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Encyclopedia > Fick's law

Fick's laws of diffusion describe diffusion. Diffusion is the spontaneous spreading of something such as particles, heat, or momentum. ...

Contents

History

Fick's laws of diffusion were derived by Adolf Fick in the year 1858. Adolf Eugen Fick (1829-1901) was a German physiologist and inventor. ... 1858 is a common year starting on Friday. ...


Fick's 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 (Jin=Jout). Diffusion is the spontaneous spreading of something such as particles, heat, or momentum. ...


J = - D frac{partial c}{partial x}


Where

  • J is the diffusion flux in dimensions of [parts length-2 time-1]
  • D is the diffusion coefficient in dimensions of [length2 time-1]
  • c is the concentration in dimensions of [parts length-3]
  • x is the position

Fick's Second Law

Fick's Second Law is used in non-steady state diffusion, i.e., when the concentration within the diffusion volume changes with respect to time.


frac{partial c}{partial t} = D frac{partial^2 c}{partial x^2}


Where

  • c is the concentration in dimensions of [parts length-3]
  • t is time
  • D is the diffusion coefficient in dimensions of [length2 time-1]
  • x is the position

A Biological Perspective

The first law gives rise to the formula

mathrm{Rate of diffusion} = frac{K A (P_2 - P_1)}{D}

It states that the rate of diffusion of a gas across a membrane is

  • Constant for a given gas at a given temperature by an experimentally determined factor, K
  • Proportional to the surface area over which diffusion is taking place, A
  • Proportional to the difference in partial pressures of the gas across the membrane, P2P1
  • Inversely proportional to the distance over which diffusion must take place, or in other words the thickness of the membrane, D.

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. Approximately, the partial pressure of a gas in atmospheres in a mixture or solution is what would be the pressure of that gas if all other components of the mixture or solution suddenly vanished without its temperature changing. ... This article or section should include material from Net flux A membrane is a thin, typically planar structure or material that separates two environments. ...


The exchange rate of a gas across a fluid membrane can be determined by using this law together with Graham's law. One of the gas laws, Grahams law states that the average kinetic energy of the molecules of two samples of different gases at the same temperature is identical. ...


See also

Gas exchange or respiration takes place at a respiratory surface - a boundary between the external environment and the interior of the body. ... The heart in relation to the lungs (from an older edition of Grays Anatomy) This x-ray of the human chest shows the lungs as dark regions The lung is an organ belonging to the respiratory system and interfacing to the circulatory system of air-breathing vertebrates. ... The alveoli (singular:alveolus), tiny hollow sacs which are continuous with the airways, are the sites of gas exchange with the blood. ...

References

  • W.F. Smith, Foundations of Materials Science and Engieering 3rd ed., McGraw-Hill (2004)

 

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