How is Fick's First Law derived?

In summary, the conversation discusses the derivation of Fick's Law, which states that the flux of a species is proportional to the concentration gradient. The conversation also mentions that Fick's Law is empirical and cannot be derived.
  • #1
yosimba2000
206
9
How do you derive it? I'm looking for the form J = -D(dC/dX)

From the image, I am assuming left side is of higher concentration. N represents the number of molecules.

My work:

Mass balance
Net molecules in from concentration gradient =
Net = N(x) - N(x+Delta X)

Net concentration in = molecule/volume
= [N(x) - N(x+delta x)] / (A * Delta X)
= dC

And then I'm stuck! I probably went about this totally wrong.
 

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  • #2
There is no derivation of Fick's Law. It's empirical (from observations). The flux of a species is proportional to the concentration gradient.

Chet
 
  • #3
The best you can get is a physical statement of Fick's law and its translation to mathematical terms. Check out the first pages of section 17.1 of Transport Phenomena by BSL.
 

1. What is Fick's First Law Derivation?

Fick's First Law Derivation is a mathematical equation that describes the diffusion of a substance through a medium. It is used to calculate the rate of diffusion based on the concentration gradient, the diffusion coefficient, and the distance traveled.

2. Who is Fick and why is this law named after him?

Fick's First Law is named after Adolf Fick, a German physiologist who first derived the equation in 1855. He was studying the process of gas exchange in the lungs and applied his understanding of diffusion to develop this law.

3. What is the equation for Fick's First Law Derivation?

The equation for Fick's First Law Derivation is: J = -D * (dC/dx), where J is the flux or rate of diffusion, D is the diffusion coefficient, and dC/dx is the concentration gradient. This equation can be used for both one-dimensional and three-dimensional systems.

4. How is Fick's First Law Derivation used in scientific research?

Fick's First Law Derivation is commonly used in scientific research to study the diffusion of substances in various systems, such as in biological tissues, polymers, and gases. It is also used in practical applications, such as in drug delivery systems and in the development of new materials.

5. What are the limitations of Fick's First Law Derivation?

Fick's First Law Derivation assumes that the system is in a steady state and that the diffusion coefficient is constant. However, in real-world situations, these assumptions may not hold true, leading to inaccuracies in the calculated diffusion rate. Additionally, the law does not account for other factors that may affect diffusion, such as temperature and pressure.

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