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How It Works
The Knudsen number compares the average distance a gas molecule travels between collisions (mean free path) to the size of the physical system. When Kn is very small, molecules collide with each other far more often than with the walls, and ordinary fluid mechanics applies. When Kn is large, molecules interact mainly with surfaces, and you must use kinetic theory instead.
Four flow regimes are defined by Kn: continuum (< 0.01), slip (0.01–0.1), transitional (0.1–10), and free molecular (> 10). Choosing the correct regime is critical for accurate modeling of microfluidic devices and vacuum systems.
Example Problem
Air at low pressure has a mean free path of 7 μm (7 × 10⁻⁶ m). It flows through a MEMS channel with a height of 50 μm. What is the Knudsen number?
- Kn = λ / L = 7 × 10⁻⁶ / 50 × 10⁻⁶
- Kn = 0.14
A Kn of 0.14 falls in the transitional regime, so neither pure continuum equations nor free-molecular models apply directly -- a slip boundary condition or DSMC simulation is needed.
Frequently Asked Questions
What is the mean free path of air at standard conditions?
At sea-level pressure (101.3 kPa) and 20 °C, the mean free path of air is about 68 nm (6.8 × 10⁻⁸ m). It increases as pressure drops -- at 1 Pa it reaches roughly 7 mm, making the Knudsen number large for centimeter-scale equipment.
Why does the Knudsen number matter for MEMS devices?
MEMS channels can be just a few micrometers wide. At those scales, even atmospheric-pressure air has Kn on the order of 0.001–0.01, pushing the flow into the slip regime. Standard no-slip Navier-Stokes equations underpredict flow rates by 10% or more unless slip corrections are applied.
How is the Knudsen number used in vacuum system design?
Vacuum engineers use Kn to choose the right pump and predict gas conductance through tubes. In high vacuum (Kn > 10), molecular flow dominates and conductance depends only on tube geometry. In rough vacuum (Kn < 0.01), viscous flow equations apply. The transition range requires more complex models.
Related Calculators
- Mach Number Calculator — ratio of flow velocity to speed of sound, important in rarefied gas dynamics.
- Schmidt Number Calculator — momentum vs. mass diffusivity, relevant to gas-phase transport.
- Prandtl Number Calculator — momentum vs. thermal diffusivity in boundary layers.
- Reynolds Number Calculator — inertial vs. viscous forces in continuum flow regimes.
- Ideal Gas Law Calculator — relate pressure, volume, and temperature for mean free path estimation.