Lewis Number

The Lewis number compares two diffusivities that have nothing obviously to do with one another: $\mathrm{Le} = \alpha/D$, how fast heat spreads through a fluid against how fast a species spreads through the same fluid. It is named for Warren Lewis, whose two-film work founded the modern treatment of interphase transfer, and its whole usefulness rests on how close to 1 it happens to be for one particular mixture — water vapour in air.

Start with why that matters. When $\mathrm{Le} \approx 1$, heat and vapour diffuse at nearly the same rate, so the thermal boundary layer and the concentration boundary layer over a wet surface grow to nearly the same thickness. The heat leaving the surface and the vapour leaving it are then governed by the same geometry, and the two transfer coefficients become tied together by a simple ratio instead of needing separate measurement. For air and water at ordinary temperatures the number is about 0.82, close enough that the relation $h/(k_c \rho c_p) \approx \mathrm{Le}^{2/3}$ — the Lewis relation — holds well and is very nearly 1. That is what makes a wet-bulb thermometer work: the wick cools until the heat arriving by convection exactly balances the heat leaving as evaporation, and because Lewis is near unity that balance point tracks the humidity in a way that can be read off a chart. It is also why the adiabatic saturation temperature and the wet-bulb temperature coincide for air and water and for essentially no other pair, and why every psychrometric chart in the trade is drawn for air and water specifically.

Lewis is a composite, and naming its parts is worth doing because it shows the dimensionless groups are a family rather than a list. $\mathrm{Le} = \mathrm{Sc}/\mathrm{Pr}$ exactly: Schmidt is $\nu/D$ and Prandtl is $\nu/\alpha$, so dividing one by the other cancels the kinematic viscosity and leaves $\alpha/D$. The catalog carries both parts already, and reaching Lewis either way must give the same answer — the anchors on this page check precisely that, working one route through $\alpha$ and $D$ and the other through Schmidt and Prandtl, and requiring the two to meet. If they did not, one of the three pages would be wrong.

Liquids are a different world and the contrast is instructive. In water, heat diffuses at about $0.146$ mm²/s and a dissolved small molecule at about $0.0015$ mm²/s, giving a Lewis number near 100. Release a warm pulse and a chemical pulse together in a still glass and the heat will have spread across the whole glass while the chemical has barely left where you put it. There is no useful analogy between heat and mass transfer under those conditions, which is why the tidy psychrometric machinery of moist air has no counterpart in liquid-phase work. As with Schmidt, the diffusivity in the denominator belongs to a PAIR of substances and moves steeply with temperature, so a Lewis number quoted without naming both species and the temperature is not usable.