Journal
JOURNAL OF FLUID MECHANICS
Volume 919, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2021.419
Keywords
drops; capillary waves
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Funding
- Cambridge India Ramanujan Scholarship from the Cambridge Commonwealth, European and International Trust
- SERB, Govt. of India
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An analytical solution for the oscillation of an inviscid sessile drop on a flat horizontal plate is presented, yielding resonant frequencies for different vibration modes. The results show excellent agreement with experimental data, particularly for flatter drops and higher vibration modes.
We present a fully analytical solution for the natural oscillation of an inviscid sessile drop with small Bond number (surface tension dominates gravity) and a fixed contact line on a flat horizontal plate. The governing equations are expressed in terms of the toroidal coordinate system which yields solutions involving hypergeometric functions. Resonant frequencies are identified for zonal, sectoral and tesseral vibration modes. The predictions show excellent agreement with experimental data reported in the literature, particularly for flatter drops (lower theta(c), but not so low as to incur significant viscous dissipation) and higher modes of vibration.
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