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For the technique of measuring cardiac output, see Fick principle.
Fick's laws of diffusion describe diffusion and can be used to solve for the diffusion coefficient D. They were derived by Adolf Fick in the year 1855.

First law

Fick's first law is used in steady-state diffusion, i.e., when the concentration within the diffusion volume does not change with respect to time . In one (spatial) dimension, this is

where
  • is the diffusion flux in dimensions of [(amount of substance) length−2 time-1], example
  • is the diffusion coefficient or diffusivity in dimensions of [length2 time−1], example
  • is the concentration in dimensions of [(amount of substance) length−3], example
  • is the position [length], example
is proportional to the velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x10-9 to 2x10-9 m2/s. For biological molecules the diffusion coefficients normally range from 10-11 to 10-10 m2/s.

In two or more dimensions we must use , the del or gradient operator, which generalises the first derivative, obtaining

.

Second law

Fick's second law is used in non-steady or continually changing state diffusion, i.e., when the concentration within the diffusion volume changes with respect to time.



Where
  • is the concentration in dimensions of [(amount of substance) length-3], [mol m-3]
  • is time [s]
  • is the diffusion coefficient in dimensions of [length2 time-1], [m2 s-1]
  • is the position [length], [m]
It can be derived from the Fick's First law and the mass balance:



Assuming the diffusion coefficient D to be a constant we can exchange the orders of the differentiating and multiplying by the constant:

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

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

,

also called the heat equation.

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



An important example is the case where is at a steady state, i.e. the concentration does not change by time, so that the left part of the above equation is identically zero. In one dimension with constant , the solution for the concentration will be a linear change of concentrations along . In two or more dimensions we obtain



which is Laplace's equation, the solutions to which are called harmonic functions by mathematicians.

Applicability

Equations based on Fick's law have been commonly used to model transport processes in foods, neurons, biopolymers, pharmaceuticals, porous soils, population dynamics, semiconductor doping process, etc. A large amount of experimental research in polymer science and food science has shown that a more general approach is required to describe transport of components in materials undergoing glass transition. In the vicinity of glass transition the flow behavior becomes "non-Fickian". See also non-diagonal coupled transport processes (Onsager relationship).

Temperature dependence of the diffusion coefficient

The diffusion coefficient at different temperatures is often found to be well predicted by



where
  • is the diffusion coefficient
  • is the maximum diffusion coefficient (at infinite temperature)
  • is the activation energy for diffusion in dimensions of [energy (amount of substance)−1]
  • is the temperature in units of [absolute temperature] (kelvins or degrees Rankine)
  • is the gas constant in dimensions of [energy temperature−1 (amount of substance)−1]
An equation of this form is known as the Arrhenius equation.

Typically, a compound's diffusion coefficient is ~10,000x greater in air than in water. Carbon dioxide in air has a diffusion coefficient of 16 mm²/s, and in water, its coefficient is 0.0016 mm²/s [1].

Biological perspective

The first law gives rise to the following formula:[1]



It states that the rate of diffusion of a gas across a membrane is
  • is experimentally determined "conductivity" for a given gas at a given temperature.
  • is proportional to the surface area over which diffusion is taking place.
  • is proportional to the difference in partial pressures of the gas across the membrane.
  • is inversely proportional to the distance over which diffusion must take place, or in other words the thickness of the membrane.
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.

Semiconductor fabrication applications

IC Fabrication technologies, model processes like CVD, Thermal Oxidation, and Wet Oxidation, Doping etc using Diffusion equations obtained from Ficks law.

In certain cases, the solutions are obtained for boundary conditions such as constant source concentration diffusion, limited source concentration, or moving boundary diffusion (where junction depth keeps moving into the substrate).

See also

References

  • A. Fick, Phil. Mag. (1855), 10, 30.
  • A. Fick, Poggendorff's Annel. Physik. (1855), 94, 59.
  • W.F. Smith, Foundations of Materials Science and Engineering 3rd ed., McGraw-Hill (2004)
  • H.C. Berg, Random Walks in Biology, Princeton (1977)

External links

Cardiac output (CO) is the volume of blood being pumped by the heart, in particular by a ventricle in a minute.

Normal Output

Cardiac output is equal to the stroke volume (SV) multiplied by the heart rate (HR).
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Fick principle is a technique for measuring cardiac output.

Variables

The following variables are measured:[1]
  • VO2 consumption per minute using a spirometer (with the subject re-breathing air) and a CO2 absorber

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This article is about the physical mechanism of diffusion. For alternative meanings, see diffusion (disambiguation).


