Editing Fick's laws of diffusion (section)

=== Variations of the first law ===

Another form for the first law is to write it with the primary variable as [[Mass fraction (chemistry)|mass fraction]] ({{mvar|y<sub>i</sub>}}, given for example in kg/kg), then the equation changes to
: <math>\mathbf{J}_i = -\frac{\rho D}{M_i}\nabla y_i , </math>
where
* the index {{mvar|i}} denotes the {{mvar|i}}<sup>th</sup> species,
* {{math|'''J'''<sub>''i''</sub>}} is the '''diffusion flux''' of the {{mvar|i}}<sup>th</sup> species (for example in mol/m<sup>2</sup>/s),
* {{math|''M''<sub>''i''</sub>}} is the [[molar mass]] of the {{mvar|i}}<sup>th</sup> species,
* {{mvar|ρ}} is the mixture [[density]] (for example in kg/m<sup>3</sup>).

The <math>\rho</math> is outside the [[gradient]] operator. This is because
: <math>y_i = \frac{\rho_{si}}{\rho} , </math>
where {{mvar|ρ<sub>si</sub>}} is the partial density of the {{mvar|i}}th species.

Beyond this, in chemical systems other than ideal solutions or mixtures, the driving force for the diffusion of each species is the gradient of [[chemical potential]] of this species. Then Fick's first law (one-dimensional case) can be written
: <math>J_i = - \frac{D c_i}{RT} \frac{\partial \mu_i}{\partial x} , </math>
where
* the index {{mvar|i}} denotes the {{mvar|i}}<sup>th</sup> species,
* {{mvar|c}} is the concentration (mol/m<sup>3</sup>),
* {{mvar|R}} is the [[universal gas constant]] (J/K/mol),
* {{mvar|T}} is the absolute temperature (K),
* {{mvar|μ}} is the chemical potential (J/mol).

The driving force of Fick's law can be expressed as a [[fugacity]] difference:
: <math>J_i = - \frac{D}{RT} \frac{\partial f_i}{\partial x} , </math>

where <math> f_i </math> is the fugacity in Pa. <math> f_i </math> is a partial pressure of component {{math|''i''}} in a vapor <math> f_i^\text{G} </math> or liquid <math> f_i^\text{L} </math> phase. At vapor liquid equilibrium the evaporation flux is zero because <math> f_i^\text{G} = f_i^\text{L} </math>.