Editing Fick's laws of diffusion (section)

=== Biological perspective ===
The first law gives rise to the following formula:<ref>{{cite book| title= Essentials of Human Physiology|  vauthors = Nosek TM | chapter=Section 3/3ch9/s3ch9_2 |chapter-url=http://humanphysiology.tuars.com/program/section3/3ch9/s3ch9_2.htm |archive-url=https://web.archive.org/web/20160324124828/http://humanphysiology.tuars.com/program/section3/3ch9/s3ch9_2.htm|archive-date=2016-03-24}}</ref>
: <math>\text{flux} = {-P \left(c_2 - c_1\right)} , </math>
where
* {{mvar|P}} is the permeability, an experimentally determined membrane "[[Electrical conductance|conductance]]" for a given gas at a given temperature,
* {{math|''c''<sub>2</sub> − ''c''<sub>1</sub>}} is the difference in [[concentration]] of the gas across the [[Artificial membrane|membrane]] for the direction of flow (from {{math|''c''<sub>1</sub>}} to {{math|''c''<sub>2</sub>}}).

Fick's first law is also important in radiation transfer equations.  However, in this context, it becomes inaccurate when the diffusion constant is low and the radiation becomes limited by the speed of light rather than by the resistance of the material the radiation is flowing through.  In this situation, one can use a [[flux limiter]].

The exchange rate of a gas across a fluid membrane can be determined by using this law together with [[Graham's law]].

Under the condition of a diluted solution when diffusion takes control, the membrane permeability mentioned in the above section can be theoretically calculated for the solute using the equation mentioned in the last section (use with particular care because the equation is derived for dense solutes, while biological molecules are not denser than water. Also, this equation assumes ideal concentration gradient forms near the membrane and evolves):<ref name = "Pyle-BJNano" />
: <math> P= 2A_p\eta_{tm} \sqrt{ \frac{D}{\pi t}} , </math>
where:
* <math>A_P</math> is the total area of the pores on the membrane (unit m<sup>2</sup>),
* <math>\eta_{tm}</math> transmembrane efficiency (unitless), which can be calculated from the stochastic theory of [[chromatography]],
* ''D'' is the diffusion constant of the solute unit m<sup>2</sup>⋅s<sup>−1</sup>,
* ''t'' is time unit s,
* ''c''<sub>2</sub>, ''c''<sub>1</sub> concentration should use unit mol m<sup>−3</sup>, so flux unit becomes mol s<sup>−1</sup>.

The flux is decay over the square root of time because a concentration gradient builds up near the membrane over time under ideal conditions. When there is flow and convection, the flux can be significantly different than the equation predicts and show an effective time t with a fixed value,<ref name=JixinMCSimuAdsorption/> which makes the flux stable instead of decay over time. A critical time has been estimated under idealized flow conditions when there is no gradient formed.<ref name=JixinMCSimuAdsorption/><ref name=JChen2022JPCA/> This strategy is adopted in biology such as blood circulation.