< u > Bottom :</ u > With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas, following Fick's laws.

Molecular diffusion is typically described mathematically using Fick's laws of diffusion.

* Fick's laws of diffusion

This smooth flow is described by Fick's laws.

Fick's work was inspired by the earlier experiments of Thomas Graham, which fell short of proposing the fundamental laws for which Fick would become famous.

When a diffusion process does not follow Fick's laws ( which does happen ), we refer to such processes as non-Fickian, in that they are exceptions that " prove " the importance of the general rules that Fick outlined in 1855.

* Fick's laws of diffusion

The transport equations for thermal energy ( Fourier's law ), mechanical momentum ( Newton's law for fluids ), and mass transfer ( Fick's laws of diffusion ) are similar

The diffusion capacity for oxygen is the proportionality factor relating the rate of oxygen uptake into the lung to the oxygen gradient between the capillary blood and the alveoli ( per Fick's laws of diffusion ).

< u > Bottom :</ u > With an enormous number of solute molecules, all apparent randomness is gone: The solute appears to move smoothly and systematically from areas of high concentration to those of low, in accordance with Fick's laws.

# REDIRECT Fick's laws of diffusion

# REDIRECT Fick's laws of diffusion

* Fick's laws of diffusion

See Fick's laws of diffusion.

# REDIRECT Fick's laws of diffusion

Example of chemical ( classical, Fick's, or Fickian ) diffusion of sodium chloride in water

Fick's second law predicts how diffusion causes the concentration to change with time:

For the case of diffusion in two or more dimensions Fick's Second Law becomes

If the diffusion coefficient is not a constant, but depends upon the coordinate and / or concentration, Fick's Second Law yields

The approach based on the Einstein's mobility and Teorell formula gives the following generalization of Fick's equation for the multicomponent diffusion of the perfect components:

It is notable that Fick's work primarily concerned diffusion in fluids, because at the time, diffusion in solids was not considered generally possible.

Today, Fick's Laws form the core of our understanding of diffusion in solids, liquids, and gases ( in the absence of bulk fluid motion in the latter two cases ).

In particular, fluctuating hydrodynamic equations include a Fick's flow term, with a given diffusion coefficient, along with

use diffusion equations obtained from Fick's law.

( Fick's law of diffusion )

As mentioned above, chemical molar flux of a component A in an isothermal, isobaric system is defined in Fick's law of diffusion as:

* Fick's law of diffusion

In realistic situations, chemists can describe diffusion as a deterministic macroscopic phenomenon ( see Fick's law s ), despite its underlying random nature.

Then Fick's first law ( one-dimensional case ) can be written as:

It can be derived from Fick's First law and the mass conservation in absence of any chemical reactions:

It can be shown that the Fick's law can be obtained from the Maxwell-Stefan equations

The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which assumes that the flux of the diffusing material in any part of the system is proportional to the local density gradient:

Dispersive mass flux is analogous to diffusion, and it can also be described using Fick's first law:

Fick's lens was large, unwieldy, and could only be worn for a couple of hours at a time.

LaRouche had asserted the outtakes could be used to impeach Fick's testimony.

Equations based on Fick's law have been commonly used to model transport processes in foods, neurons, biopolymers, pharmaceuticals, porous soils, population dynamics, nuclear materials, semiconductor doping process, etc.

The molecular transfer equations of Newton's law for fluid momentum at low Reynolds number ( Stokes flow ), Fourier's law for heat, and Fick's law for mass are very similar, since they are all linear approximations to transport of conserved quantities in a flow field.

It had been pointed out previously by J. J. Thomson in his series of lectures at Yale University in May 1903 that the dynamic equilibrium between the velocity generated by a concentration gradient given by Fick's law and the velocity due to the variation of the partial pressure caused when ions are set in motion " gives us a method of determining Avogadro's Constant which is independent of any hypothesis as to the shape or size of molecules, or of the way in which they act upon each other ".

Fick's first law relates the diffusive flux to the concentration under the assumption of steady state.

and, thus, receive the form of the Fick's equations as was stated above.

Fick's experiments ( modeled on Graham's ) dealt with measuring the concentrations and fluxes of salt, diffusing between two reservoirs through tubes of water.

Theory of all voltammetric methods is based on solutions of Fick's equation.

The Fick's law is limiting case of the Maxwell-Stefan equations, when the mixture is extremely dilute and every chemical species is interacting only with the bulk mixture and not with other species.

Fick's first law is also important in radiation transfer equations.

evolves following Fick's law.

approach, the zero order approximation is Fick's law.

* Fick's equations, Boltzmann's transformation, etc.

Fick's Second Law.

( Either an alternate form of Fick's law that includes the molecular mass, or an alternate form of Darcy's law that includes the density.