Lewis Number (Le): Thermal-to-Mass Diffusivity Ratio
The Lewis number (Le) compares thermal diffusivity to mass diffusivity, expressing how quickly heat spreads relative to species concentration. As a dimensionless group in ISO 80000-11, Le links heat and mass-transfer analyses, guiding models for drying, combustion, humidification, and atmospheric transport. This article covers Le’s definition, historical evolution from Lewis and Whitman’s boundary-layer theory, conceptual interpretations, experimental evaluation, and modern applications ranging from HVAC to additive manufacturing.
Couple Le calculations with the Reynolds number calculator to select the appropriate convection regime, and quantify associated energy balances using the specific heat energy tool.
Definition and Mathematical Form
Lewis number is defined as the ratio of thermal diffusivity α to mass diffusivity D:
Le = α / D = (k / ρ c_p) / D,
where k is thermal conductivity, ρ density, and c_p specific heat at constant pressure. All properties use coherent SI units (W·m⁻¹·K⁻¹, kg·m⁻³, J·kg⁻¹·K⁻¹, m²·s⁻¹), rendering Le dimensionless. Air at ambient conditions has Le ≈ 1, signifying similar rates of thermal and mass diffusion, while liquid metals (large α, small D) exhibit Le ≫ 1.
Alternative forms include the inverse Lewis number (Le⁻¹ = D/α) and the Schmidt-to-Prandtl ratio (Le = Sc/Pr), linking Le to the Schmidt and Prandtl numbers.
Historical Perspective
Warren K. Lewis and W.G. Whitman introduced the concept of analogous heat and mass-transfer boundary layers in the 1920s. Their film theory equated convective fluxes by assuming similar driving forces and thicknesses for temperature and concentration profiles. Subsequent researchers, including Colburn and Chilton, extended the analogy, resulting in the well-known Chilton–Colburn j-factors that express heat and mass-transfer coefficients in terms of Pr, Sc, and Re. The Lewis number emerged as the parameter connecting these analogies, ensuring that transfer coefficients scaled correctly across fluids and flow regimes.
Standardisation efforts by ASME, AIChE, and ISO codified Le-based correlations for evaporative cooling towers, dryers, and combustors. Today, Le features in computational models, building energy simulations, and meteorological codes, reflecting nearly a century of empirical and theoretical refinement.
Conceptual Insights
Heat–mass transfer analogy
When Le ≈ 1, temperature and concentration boundary layers have similar thickness, enabling direct analogies between heat and mass transfer (e.g., the Chilton–Colburn analogy). Deviations from unity indicate that one transport mode diffuses faster, requiring correction factors when translating between Nusselt and Sherwood correlations. Engineers compare Le to evaluate whether simplified analogies remain valid.
Combustion and flame structure
In premixed flames, Le influences flame thickness and stability. Fuels with Le < 1 (e.g., hydrogen–air mixtures) exhibit preferential diffusion of species relative to heat, affecting flame curvature and susceptibility to flashback. Combustion models incorporate Le when predicting extinction or blow-off limits, working alongside Damköhler and Mach numbers in propulsion design.
Drying and humidification
In drying operations, Le governs the relationship between heat supplied and moisture removed. Systems with Le ≫ 1 (liquid metals, some oils) require additional heat input to drive mass transfer, while Le ≪ 1 systems experience rapid moisture removal relative to heating. Designers adjust operating temperatures, airflow, and humidity targets based on Le to prevent product degradation or energy waste.
Measurement and Modelling
Property determination
Thermal diffusivity follows from conductivity, density, and specific heat measurements—topics detailed in the thermal diffusivity article. Mass diffusivity derives from tracer experiments, Stefan tubes, or correlations tied to molecular structure. Laboratories maintain SI traceability for property measurements via calibration against standards defined by the International System of Units overview.
Analytical correlations
Engineers employ correlations such as Nu = f(Re, Pr) and Sh = g(Re, Sc) to compute transfer coefficients. Le enters when converting between these forms, particularly via Chilton–Colburn factors j_H = St_H · Pr^0.6666666666666666 and j_D = St_D · Sc^0.6666666666666666. When Le differs significantly from unity, correction terms adjust the exponents to maintain accuracy.
Numerical simulation
CFD tools explicitly include Le when solving coupled energy and species equations. Multi-physics solvers for additive manufacturing or food drying treat Le as a control parameter, running parametric sweeps to examine sensitivity. Documenting Le in simulation reports enables reproducibility and aligns with ISO 80000-11 notation.
Applications
HVAC and building science
Ventilation and evaporative cooling systems rely on Le to balance temperature and humidity control. Engineers combine Le with airflow calculations from the air changes per hour calculator to size humidifiers, energy-recovery ventilators, and desiccant wheels.
Food and pharmaceutical drying
Spray dryers, freeze dryers, and tray dryers monitor Le to avoid case hardening or overdrying. Coupling Le with Damköhler analysis ensures that reaction kinetics (e.g., enzyme deactivation) align with mass-removal rates, protecting product quality. Process engineers use liquid cooling load estimates to manage latent heat removal.
Additive manufacturing and coatings
Polymer and metal additive manufacturing involves simultaneous heat and mass transport (e.g., solvent evaporation, sintering). Le informs laser scanning strategies and powder bed conditioning, complementing analysis of the Biot number and specific surface area of powders.
Atmospheric and environmental science
Le shapes modelling of evaporation from water bodies, soil moisture fluxes, and pollutant dispersion. Coupled with the Brunt–Väisälä frequency, Le helps diagnose atmospheric stability and cloud formation dynamics.
Why Lewis Number Matters
Lewis number links heat and mass transport through a single dimensionless ratio, enabling engineers to transfer correlations across disparate systems. Whether tuning a combustion chamber, designing a dryer, or modelling humid climates, Le clarifies whether temperature or concentration gradients dominate. Documenting Le alongside complementary groups such as Péclet and Damköhler ensures transparent communication across interdisciplinary teams.
As digital twins and optimisation workflows proliferate, Le becomes a valuable feature for surrogate models predicting moisture content, heat flux, or species concentrations. Maintaining SI/ISO notation and citing property sources fosters reproducibility and compliance with international standards.
Where to Go Next
Continue exploring coupled transport phenomena via the Damköhler number article and the Sherwood number guide. Apply Le-based reasoning to building projects with the air changes per hour calculator and evaluate energy budgets using the specific heat energy calculator.