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How It Works
The Schmidt number compares momentum diffusivity (kinematic viscosity) to mass diffusivity. It is the mass-transfer counterpart of the Prandtl number. When Sc ≈ 1, the velocity and concentration boundary layers grow at the same rate. When Sc >> 1, mass diffuses much more slowly than momentum.
Sc appears in Sherwood-number correlations used to predict mass-transfer coefficients in chemical reactors, absorbers, and separation columns, just as Pr appears in Nusselt-number correlations for heat transfer.
Example Problem
CO₂ diffuses in water at 25 °C. The kinematic viscosity of water is 8.9 × 10⁻⁷ m²/s and the diffusion coefficient of CO₂ in water is 1.92 × 10⁻⁹ m²/s. What is the Schmidt number?
- Sc = ν / D = 8.9 × 10⁻⁷ / 1.92 × 10⁻⁹
- Sc = 464
A Schmidt number of 464 means the concentration boundary layer is much thinner than the velocity boundary layer, which is typical for dissolved gases in liquids.
Frequently Asked Questions
What is a typical Schmidt number for gases vs. liquids?
For gases at atmospheric pressure, Sc is usually between 0.5 and 2 (e.g., Sc ≈ 0.6 for H₂ in air, Sc ≈ 1.0 for CO in air). For dissolved species in liquids, Sc ranges from about 100 to over 1,000 because liquid-phase diffusion is much slower.
How is the Schmidt number used in mass transfer calculations?
It enters Sherwood-number correlations such as Sh = 0.023 Re⁰⋅⁸ Sc⁰⋅⁴ (analogous to Dittus-Boelter for heat transfer). From Sh, engineers calculate the mass-transfer coefficient needed to size absorbers, strippers, and other separation equipment.
What is the relationship between Schmidt, Prandtl, and Lewis numbers?
Le = Sc / Pr. If you know any two of these three dimensionless numbers, you can compute the third. This relationship is particularly useful in combustion modeling where all three appear together.
Related Calculators
- Prandtl Number Calculator — the heat-transfer analogue of the Schmidt number.
- Lewis Number Calculator — ratio of thermal to mass diffusivity (Sc/Pr).
- Sherwood Number Calculator — convective mass transfer ratio that depends on Sc.
- Reynolds Number Calculator — characterize flow regime for mass transfer correlations.
- Viscosity Converter — convert kinematic and dynamic viscosity units used in Sc calculations.