Encyclopedia of Membranes

2016 Edition
| Editors: Enrico Drioli, Lidietta Giorno

Fick’s Laws

  • Alessio Caravella
Reference work entry
DOI: https://doi.org/10.1007/978-3-662-44324-8_1738

Fick’s laws (first and second Fick’s laws). These two laws of diffusion were originally postulated by the medical doctor Adolf Eugen Fick (1829–1901) (from whom they take their name) by analogy with energy transfer in conduction and not by experiment (Fick 1855; Bird et al. 2002).

First Fick’s law. For a generic species A in a mixture, first Fick’s law is referred to as the constitutive equation for mass flux of A stating the proportionality between flux and mass gradient in a certain domain, which can be used in solid, liquid, and gas phase (Bird et al. 2002; Krishna and Taylor 1993). This relationship can be expressed both in term of mass (Eq. 1) and molar quantities (Eq. 2) as
$$ \underline {j_A}=-\rho {D}_A\nabla {w}_A $$
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  1. Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. Wiley, New YorkGoogle Scholar
  2. Fick A (1855) Ueber diffusion. Ann Phys 94:59–86CrossRefGoogle Scholar
  3. Krishna R, Taylor R (1993) Multicomponent mass transfer. Wiley, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.National Institute of Advanced Industrial Science and Technology – Research Institute for Innovation in Sustainable Chemistry, ISC-AISTTsukubaJapan