Footprint geometry and sessile drop resonance

Chun-Ti Chang, Susan Daniel, and Paul H. Steen
Phys. Rev. E 95, 033109 – Published 15 March 2017
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Abstract

In this work, we examine experimentally the resonance of a sessile drop with a square footprint (square drop) on a flat plate. Two families of modal behaviors are reported. One family is identified with the modes of sessile drops with circular footprints (circular drop), denoted as “spherical modes.” The other family is associated with Faraday waves on a square liquid bath (square Faraday waves), denoted as “grid modes.” The two families are distinguished based on their dispersion behaviors. By comparing the occurrence of the modes, we recognize spherical modes as the characteristic of sessile drops, and grid modes as the constrained response. Within a broader context, we further discuss the resonance modes of circular sessile drops and free spherical drops, and we recognize various modal behaviors as surface waves under different extents of constraint. From these, we conclude that sessile drops resonate according to how wave-number selection by footprint geometry and capillarity compete. For square drops, a dominant effect of footprint constraint leads to grid modes; otherwise, the drops exhibit spherical modes, the characteristic of sessile drops on flat plates.

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  • Received 5 August 2016
  • Revised 9 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.033109

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Chun-Ti Chang1,*, Susan Daniel2,3,†, and Paul H. Steen2,4,‡

  • 1Department of Mechanical Engineering, National Taiwan University, Taipei 16017, Taiwan, Republic of China
  • 2School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
  • 3Theoretical and Applied Mechanics, Cornell University, Ithaca, New York 14853, USA
  • 4Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA

  • *chuntichang@ntu.edu.tw
  • sd386@cornell.edu
  • phs7@cornell.edu

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Issue

Vol. 95, Iss. 3 — March 2017

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