Lewis number Le dimensionless ratio of thermal diffusivity to mass diffusivity in simultaneous heat and mass transfer: Le = alpha / D. alpha thermal diffusivity m^2/s (air 25°C 2.2e-5; water 1.4e-7); D mass diffusivity Fickian m^2/s (water vapor-air 25°C 2.6e-5; CO2-air 1.6e-5; oxygen-water 2e-9; salt-water 1.5e-9). Equivalent Le = Sc/Pr Schmidt over Prandtl.

Regimes: Le<0.5 mass diffusion fast unitary Lewis fail + premixed flame cellular instability Le<<1; 0.5<Le<1.5 unitary Lewis heat=mass air-water vapor Le=0.85 + heat-mass transfer Chilton-Colburn analogy + cooling tower wet-bulb; 1.5<Le<10 mass slow drying agro-food + thermal evaporation; 10<Le<100 strong limit premixed combustion lean Le>1 + heavy hydrocarbons; Le>100 mass dominated liquids slow + dissolved gases water + molten salts.

Related numbers: Prandtl Pr = nu/alpha; Schmidt Sc = nu/D; Stanton St = h/(rho*cp*v); Sherwood Sh = h_m*L/D; Nusselt Nu = h*L/k.

Chilton-Colburn analogy: j_H = j_M = St*Pr^(2/3) + heat-mass analogy + valid Le~1 + cooling tower + dryer + spray.

Wet-bulb temperature: psychrometric chart + Lewis relation k_H/k_M = rho*cp + cooling tower industrial. History: Warren Kendall Lewis (Laurel DE USA 1882 - Boston MA 1975) MIT + Princeton AB chemistry 1905 + MIT MS 1908 + Universitat Breslau Germany PhD 1908 + MIT Department Chemical Engineering professor 1910-1948 + Department head 1920-1929 + AIChE president 1924 + George Westinghouse Professor 1933-1948 + Founders Award 1947; 1922 founding paper Mech Eng 44:445 'The evaporation of a liquid into a gas' Lewis number eponym + Lewis relation + cooling tower analogy; 1923 textbook with Walker-Lewis-McAdams 'Principles of Chemical Engineering' McGraw-Hill classic + Lewis acid theory 1923 + Lewis-Randall rule 1923.

Edwin R Gilliland (Indianapolis IN 1909 - Cambridge MA 1973) MIT 1936-1973 + Manhattan Project + Gilliland correlation distillation.

Adolf Eugen Fick (Kassel Germany 1829-1901) Marburg + Wurzburg; 1855 paper Annalen Physik 94:59 'Uber Diffusion' Fick's first and second laws + diffusion classic + Fick principle cardiac output 1870.

Joseph Fourier (Auxerre France 1768-1830); 1822 'Theorie analytique de la chaleur' heat conduction + Fourier series.

Allan P Colburn (Madison WI 1904-1955) University Delaware + DuPont; 1934 Trans AIChE 26:174 j-factor analogy.

Thomas H Chilton (Wilmington DE 1899-1972) DuPont; 1934 paper Ind Eng Chem 26:1183 'Mass transfer absorption coefficients' Chilton-Colburn j-factor analogy. Legacy: Bird-Stewart-Lightfoot 'Transport Phenomena' 2nd ed 2007 Wiley 905 pages classic chemical engineering + Welty-Wilson-Wicks-Rorrer 6th ed 2014 + Cussler 'Diffusion Mass Transfer' 3rd ed 2009 Cambridge + Treybal 'Mass Transfer Operations' 3rd ed 1980 McGraw-Hill classic.

USA research heat-mass transfer + HVAC + drying: NIST Gaithersburg MD 1901 3500 heat transfer + ASHRAE collaboration + Standard Reference Data; NREL National Renewable Energy Laboratory Golden CO 1977 2900 CSP + thermal storage + buildings + cooling tower; ORNL Oak Ridge TN 1943 6500 nuclear thermal hydraulics + HFIR + ATR + cooling tower; Sandia Albuquerque NM 1949 14000 Combustion Research Facility CRF + premixed flame + Lewis cellular instability; LBNL Berkeley CA 1931 4400 Building Technology + Mary Ann Piette HVAC; PNNL Richland WA 1965 4500; Argonne IL 1946 3400; EPRI Palo Alto CA 1972 600; ASHRAE Atlanta GA 1894 56000 members standards 90.1 + 62.1 + 55 thermal comfort + Standard 64 + Handbook Fundamentals 2017.

