Schmidtnumber

Schmidt number

The Schmidt number, denoted Sc, is a dimensionless quantity used in fluid dynamics and mass transfer to compare momentum diffusion to mass diffusion. It is defined as Sc = ν / D_AB = μ / (ρ D_AB), where ν is the kinematic viscosity of the fluid, μ is the dynamic viscosity, ρ is the density, and D_AB is the mutual diffusion coefficient of species A in species B. The quantity Sc therefore characterizes how quickly momentum diffuses relative to how quickly mass is transported by diffusion alone.

Interpretation and context: A high Schmidt number indicates that momentum diffuses much faster than mass, so mass diffusion is the limiting transport process in many problems. Conversely, a low Sc means mass diffuses relatively quickly compared with momentum diffusion. The Schmidt number is analogous to the Prandtl number in heat transfer, which compares momentum diffusion to thermal diffusion.

Typical ranges and applications: In gases, Sc is usually around 0.6–1. In liquids, Sc tends to be large, often in the range of 10^2–10^4 or higher, depending on temperature, solvent, and solute. The Schmidt number appears in mass-transfer correlations and similarity solutions, and in conjunction with Reynolds number to form Peclet-type quantities that describe convective-diffusive transport. It also features in correlations for Sherwood numbers and in boundary-layer analyses for combined momentum and species transport.

Measurement and use: Sc is determined from fluid properties and the diffusion coefficient of the species of interest. It is a dimensionless tool for comparing transport processes and for scaling experimental and numerical results across different systems.