Schmidt number, abbreviated as Sc, a dimensionless number, is used in fluid mechanics and heat transfer to characterize the relative importance of mass transfer (diffusion) to momentum transfer (viscous forces). The Schmidt number is particularly important in problems involving mass transfer, such as the diffusion of solute in a solvent or the transfer of heat in a fluid through convection and conduction.
Schmidt Number Interpretation
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High Schmidt Number (Sc >> 1) - Viscous diffusion outpaces mass diffusion. Momentum spreads through the fluid much faster than the species does. This is typical in liquids, where viscosity is significant but molecular diffusion is slow (sugar dissolving in water). The concentration boundary layer (where species concentration changes) is much thinner than the velocity boundary layer.
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Low Schmidt Number (Sc << 1) - Mass diffusion is faster than viscous diffusion. The species spreads out more quickly than momentum does. This is common in gases, where diffusion of molecules (like a gas mixing in air) happens faster than the fluid’s momentum smooths out. Here, the concentration boundary layer is thicker than the velocity boundary layer.
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Schmidt Number (Sc ≈ 1) - Viscous and mass diffusion occur at roughly the same rate. This is often seen in gases under certain conditions (air with small molecules), where kinetic viscosity and mass diffusivity are of similar magnitude, simplifying some analyses.
In many cases, for common fluids and solutes, the Schmidt number can be approximated as a constant, simplifying calculations involving mass transfer. For example, in the case of heat transfer in a fluid, the Prandtl number is used to characterize the ratio of momentum diffusivity to thermal diffusivity, and the Schmidt number plays a similar role but for mass transfer.
Schmidt Number Formula |
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\( Sc \;=\; \dfrac{ \nu }{ D_m }\) (Schmidt Number) \( \nu \;=\; Sc \cdot D_m \) \( D_m \;=\; \dfrac{ \nu }{ Sc }\) |
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| Symbol | English | Metric |
| \( Sc \) = Schmidt Number | \(dimensionless\) | \(dimensionless\) |
| \( \nu \) (Greek symbol nu) = Kinematic Viscosity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
| \( D_m \) = Mass Diffusivity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
Schmidt Number Formula |
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\( Sc \;=\; \dfrac{ \mu }{ \rho \cdot D_m }\) (Schmidt Number) \( \mu \;=\; Sc \cdot \rho \cdot D_m \) \( \rho \;=\; \dfrac{ \mu }{ Sc \cdot D_m } \) \( D_m \;=\; \dfrac{ \mu }{ Sc \cdot \rho } \) |
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| Symbol | English | Metric |
| \( Sc \) = Schmidt Number | \(dimensionless\) | \(dimensionless\) |
| \( \mu \) (Greek symbol mu) = Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
| \( \rho \) (Greek symbol rho) = Density | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( D_m \) = Mass Diffusivity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