USA universities heat-mass transfer: MIT Cambridge MA 1861 11700 + Mech Eng + ChemE Lewis school + Bergman-Lavine textbook; Stanford CA 1885 17000 + Mech Eng + ChemE; Caltech Pasadena 1891 2400 + GALCIT + Bejan textbook author Adrian Bejan; UC Berkeley 1868 45000 + ChemE Cussler protégé + Van Carey free convection; Princeton NJ 1746 8000 + MAE + ChemE Howard Stone microfluidics + Sankaran Sundaresan; Cornell Ithaca NY 1865 25000 + ChemE; Georgia Tech Atlanta 1885 36000 + ChemE; UIUC Urbana 1867 56000 + ChemE; Penn State 1855 50000 + ChemE; UT Austin TX 1883 51000; Univ Michigan Ann Arbor 1817 50000 + ChemE; Purdue West Lafayette IN 1869 47000 + ChemE; Univ Wisconsin-Madison 1848 49000 + ChemE Bird-Stewart-Lightfoot legacy + Edwin Lightfoot; Univ Minnesota Twin Cities 1851 51000 + ChemE Bird school; Univ Delaware Newark 1743 24000 Colburn legacy ChemE + Allan P Colburn lab; UCLA 1919 45000; UC Davis 1908 40000 Drying Olive Oil.

USA HVAC industry: Carrier Global Palm Beach Gardens FL 1915 53000 commercial HVAC chillers cooling tower; Trane Technologies Davidson NC 2020 39000 chillers RTU; Lennox Richardson TX 1895 10000; Daikin Applied Plymouth MN 12000; Johnson Controls York PA 1885 105000 York chillers; SPX Cooling Technologies Overland Park KS 4000 cooling tower Marley Class 200 + cooling tower industrial; Baltimore Aircoil BAC Jessup MD 1938 1000 cooling tower industrial counterflow crossflow; Evapco Taneytown MD 1976 4000 cooling tower closed circuit; Rheem Atlanta GA 1925 4000 water heaters; AO Smith Milwaukee 12000.

USA spray drying food + dairy + coffee: Niro USA Hudson WI (now SPX FLOW) 200 spray dryer industrial; GEA Niro Group German DK origin 4000 worldwide; Anhydro SPX FLOW Soeborg DK 200; BUCHI Switzerland 800 lab spray dryer; Nestle USA Solon OH 47000 + coffee instant Nescafe spray dry; Kraft Heinz Pittsburgh PA 38000; General Mills Minneapolis MN 1928 35000; Kellogg's Battle Creek MI 1906 31000 + cereal spray drying; PepsiCo Purchase NY 318000; Coca-Cola Atlanta GA 79000.

USA cooling tower power plant + nuclear + petrochemicals: Duke Energy Charlotte NC 1900 28000; NextEra Energy Juno Beach FL 14000; Southern Company Atlanta GA 1945 28000 + Vogtle nuclear + cooling tower; Westinghouse Cranberry Township PA 1886 9500 AP1000 nuclear + passive cooling; GE Power Schenectady NY 30000 + gas turbines combined cycle + cooling tower; Babcock&Wilcox Akron OH 1867 5300; ExxonMobil Irving TX 1882 62000 + refineries cooling tower; Chevron San Ramon CA 1879 45000.

USA pharmaceutical spray drying lyophilization: Pfizer NY 1849 80000; Merck Kenilworth NJ 1891 73000; Johnson&Johnson NJ 1886 152000; Eli Lilly Indianapolis IN 1876 39000; AbbVie Lake Bluff IL 50000; Bristol-Myers Squibb NY 33000; Amgen Thousand Oaks CA 24000; Gilead Foster City CA 16000.

USA combustion premixed flame: GE Aerospace Cincinnati OH 1892 50000 + jet engine premixed combustion; Pratt&Whitney East Hartford CT 1925 38000; Honeywell Aerospace Phoenix AZ 23000; RTX Raytheon Technologies Waltham MA 174000; Boeing Arlington VA 1916 156000; Lockheed Martin Bethesda MD 1995 116000; Northrop Grumman Falls Church VA 1939 102000.

Lewis formula

Definition: Le = alpha / D. Equivalent Le = Sc/Pr.

Typical coefficients: air 25°C alpha=2.2e-5, water vapor-air D=2.6e-5, Le=0.85; air-CO2 Le=1.36; air-He Le=0.31; water-salt D=1.5e-9 alpha=1.4e-7 Le=93; methane-air combustion Le=1.1; hydrogen-air Le=0.31.

Chilton-Colburn analogy: j_H = j_M 1934 + valid Le~1 + cooling tower + ASHRAE.

