Lewis number

{{short description|Ratio of thermal diffusivity to mass diffusivity}}

In fluid dynamics and thermodynamics, the Lewis number (denoted {{math|Le}}) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the thermal boundary layer in relation to the concentration boundary layer.{{Cite web|date=10 May 2020|title=Lewis number|url=https://www.tec-science.com/mechanics/gases-and-liquids/lewis-number/|access-date=25 June 2020|website=tec-science}} The Lewis number is defined as{{cite book |last1=Cohen |first1=E. Richard |last2=Cvitaš |first2=Tomislav |last3=Frey |first3=Jeremy G. |last4=Homström |first4=Bertil |last5=Kuchitsu |first5=Kozo |last6=Marquardt |first6=Roberto |last7=Mills |first7=Ian |last8=Pavese |first8=Franco |last9=Quack |first9=Martin |last10=Stohner |first10=Jürgen |last11=Strauss |first11=Herbert L. |last12=Takami |first12=Michio |last13=Thor |first13=Anders J. |author9-link=Martin Quack |author11-link=Herbert L. Strauss |author13-link=Anders Thor |title=Quantities, Units and Symbols in Physical Chemistry |date=2007 |publisher=IUPAC |page=82 |edition=3rd |url=http://iupac.org/wp-content/uploads/2019/05/IUPAC-GB3-2012-2ndPrinting-PDFsearchable.pdf}}

:$\backslash mathrm\{Le\}\; =\; \backslash frac\{\backslash alpha\}\{D\}\; =\; \backslash frac\{\backslash lambda\}\{\backslash rho\; D\_\{im\}\; c\_p\}$.

where:

• {{mvar|α}} is the thermal diffusivity,
• {{mvar|D}} is the mass diffusivity,
• {{mvar|λ}} is the thermal conductivity,
• {{mvar|ρ}} is the density,
• {{mvar|D{{sub|im}}}} is the mixture-averaged diffusion coefficient,
• {{mvar|c{{sub|p}}}} is the specific heat capacity at constant pressure.

In the field of fluid mechanics, many sources define the Lewis number to be the inverse of the above definition.{{Cite report |id=RTO-EN-AVT-162 |last1=Candler |first1=Graham V. |last2=Nompelis |first2=Ioannis |date=September 2009 |title=Computational Fluid Dynamics for Atmospheric Entry |url=https://apps.dtic.mil/sti/pdfs/ADA568031.pdf |publisher=Von Karman Institute |series=Von Karman Institute for Fluid Dynamics Lecture Series: Hypersonic Entry and Cruise Vehicles |language=en |via=Defence Technical Information Centre}}{{Cite book |last=White |first=Frank M. |title=Viscous fluid flow |date=1991 |publisher=McGraw-Hill |isbn=0-07-069712-4 |edition=2nd |location=New York |pages=31–34 |oclc=21874250}}

The Lewis number can also be expressed in terms of the Prandtl number ({{math|Pr}}) and the Schmidt number ({{math|Sc}}):{{Cite web |last=Guruge |first=Amila Ruwan |date=2022-02-10 |title=What is the Lewis Number |url=https://www.arhse.com/what-is-the-lewis-number/ |access-date=2022-12-20 |website=Chemical and Process Engineering |language=en-US}}

:$\backslash mathrm\{Le\}\; =\; \backslash frac\{\backslash mathrm\{Sc\}\}\{\backslash mathrm\{Pr\}\}$

It is named after Warren K. Lewis (1882–1975),{{cite journal |last1=Lewis |first1=W. K. |title=The Evaporation of a Liquid into a Gas |journal=Transactions of the American Society of Mechanical Engineers |date=1922 |volume=44 |issue=1849 |pages=325–340 |location=New York |doi=10.1115/1.4058175 |hdl=2027/mdp.39015023119749}}{{cite journal |last1=Klinkenberg |first1=A. |last2=Mooy |first2=H. H. |title=Dimensionless Groups in Fluid Friction, Heat, and Material Transfer |journal=Chemical Engineering Progress |date=1948 |volume=44 |issue=1 |pages=17–36}} who was the first head of the Chemical Engineering Department at MIT. Some workers in the field of combustion assume (incorrectly) that the Lewis number was named for Bernard Lewis (1899–1993), who for many years was a major figure in the field of combustion research.{{Citation needed|date=February 2024}}

== Relevance in biology ==

The Lewis number is large for water $(\backslash mathrm\{Le\}\; \backslash approx\; 90\; \backslash gg\; 1)$, and this is likely the reason why mammals do not have gills.{{cite web |title=The Lewis Number |url=http://hobbieroth.blogspot.com/2015/10/the-lewis-number.html |website=Intermediate physics for medicine and biology |access-date=22 September 2024}} In gills, oxygen is extracted from seawater into the mammal. Since the Lewis number for water is high, this means that during this diffusion process, a relatively large amount of heat would also be extracted from the animal, as heat diffuses faster than oxygen. This would cause the animal to cool down too much while breathing.