Schmidt Number Calculator

At a glance:The Schmidt number (Sc) is the key dimensionless number in mass transfer (the transfer of a substance), defined as the ratio of momentum diffusivity to mass diffusivity: Sc=ν/D, where Sc is dimensionless, ν the kinematic viscosity (m²/s, i.e. momentum diffusivity) and D the mass (molecular) diffusivity (m²/s). Term by term: ν describes how fast momentum diffuses in the fluid; D describes how fast a species' molecules diffuse. Sc is their ratio: a large Sc means momentum diffuses faster than mass (the velocity boundary layer is thicker than the concentration layer); a small Sc the opposite. Sc plays in mass transfer the role the Prandtl number Pr plays in heat transfer — it is a pure fluid property (independent of velocity and geometry) and the core variable of mass-transfer correlations. Common values: gases Sc≈0.6–2 (water vapour in air ≈0.6); liquids Sc often hundreds to thousands (water-dissolved gas or solute, because D is tiny — water CO₂ Sc≈500). Example: air-water vapour ν=1.57e-5, D=2.5e-5 → Sc≈0.628; water CO₂ ν=1e-6, D=1.9e-9 → Sc≈526. Mass transfer is fully analogous to heat transfer: replace Nu by Sherwood Sh and Pr by Sc, giving Sh=C·Reᵐ·Scⁿ (forced convective mass transfer) and the boundary-layer ratio δ/δ_c≈Sc^(1/3). Uses: (1) core independent variable of mass-transfer correlations (find the transfer coefficient); (2) estimate concentration boundary-layer thickness; (3) evaporation, drying, absorption, extraction; (4) link with Pr and the Lewis number Le=Sc/Pr for simultaneous heat and mass transfer. Notes: (1) take ν and D at the same temperature and medium; (2) D depends on solute/solvent and temperature (look up); (3) keep SI units (both m²/s); (4) Sc is defined for single-phase molecular diffusion. In short, Sc=ν/D connects the flow field with the concentration field and threads every convective mass-transfer correlation.