Wet-bulb temperature: psychrometric chart + Lewis relation k_H/k_M = rho*cp + cooling tower industrial 1922.

History and context

Warren Kendall Lewis (Laurel DE USA 1882 - Boston MA 1975) MIT Cambridge MA + Princeton AB chemistry 1905 + MIT MS chemical engineering 1908 + Universitat Breslau Germany PhD 1908 + MIT Department Chemical Engineering professor 1910-1948 + Department head 1920-1929 + George Westinghouse Professor 1933-1948 founding father chemical engineering education in USA + AIChE American Institute Chemical Engineers president 1924 + Founders Award 1947; 1922 founding paper Mech Eng 44:445 'The evaporation of a liquid into a gas' simultaneous heat and mass transfer + Lewis number eponym + Lewis relation + cooling tower; 1923 textbook Walker-Lewis-McAdams 'Principles of Chemical Engineering' McGraw-Hill classic + 1937 2nd ed + 1955 3rd ed Gilliland; Lewis acid theory 1923 + Lewis structure dot diagrams + Lewis-Randall rule 1923 fugacity. Edwin Gilliland MIT + Manhattan Project. Adolf Fick (Kassel Germany 1829-1901) + 1855 'Uber Diffusion' Fick's laws + Fick principle cardiac output 1870. Joseph Fourier (Auxerre 1768-1830) + 1822 'Theorie analytique chaleur' heat conduction. Allan Colburn (Madison WI 1904-1955) Delaware + DuPont. Thomas Chilton (Wilmington DE 1899-1972) DuPont + 1934 Ind Eng Chem 26:1183 j-factor analogy. Legacy: Bird-Stewart-Lightfoot 'Transport Phenomena' 2nd ed 2007 Wiley + Cussler 'Diffusion' 3rd ed 2009 Cambridge + Treybal 'Mass Transfer' 3rd ed 1980.

USA research heat-mass: NIST Gaithersburg 3500 ASHRAE + Reference Data; NREL Golden 2900 CSP cooling tower; ORNL 6500 nuclear thermal HFIR ATR; Sandia CRF 14000 premixed flame Lewis cellular; LBNL Berkeley 4400 Building Tech Piette HVAC; EPRI 600; ASHRAE Atlanta 56000 standards 90.1 62.1 55.

USA universities: MIT 11700 ChemE Lewis school; Stanford 17000; UC Berkeley 45000 Cussler ChemE; Princeton 8000 Stone ChemE microfluidics; Cornell 25000; Georgia Tech 36000; UIUC 56000; Penn State 50000; Michigan 50000 ChemE; Purdue 47000; Wisconsin-Madison 49000 ChemE Bird-Stewart-Lightfoot legacy; Minnesota 51000 ChemE; Delaware 24000 Colburn legacy ChemE; UCLA 45000; UC Davis 40000.

USA HVAC industry: Carrier Palm Beach Gardens 53000 chillers cooling tower; Trane Davidson 39000; Lennox 10000; Johnson Controls 105000 York chillers; SPX Cooling Marley Overland Park KS 4000 cooling tower; Baltimore Aircoil BAC Jessup MD 1000 cooling tower; Evapco Taneytown MD 4000; Rheem Atlanta 4000; AO Smith 12000.

USA spray drying food: GEA Niro 4000; SPX FLOW Anhydro 200; Nestle USA Solon 47000 Nescafe; Kraft Heinz 38000; General Mills 35000; Kellogg's 31000 cereal; PepsiCo 318000; Coca-Cola 79000.

USA cooling tower power: Duke Energy Charlotte 28000; NextEra 14000; Southern Atlanta 28000 Vogtle nuclear; Westinghouse 9500 AP1000 passive; GE Power Schenectady 30000; Babcock&Wilcox Akron 5300; ExxonMobil Irving TX 62000 refineries; Chevron 45000.

USA pharma: Pfizer 80000; Merck 73000; JNJ 152000; Lilly 39000; AbbVie 50000; BMS 33000; Amgen 24000; Gilead 16000.

USA combustion: GE Aerospace 50000; Pratt&Whitney 38000; Honeywell Aerospace 23000; RTX 174000; Boeing 156000; Lockheed Martin 116000; Northrop Grumman 102000.

