Lewis Number (Le): Thermal-to-Mass Diffusivity Ratio
The Lewis number (symbol Le) compares thermal diffusivity \u03b1 to mass diffusivity D via Le = \u03b1 / D. Because \u03b1 = k/(\u03c1 c\u209b) and D are both expressed in m²·s⁻¹, Le is dimensionless. It indicates whether heat diffuses faster than mass; Le > 1 implies heat spreads more rapidly, while Le < 1 signals that mass transport is quicker. The ratio underpins coupled heat- and mass-transfer analysis in drying, combustion, and climate science.
Definition and Relationships
Expressing Le in SI units keeps calculations straightforward: \u03b1 in m²·s⁻¹, D in m²·s⁻¹. Because Le = Sc/Pr, property data for viscosity, density, specific heat, thermal conductivity, and diffusivity all influence the result. Many gases at room conditions have Le near unity, simplifying design by aligning thermal and mass boundary-layer thicknesses. Liquids and gas mixtures can deviate significantly, making explicit Le evaluation essential.
When property data are temperature-dependent, evaluate Le at film conditions to match correlation assumptions. Document the reference state to support audits and reproducibility, and avoid mixing SI with legacy units that could obscure the dimensionless ratio.
Historical Context
Warren K. Lewis, a pioneer of chemical engineering, promoted analogies between heat and mass transfer in the early twentieth century. His work with Edwin R. Gilliland on distillation and absorption laid the foundation for using dimensionless groups like Le to scale equipment. Later researchers embedded Le in combustion theory, recognising that flame structure depends on relative heat and mass diffusion rates.
Standards such as ISO 80000-11 record the Lewis number symbol and definition, reinforcing consistent notation in textbooks, CFD software, and industry practice. The parameter remains central to educational courses linking transport theory with practical operations.
Conceptual Foundations
Coupled Boundary Layers
Le dictates the relative thickness of thermal and concentration boundary layers. When Le ≈ 1, temperature and species profiles align, enabling straightforward use of heat–mass analogies. For Le \u226b 1, thermal layers are thinner, meaning temperature equilibrates faster than composition. Le \u226a 1 reverses that relationship and can increase susceptibility to mass-diffusion limits.
Combustion and Evaporation
In premixed flames, Le influences stability and flame speed; fuels with Le < 1 can exhibit cellular instabilities. In drying and evaporative cooling, Le links Sherwood and Nusselt numbers, guiding predictions of surface temperature depression and moisture removal. Accounting for Le keeps coupled heat- and mass-transfer models physically consistent.
Applications and Importance
Process engineers apply Le when designing humidifiers, cooling towers, and dryers, ensuring that correlations derived under certain Le ranges remain valid. In meteorology, Le helps interpret evaporation from oceans and lakes, connecting surface fluxes to atmospheric stability. Combustion engineers use Le to adjust flame models and predict pollutant formation in gas turbines and engines.
Microfluidics and porous-media researchers also track Le to anticipate whether heat or mass will equalise first within intricate geometries. Documenting Le alongside Pr, Sc, and Sh supports transparent collaboration between disciplines and suppliers.
Working with Lewis Numbers
Calculate Le with consistent SI properties and note data sources, measurement uncertainties, and temperature dependence. Use the Reynolds calculator alongside humidity and NTU tools to integrate Le into design workflows. When applying analogies such as the Chilton–Colburn j-factors, confirm that the assumed Le range matches your system.
Finally, communicate clearly: specify whether Le was evaluated at bulk, film, or reference conditions; provide at least two significant digits; and align notation with ISO conventions. This transparency allows others to reproduce calculations and maintain mass- and heat-transfer consistency across projects.