at all points? Drawing a parallel with electrostatics can be done where electric field is defined at every point as soon as we apply potential difference between two points. Molar flux is replaced by current density and concentration gradient with electric field. We can think of concentration gradient as some kind of ''chemical force'' field (analogous to electric field - electric force relationship) creating a molar flux (current density).
However, there is no force here in reality and that's the reason why the analogy with electrostatics doesn't actually work. It's just statistics and probability theory applied to the large collection of randomly moving particles. In electrostatics, electric force acts on charges creating current density. This force (and electric field) decreases with the distance squared (inverse square law). There is no any such force in diffusion acting on particles and creating molar flux. In that sense, if the concentration gradients don't exist initially inside the sample, how can they suddenly come into existence everywhere when diffusion starts? Diffusion molar fluxes don't arise from interaction unlike electric currents created by electric fields. My picture is that they need to be created at some points and then propagate through space as time goes.
As there is no force here, diffusion should propagate point to point, following the concentration gradient field and there can't be simultaneous time change in concentration at all points.
What am I missing?
When I think about the simulations of the non-stationary diffusion in Matlab for example (finite difference numerical solution), I remember how time change in concentration happens simultaneously at all points and concentration gradient also decreases continuously. Diffusion profile becomes flater and flater.
However, when I think about the process in the head, I think about it as the component diffusing from the edge inwards (1st paragraph). It's a process happening in series not parallel where component diffuses from point to point following the concentration gradient and time change in concentration doesn't happen simultaneously at all points. Mole flux and concentration gradient are vectors and therefore defined at the point. Component only knows what is happening at the point and follows the vector field of molar flux from point to point. As the time goes, diffusion progresses deeper and deeper into the sample (diffusion length goes up).
It seems that this picture is incorrect and process actually happens in parallel, simultaneously at all points. What isn't intuitive to me is how can concentration gradient field come into existence immediately at all points? Drawing a parallel with electrostatics can be done where electric field is defined at every point as soon as we apply potential difference between two points. Molar flux is replaced by current density and concentration gradient with electric field. We can think of concentration gradient as some kind of ''chemical force'' field (analogous to electric field - electric force relationship) creating a molar flux (current density).
However, there is no force here in reality and that's the reason why the analogy with electrostatics doesn't actually work. It's just statistics and probability theory applied to the large collection of randomly moving particles. In electrostatics, electric force acts on charges creating current density. This force (and electric field) decreases with the distance squared (inverse square law). There is no any such force in diffusion acting on particles and creating molar flux. In that sense, if the concentration gradients don't exist initially inside the sample, how can they suddenly come into existence everywhere when diffusion starts? Diffusion molar fluxes don't arise from interaction unlike electric currents created by electric fields. My picture is that they need to be created at some points and then propagate through space as time goes.
As there is no force here, diffusion should propagate point to point, following the concentration gradient field and there can't be simultaneous time change in concentration at all points.
What am I missing?