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Persistent URL http://purl.org/net/epubs/work/29570
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Record Id 29570
Title Analytical solution of low Reynolds number slip flow past a sphere
Abstract An analytical solution is derived for predicting low Reynolds number rarefied gas flow past an unconfined sphere. In Stokes' original analysis of creeping flow past a sphere, a continuum flow hypothesis was implemented and no-slip boundary conditions were utilised on the surface. However, when the size of the sphere approaches the mean free path of the gas molecules, Stokes' continuum hypothesis breaks down and it is then important to account for rarefaction effects. In the present work, Stokes' solution has been extended for use in the slip-flow regime which is valid for Knudsen numbers, Kn-<0.1 The total drag on the sphere is shown to be equivalent to Stokes' solution for continuum flows multiplied by a rarefaction coefficient which is dependent upon the Knudsen number. Applying the slip-flow technique to the estimation of the terminal velocity of a microsphere shows that rarefaction effects increase the predicted settling speed. This result is confirmed by comparing the analytical solution with the experimental terminal velocities obtained in Millikan's landmark oil drop experiment. An additional validation study has also been conducted which compares the analytical drag formulae against numerical predictions from a finite-volume Navier-Stokes solver.
Organisation CCLRC , CSE , CSE-CEG
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report DL Technical Reports DL-TR-2000-001. 2000. dltr-2000001.pdf 2000