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Dynamics of sessile drops. Part 2. Experiment

Published online by Cambridge University Press:  10 March 2015

Chun-Ti Chang ,
J. B. Bostwick ,
Susan Daniel  and
P. H. Steen
Chun-Ti Chang*
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
J. B. Bostwick
Affiliation:
Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Susan Daniel
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
P. H. Steen
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA
*
†Email addresses for correspondence: phs7@cornell.edu, cc836@cornell.edu
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Abstract

High-speed images of driven sessile water drops recorded under frequency scans are analysed for resonance peaks, resonance bands and hysteresis of characteristic modes. Visual mode recognition using back-lit surface distortion enables modes to be associated with frequencies, aided by the identifications in Part 1 (Bostwick & Steen, J. Fluid Mech., vol. 760, 2014, pp. 5–38). Part 1 is a linear stability analysis that predicts how inviscid drop spectra depend on base state geometry. Theoretically, the base states are spherical caps characterized by their ‘flatness’ or fraction of the full sphere. Experimentally, quiescent shapes are controlled by pinning the drop at a circular contact line on the flat substrate and varying the drop volume. The response frequencies of the resonating drop are compared with Part 1 predictions. Agreement with theory is generally good but does deteriorate for flatter drops and higher modes. The measured frequency bands agree better with an extended model, introduced here, that accounts for forcing and weak viscous effects using viscous potential flow. As the flatness varies, regions are predicted where modal frequencies cross and where the spectra crowd. Frequency crossings and spectral crowding favour interaction of modes. Modal interactions of two kinds are documented, called ‘mixing’ and ‘competing’. Mixed modes are two pure modes superposed with little evidence of hysteresis. In contrast, modal competition involves hysteresis whereby one or the other mode disappears depending on the scan direction. Perhaps surprisingly, a linear inviscid irrotational theory provides a useful framework for understanding observations of forced sessile drop oscillations.

JFM classification

Drops and Bubbles: Drops Drops and Bubbles: Drops and Bubbles

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Papers
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Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 442 - 467
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© 2015 Cambridge University Press 

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