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Fick's Law
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The particle flow is proportional to the difference in concentration by distance, in other words to the concentration gradient. The proportionality constant, which we call constant diffusion, depends on particle parameters, their displacement and temperature.

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Concept of Diffusion
Definition

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Mechanisms
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Model
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Fick's Law
Description

The particle flow is proportional to the difference in concentration by distance, in other words to the concentration gradient. The proportionality constant, which we call constant diffusion, depends on particle parameters, their displacement and temperature.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$\bar{v}$
v
Average speed of a particle
m/s
$c_1$
c_1
Concentration 1
mol/m^3
$c_2$
c_2
Concentration 2
mol/m^3
$dc_n$
dc_n
Concentration variation
mol/m^3
$D$
D
Diffusion Constant
m/s^2
$dx$
dx
Distancia de Posiciones
m
$l_r$
l_r
Free Path in Function of the Radio and Particle Concentration
m
$\Delta c$
Dc
Molar concentration difference
mol/m^3
$j$
j
Particle flux density
1/m^2s

Calculations

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Symbol
Equation
Solved
Translated

Calculations

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Equation
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Equations

Examples

The difference in concentration $c_1$ and $c_2$ at the ends of the membrane results in the difference:

$dc=c_2-c_1$

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The diffusion constant $D$ can be calculated from the average velocity $\bar{v}$ and the mean free path $\bar{l}$ of the particles.

$ D =\displaystyle\frac{1}{3} \bar{v} \bar{l} $



It is important to recognize that both the mean free path and the average velocity depend on temperature, and consequently, so does the diffusion constant. Therefore, when values for the so-called constant are published, the temperature to which it applies is always specified.

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Calculating the particle flux density ($j$) in one dimension involves utilizing the values the diffusion Constant ($D$), the particle concentration ($c_n$), and the position along an axis ($z$), as dictated by Fick's law [1]::

$ j =- D \displaystyle\frac{ dc_n }{ dz }$



This formula can be generalized for more than one dimension as follows:

$ \vec{j} =- D \nabla c_n $

[1] " ber Diffusion" (On Diffusion), Adolf Fick, Annalen der Physik und Chemie, Volume 170, pages 59-86 (1855)

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In 1855, Adolf Fick [1] formulated an equation for the calculation of the diffusion Constant ($D$), resulting in the particle flux density ($j$) due to the concentration variation ($dc_n$) along ERROR:10192,0:

$ j =- D \displaystyle\frac{ dc_n }{ dz }$

[1] " ber Diffusion" (On Diffusion), Adolf Fick, Annalen der Physik und Chemie, Volume 170, pages 59-86 (1855)

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