Question

Schmidt number is defined as

• A. \(\frac{{Mass Diffusivity}}{{Thermal Diffusivity}}\)
• B. \(\frac{{Momentum Diffusivity}}{{Mass Diffusivity}}\)
• C. \(\frac{{Momentum Diffusivity}}{{Thermal Diffusivity}}\)
• D. \(\frac{{Thermal Diffusivity}}{{Mass Diffusivity}}\)

Hint:

When dealing with problems involving both fluid flow and mass transfer, consider both the Reynolds number and the Schmidt number to fully understand the dynamics at play.

Answer 1

The Correct Option is B

The Schmidt number \( Sc \) is a dimensionless quantity used in fluid dynamics to characterize how momentum diffusivity (viscosity) compares to mass diffusivity. It is especially relevant in situations where fluid flow and mass transfer are coupled, such as in chemical reactor design and environmental engineering.

Step 1: Understanding Momentum Diffusivity (Kinematic Viscosity)
Momentum diffusivity, also known as kinematic viscosity \( \nu \), measures the rate at which momentum is diffused within the fluid. It is typically expressed in \( m^2/s \) and is a fundamental property that describes how viscous a fluid is.

Step 2: Understanding Mass Diffusivity
Mass diffusivity \( D \), on the other hand, measures the rate at which mass is diffused within a fluid. This property is crucial for describing how species (like solutes in a solvent) spread out over time, also expressed in \( m^2/s \).

Step 3: Ratio of Momentum to Mass Diffusivity
\[ Sc = \frac{\nu}{D} \] This ratio, the Schmidt number, tells us how the thickness of the velocity boundary layer compares to the thickness of the mass transfer boundary layer in a fluid flow scenario. A higher Schmidt number indicates that the momentum boundary layer is thicker than the mass transfer boundary layer, which has implications for the design and operation of equipment where heat and mass transfer processes are significant.

Step 4: Practical Implications
For high Schmidt numbers, momentum diffuses much more slowly than mass. This is particularly important in gaseous systems where gases have low viscosity. In liquid systems, where the Schmidt number can be very high, mass transfer operations must be carefully designed to ensure efficient mixing and mass transport.