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The diffusive tortuosity factor of a porous media quantifies the material’s resistance to diffusion, an important component of modeling flows in porous structures at the macroscale. Advances in X-ray micro-computed tomography (-CT) imaging provide the geometry of the material at the microscale (microstructure) thus enabling direct numerical simulation (DNS) of transport at the microscale. The data from these DNS are then used to close material’s macroscale transport models, which rely on effective material properties. In this work, we present numerical methods suitable for large scale simulations of diffusive transport through complex microstructures for the full range of Knudsen regimes. These numerical methods include a finite-volume method for continuum conditions, a random walk method for all regimes from continuum to rarefied, and the direct simulation Monte Carlo method. We show that for particle methods, the surface representation significantly affects the accuracy of the simulation for high Knudsen numbers, but not for continuum conditions. We discuss the upscaling of pore-resolved simulations to single species and multi-species volume-averaged models. Finally, diffusive tortuosities of a fibrous material are computed by applying the discussed numerical methods to 3D images of the actual microstructure obtained from X-ray computed micro-tomography.
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This content will become publicly available on February 10, 2026
Direct measurement of thermal Knudsen forces in rarefied gas environments
At micro- and nanoscales, momentum transfer between surfaces is influenced by various physical mechanisms, including quantum fluctuations, electromagnetic interactions, electric charges, and the dynamics of (rarefied) gases. Under non-isothermal conditions, rarefied gases give rise to thermal Knudsen forces whose magnitudes strongly depend on the gas species and surface characteristics. Knudsen forces are particularly relevant in nanotechnology, optical manipulation, and aerospace systems, where gas rarefaction occurs due to highly confined geometries, sub-micrometer length scales, and reduced particle densities. Despite their significance, predictive modeling of Knudsen forces is limited by a lack of comprehensive experimental data across diverse materials and surface morphologies. In this work, we present a highly sensitive and adaptable measurement platform capable of directly quantifying Knudsen forces using a suspended, interchangeable micro-cantilever within controlled rarefied helium and nitrogen environments. The system integrates optical fiber interferometry to precisely capture out-of-plane displacements at sub-micrometer resolution, driven by Knudsen forces. From the empirical data, we derive a robust correlation linking the magnitudes of Knudsen forces to energy accommodation coefficients, offering deeper insights into the underlying gas–surface interaction mechanisms.
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- Award ID(s):
- 2044049
- PAR ID:
- 10636337
- Publisher / Repository:
- Applied Physics Letters
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 126
- Issue:
- 6
- ISSN:
- 0003-6951
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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