Diffusion is the net movement of particles from an area of high concentration to an area of low concentration.
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Adolf Eugen Fick (born 3 September, 1829, in Kassel, Germany; died 21 August, 1901, in Blankenberge, Flanders) was a German physiologist usually credited with the invention of contact lenses. He earned a 1851 doctorate at Marburg in medicine.
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18th century - 19th century - 20th century
1820s  1830s  1840s  - 1850s -  1860s  1870s  1880s
1852 1853 1854 - 1855 - 1856 1857 1858

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Subjects:     Archaeology - Architecture -
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This article is about the physical mechanism of diffusion. For alternative meanings, see diffusion (disambiguation).


Diffusion is the net movement of particles from an area of high concentration to an area of low concentration.
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The amount of substance, n, of a sample or system is a physical quantity which is proportional to the number of elementary entities present. "Elementary entities" may be atoms, molecules, ions, electrons, or particles, the choice of which is dependent upon context and must
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This is the diffusion coefficient in Fick's Law. It is a proportionality constant between the mass flux due to diffusion and the gradient in the concentration of the species.

It is generally prescribed for a given pair of species.
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Viscosity is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow.
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In physics (namely, in kinetic theory) the Einstein relation is a previously unexpected connection revealed by Einstein in his 1905 paper on Brownian motion:



linking D, the Diffusion constant, and μp
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In vector calculus, del is a vector differential operator represented by the nabla symbol: .

Del is a mathematical tool serving primarily as a convention for mathematical notation; it makes many equations easier to comprehend, write, and remember.
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gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.
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The heat equation is an important partial differential equation which describes the variation of temperature in a given region over time.

General-audience description

Suppose one has a function u which describes the temperature at a given location (x,
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In mathematics, Laplace's equation is a partial differential equation named after its discoverer, Pierre-Simon Laplace. The solutions of Laplace's equation are important in many fields of science, notably the fields of electromagnetism, astronomy, and fluid dynamics, because they
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harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplace's equation, i.e.

everywhere on U.
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Passive transport means moving biochemicals and other atomic or molecular substances across membranes. Unlike active transport, this process does not involve chemical energy.
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Food is any substance, usually composed primarily of carbohydrates, fats, water and/or proteins, that can be eaten or drunk by an animal or human being for nutrition or pleasure.
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Neurons (also known as neurones and nerve cells) are electrically excitable cells in the nervous system that process and transmit information. In vertebrate animals, neurons are the core components of the brain, spinal cord and peripheral nerves.
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Biopolymers are a class of polymers produced by living organisms. Starch, proteins and peptides, DNA, and RNA are all examples of biopolymers, in which the monomer units, respectively, are sugars, amino acids, and nucleic acids.
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Pharmacology is the study of how drugs interact with living organisms to produce a change in function.[1] If substances have medicinal properties, they are considered pharmaceuticals.
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Porosity is a measure of the void spaces in a material, and is measured as a fraction, between 0–1, or as a percentage between 0–100%. The term porosity is used in multiple fields including manufacturing, earth sciences and construction.
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SOiL is a five-piece Hard Rock band from Chicago, Illinois, United States. They formed in 1997 and are still active. They are signed to DRT Entertainment and have released four albums, their most recent being True Self which was released in March 27 2006.
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Population dynamics is the study of marginal and long-term changes in the numbers, individual weights and age composition of individuals in one or several populations, and biological and environmental processes influencing those changes.
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In semiconductor production, doping refers to the process of intentionally introducing impurities into an extremely pure (also referred to as intrinsic) semiconductor in order to change its electrical properties. The impurities are dependent upon the type of semiconductor.
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In the scientific method, an experiment (Latin: ex- periri, "of (or from) trying") is a set of observations performed in the context of solving a particular problem or question, to support or falsify a hypothesis or research concerning phenomena.
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polymer is a substance composed of molecules with large molecular mass composed of repeating structural units, or monomers, connected by covalent chemical bonds. The word is derived from the Greek, πολυ, polu, "many"; and μέρος, meros,
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Glass transition is a second order phase transition in which a supercooled melt yields, on cooling, a glassy structure and properties similar to those of crystalline materials e.g. of an isotropic solid material [1].
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Lars Onsager

Lars Onsager
Born November 27 1903(1903--)
Christiania, (Oslo), Norway
Died September 5 1976 (aged 74)
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activation energy to initiate combustion in this Bunsen burner. The blue flame will sustain itself after the sparks are extinguished because the continued combustion of the flame is now energetically favorable.
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The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. The Kelvin scale is a thermodynamic (absolute) temperature scale where absolute zero — the coldest possible temperature — is zero kelvins
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