{"term":{"id":"04540","doi":"10.1351\/goldbook.P04540","code":"P04540","status":"current","longtitle":"IUPAC Gold Book - phenomenological equation","title":"phenomenological equation","termversion":"2.3.3","lastupdated":"2014-02-24","definitions":[{"id":"1","text":"In the following only media which are isotropic with respect to mass transport (i.e. the transport coefficients are independent of direction) are being considered. In the linear range (not too far from equilibrium), for uniform temperature and neglecting external fields such as the earth's gravitational field, the flux density of species B is related to the gradients of the electrochemical potentials of all species by the phenomenological equation: N B- c B v A =- ∑ i i ≠ A L B is the gradient of the electrochemical potential of species i. The proportionality factors LBiA are called phenomenological coefficients. Their values depend on the frame of reference. The latter is taken here to move with the velocity v A of species A, and hence: .","links":[{"title":"isotropic","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/I03353"},{"title":"linear range","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/L03558"},{"title":"gradient","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/G02669"},{"title":"electrochemical potential","type":"goldify","url":"https:\/\/goldbook.iupac.org\/terms\/view\/E01945"}],"math":[{"alttext":"N B- c B v A =- ∑ i i ≠ A L B ","latex":"N_{\\text{B}}- c_{\\text{B}}\\ v_{\\text{A}}=- \\sum _{\\begin{array}{c}\ni\\\\\ni\\neq A\n\\end{array}}L_{\\text{B}i}^{\\text{A}}\\ \\nabla \\mu _{i}"},{"type":"math","alttext":"i = B, C, ...","latex":"i=\\text{B},\\text{C},..."},{"type":"quantity","alttext":"∇µi","latex":"\\nabla \\mu _{i}"},{"meaning":"Phenomenogical coefficient","type":"symbol","alttext":"LBiA","latex":"L_{\\text{B}i}^{\\text{A}}"},{"alttext":"v A","latex":"v_{\\text{A}}"},{"meaning":"Phenomenogical coefficient","type":"math","alttext":"LAiA = 0","latex":"L_{\\text{A}i}^{\\text{A}}=0"}],"sources":["PAC, 1981, 53, 1827. 'Nomenclature for transport phenomena in electrolytic systems' on page 1830 (https:\/\/doi.org\/10.1351\/pac198153101827)"]}],"referencedin":[{"title":"Wikipedia - Феноменологічне рівняння кінетики (uk)","url":"https:\/\/uk.wikipedia.org\/wiki\/Феноменологічне_рівняння_кінетики"}],"links":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/P04540\/html","json":"https:\/\/goldbook.iupac.org\/terms\/view\/P04540\/json","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/P04540\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/P04540\/plain","pdf":"https:\/\/goldbook.iupac.org\/terms\/view\/P04540\/pdf"},"citation":"Citation: 'phenomenological equation' in IUPAC Compendium of Chemical Terminology, 3rd ed. International Union of Pure and Applied Chemistry; 2006. Online version 3.0.1, 2019. 10.1351\/goldbook.P04540","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2024-07-17T23:24:08+00:00"}}