Lewis values table

• Le = alpha/D: definition
• Le = Sc/Pr: equivalent
• Le<0.5 mass fast: H2 He light
• 0.5<Le<1.5 unitary: air-water vapor 0.85
• 1.5<Le<10 mass slow: drying
• 10<Le<100 strong limit: combustion lean
• Le>100 mass dominated: liquids
• Air-vapor Le=0.85: cooling tower
• Air-CO2 Le=1.36
• Air-He Le=0.31
• Water-salt Le=93
• Methane Le=1.1: combustion
• Hydrogen Le=0.31: cellular flame
• Drying Le~1400: agro-food
• Lewis MIT 1882-1975: 1922 Mech Eng 44:445
• Fick Germany 1855: diffusion law
• Fourier 1822: heat conduction
• Chilton-Colburn 1934: j_H=j_M
• Bird-Stewart-Lightfoot 2007: classic textbook
• USA NIST 3500
• USA Carrier 53000
• USA SPX Cooling Marley 4000
• USA BAC Baltimore Aircoil 1000
• USA Nestle Nescafe 47000
• USA Pfizer 80000
• USA GE Aerospace 50000

Numerical examples

Example 1 - Air-water vapor cooling tower. alpha=2.2e-5, D=2.6e-5. Le=0.85 unitary. USA: Carrier 53000 + Trane 39000 + SPX Marley + BAC + ASHRAE Handbook.

Example 2 - Air-CO2 carbon capture. Le=1.31. USA: ExxonMobil + Chevron + DOE CCS programs.

Example 3 - Water-salt desalination. Le=93. USA: Carlsbad CA desalination + Tampa Bay FL + Israel partnerships.

Example 4 - Methane combustion premixed. Le=1.1. USA: GE Aerospace + Pratt&Whitney + Sandia CRF Livermore.

Example 5 - Apple drying agro-food. Le=1400. USA: Nestle Nescafe Solon + Kellogg's cereal + General Mills.

Limits and considerations

1. Le function of T composition: Le varies with T multicomponent.
2. Multicomponent: 3+ species + Maxwell-Stefan diffusion + Onsager reciprocity.
3. Non-Fickian diffusion: anomalous + porous + zeolites + membranes.
4. Soret effect: thermal diffusion thermophoresis + Soret coefficient.
5. Dufour effect: concentration gradient generates heat flux + Onsager.
6. Knudsen regime: low pressure + Knudsen diffusion + nanopore.
7. Reaction-diffusion: chemical reaction + Damkohler + Le coupling combustion.
8. Turbulent transport: Le_t turbulent often Le_t~1.
9. High pressure: real gas + supercritical + Lewis varies.
10. Non-equilibrium thermodynamics: cross-coupling Onsager.

Common errors

Confusing Le and Pr: Le = alpha/D mass; Pr = nu/alpha thermal.

Le=Sc/Pr: fundamental relation.

Lewis unitary fail: Le~1 only air-water vapor + others diverge + premixed flame Le<<1 cellular.

Chilton-Colburn analogy: j_H=j_M valid Le~1 + extension Le^(1-n).

Unit consistency: alpha + D both m^2/s + not cm^2/s.

Practical applications

1. HVAC cooling tower psychrometric: USA Carrier 53000 + Trane 39000 + Lennox 10000 + Johnson Controls 105000 + SPX Marley 4000 + BAC 1000 + Evapco 4000 + ASHRAE.
2. Air conditioning psychrometric chart wet-bulb: USA ASHRAE Atlanta 56000 + NIST + ORNL Building + LBNL Piette Building Tech.
3. Cooling tower power plant nuclear: USA Duke Energy 28000 + NextEra 14000 + Southern Vogtle nuclear + Westinghouse AP1000 + GE Power Schenectady + Babcock&Wilcox.
4. Spray drying food milk coffee: USA Nestle Solon Nescafe 47000 + Kraft Heinz 38000 + General Mills 35000 + Kellogg's cereal 31000 + PepsiCo + Coca-Cola.
5. Industrial dryers food drying: USA GEA Niro 4000 + SPX FLOW Anhydro + Bowen + APV.
6. Petroleum refinery cooling tower: USA ExxonMobil 62000 + Chevron 45000 + Marathon Petroleum + Phillips 66 + Valero.
7. Pharmaceutical spray drying lyophilization: USA Pfizer 80000 + Merck 73000 + JNJ 152000 + Lilly 39000 + AbbVie 50000 + BMS 33000 + Amgen 24000.
8. Combustion premixed lean burner gas turbine: USA GE Aerospace 50000 + Pratt&Whitney 38000 + Honeywell Aerospace + Sandia CRF Livermore premixed flame Lewis cellular.
9. Carbon capture CO2 scrubbing: USA ExxonMobil + Chevron + DOE CCS programs + Petra Nova + Boundary Dam Canada partnership.
10. Desalination thermal MED MSF + reverse osmosis: USA Carlsbad CA + Tampa Bay FL + IDE Tech + Aqua Tech.

Updated July 2026