Abstract
A major part of this paper is taken up by the calculation of the first axisymmetric surface oscillation frequency and the (2, 0) mode of an ellipsoidal bubble, in order to compare with experimentally obtained values of bubbles rising in water. First, an energy method is used for an ellipsoid oscillating in stagnant water. Interestingly, with help of a paper by Bjerknes [12] at 1873!. The results compare poorly with experiments. Agreement improves when the oscillation of the rise velocity is taken into account. The remaining difference between the results of theory and experimental values is ascribed to deviation of the bubble shape from an ellipsoid. Finally, volume oscillations of ellipsoidal bubbles are calculated with the energy method and the results compare well with those of an earlier work, based on an electrical analogon.
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Dedicated to Professor Wilhelm Schneider on the occasion of his 70th birthday
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van Wijngaarden, L., Veldhuis, C. On hydrodynamical properties of ellipsoidal bubbles. Acta Mech 201, 37–46 (2008). https://doi.org/10.1007/s00707-008-0071-1
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DOI: https://doi.org/10.1007/s00707-008-0071-1