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Exploring the Klinkenberg effect at different scales.

Boujema Izrar1, Jean-Louis Rouet2

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Summary
This summary is machine-generated.

This study simplifies microflow simulations by using hydrodynamic equations with slip boundary conditions to model the Klinkenberg effect. Results show this approach accurately captures microchannel flow behavior across different Knudsen numbers.

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Area of Science:

  • Fluid Dynamics
  • Microfluidics
  • Computational Physics

Background:

  • Simulating microflows typically demands complex numerical methods.
  • The Klinkenberg effect, significant in microchannel flows, describes gas rarefaction influences on apparent viscosity.
  • Hydrodynamic equations with slip boundary conditions offer a potentially simpler alternative for modeling this effect.

Purpose of the Study:

  • To investigate the Klinkenberg effect in microchannels using a simplified network model.
  • To derive an equivalent hydraulic conductivity for microflows up to second order.
  • To establish a criterion for distinguishing slip and transitional flow regimes.

Main Methods:

  • Utilizing a basic microchannel network to progressively increase the Knudsen number.
  • Deriving an equivalent hydraulic conductivity using theoretical analysis.
  • Comparing derived results with Navier-Stokes simulations (with slip) and a Bhatnagar-Gross-Krook-Hermite model.

Main Results:

  • An equivalent hydraulic conductivity was derived, accurate to the second order.
  • The simplified hydrodynamic model showed good agreement with more complex simulation methods.
  • A criterion was successfully established to differentiate between slip and transitional flow regimes.

Conclusions:

  • Hydrodynamic equations with slip boundary conditions are effective for modeling the Klinkenberg effect in microflows.
  • The proposed network model and derived conductivity offer a computationally efficient approach.
  • The established criterion aids in selecting appropriate models for microchannel flow analysis.