Diffusion flux from diffusion coefficient and concentration gradient

Fick’s first law relates the diffusion flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or, in simplistic terms, the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. The minus sign in the law indicates that the directions of the diffusion flow and the gradient are opposite: the gas diffuses towards a lower concentration, and the gradient is directed towards a higher concentration.

Conditions:

1. The mixture is ideal.

Links:

1. Wikipedia, first formula.

position

position of particles.

Symbol:

x

Latex:

\(x\)

Dimension:

length

diffusion_flux

diffusion_flux as a function of position.

Symbol:

J(x)

Latex:

\(J{\left(x \right)}\)

Dimension:

amount_of_substance/(area*time)

diffusion_coefficient

diffusion_coefficient.

Symbol:

D

Latex:

\(D\)

Dimension:

area/time

concentration

molar_concentration of particles as a function of position.

Symbol:

c(x)

Latex:

\(c{\left(x \right)}\)

Dimension:

amount_of_substance/volume

law

J(x) = -D * Derivative(c(x), x)

Latex:

\[J{\left(x \right)} = - D \frac{d}{d x} c{\left(x \right)}\]