Talk:Fick's law of diffusion

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[edit] Suggestions for improvement

"Your Mum Goes To College" - Fick _ 1802 —Preceding unsigned comment added by 217.43.102.65 (talk) 19:47, 15 October 2007 (UTC)

1. The reasoning behind Fick's 1st Law is pretty evident; can someone provide an explanation or brief derivation of Fick's 2nd Law?

~Consider Fick's 1st law acting either side of a given point. Then, as I believe Darken put it: "What goes in but doesn't come out, stays there", hence Fick's 2nd! —Preceding unsigned comment added by 143.167.129.202 (talk) 10:14, 9 October 2007 (UTC)

2. I've seen another form of Fick's 2nd Law that goes:

\frac{\partial \phi}{\partial t} = \frac{\partial}{\partial x} (D \frac{\partial \phi}{\partial x})

What's the difference between this form and the form listed in the article?

3. Including the del-operator forms of the equations would be helpful.

[edit] Dimensions for D

Could someone explain how we obtain the dimensions of [length2 time-1] for the diffusion coefficient/diffusivity D?

  • Well assuming x is in [length], t is in [time] and φ on the both sides is in the same units, then we don't have other choices. abakharev 01:39, 23 March 2006 (UTC)

[edit] Article name

Shouldn't the article be called Fick's laws of diffusion ? MP (talk) 09:20, 25 September 2006 (UTC)

I was just thinking the same, although it's only minor maybe we should change itAzo bob (talk) 10:38, 31 March 2008 (UTC)

[edit] variant phi characters

This is picky, but some sources distinguish between the two ways of drawing phi, i.e. ɸ and φ. It's the same character, but different equations pick one or the other for historical reasons. I suggest picking one and sticking with it. Ojcit 22:59, 2 October 2006 (UTC)

I prefer φ, to ensure that the symbol in text is identical to the symbol in equations (typeset with latex). Berland 11:21, 29 January 2007 (UTC)

[edit] A Biological Perspective

How does it combine with Graham's law to show "the exchange rate of a gas across a fluid membrane?" Graham's law deals with different molar masses, does that mean you just have to worry about the different molar masses of the gas with the fluid?

In a shake flask of microorganisms the demand for oxygen exceeds the supply; if you measure the oxygen in the liquid phase when the microorganisms are trying to grow exponentially, the oxygen concentration is observed to be zero. Does Fick's Law term of (P2-P1) change the partial pressure of oxygen only so as to raise the oxygen concentration only, when the experimenter mixes in some extra oxygen into the gas phase? Richard8081 21:46, 14 August 2007 (UTC)

[edit] History Section

Can somebody please improve the history section? It's not particularly important but still, for people who need to know the background information, there's a lot left to be desired.--Gabycs 21:12, 14 March 2007 (UTC)

[edit] Vandalism removed

Removed something about his cod piece. —Preceding unsigned comment added by 80.202.72.196 (talk) 21:08, 15 October 2007 (UTC)

[edit] Fick's law in biology

For the transport of CO2 across cell walls of leaves Fick's law takes the form dq/dt = -(c2 - c1)/R where c2 < c1 and R is referred to as the resistance and is used for uniform flow, i.e., the flow is constant in time. It would appear that the area of the membrane and its thickness would have to be constant. dc/dt=d(q/V)/dt=(dq/dt)/V=-Δc/RAΔx=-(1/RA)Δc/Δx so Fick's law is of the form,

dc/dt = - K Δc/Δx

which is not the diffusion equation. The flow goes down a concentration gradient. Also by the ideal gas law P=cR'T so dq/dt = -Δc/R = -ΔP/(R*R'T) = - K'ΔP so we have,

dq/dt = - K' ΔP

It might be better to redo Fick's law to make the constants independent of the area and thickness of the membrane so that they are characteristic of the material of the membrane and not the dimensions.

I will restore some of the changes I made. —Preceding unsigned comment added by Jbergquist (talk • contribs) 11:19, 21 October 2007 (UTC)

I have been reviewing the derivation of the diffusion equations for temperature and concentration. Both use a constitutive equation and a continuity equation stated in vector form. For thermal conductivity heat transfer takes place with no net exchange of carriers which would involve convection. Diffusion takes place at constant temperature and pressure.

The biological usage is that of Fick's first law. It differs from conduction which the resistance causes Joule heating while the passage of a gas through a barrier is associated with the Joule-Thomson effect which causes cooling. The matter requires further study. As stated the "flow law" may require some modification such as an A² term as in Poiseuille's law which also involves a connection between a flow and pressure differences. --Jbergquist 00:26, 22 October 2007 (UTC)

The term "rate of diffusion" can be confusing. The reference cited uses flux = P A Δc where the flux would contain an extra A. P is the permeability of the membrane and is more easily determined than a conductivity K. One should probably use K if one wants to express the law in terms of a constant which is not dependent on the amount of material or its geometry. So one would arrive at R = d/KA² as the formula for the resistance. --Jbergquist 23:33, 22 October 2007 (UTC)

The reason why one might want to use permeability is because it follows the same rules of combination as conductance since P=KA/d. Hence doubling the thickness of a membrane halves the permeability and doubling the area would double the permeability. --Jbergquist 00:11, 23 October 2007 (UTC)