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Updated: May 30, 2026
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Atomic Force Microscopy Cantilever-Based Nanoindentation: Mechanical Property Measurements at the Nanoscale in Air and Fluid
Published on: December 2, 2022
Quantifying the Knudsen force on heated microbeams: a compact model and direct comparison with measurements
Jeremy Nabeth1, Sruti Chigullapalli, Alina A Alexeenko
1School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana 47907, USA.
Summary
Microscale thermal nonequilibrium generates significant Knudsen forces. This study validates simulations with experiments, providing a model to quantify these forces in microsystems.
Area of Science:
- Physics
- Microscale Engineering
- Kinetic Theory
Background:
- Thermal nonequilibrium at the microscale generates Knudsen forces.
- Previous experimental measurements exist for microcantilevers.
Purpose of the Study:
- Investigate Knudsen force mechanism and magnitude.
- Compare numerical simulations with experimental data.
- Develop a model for quantifying Knudsen forces.
Main Methods:
- Numerical solution of the Boltzmann kinetic equation.
- Ellipsoidal statistical Bhatnagar-Gross-Krook approximation.
- Comparison with experimental data from literature.
Main Results:
- Simulations match experimental data for argon and nitrogen with diffuse interaction.
- Helium simulations require incomplete accommodation for agreement.
- A closed-form model for the Knudsen force coefficient was derived.
Conclusions:
- The study successfully models Knudsen forces.
- The derived model aids in microsystem design.
- Gas-surface interaction models are crucial for accurate predictions.
