Article: Chang, CT; Daniel, S; Steen, PH; “Footprint Geometry and Sessile Drop Resonance”, Physical Review E, 95 (3)
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.
Funding Acknowledgement: Technical University Dortmund; NASA [NNX09AI83G]; National Science Foundation [CBET-1236582]; Xerox Corporation
Funding Text: The authors thank M.Y. Louge for supplying the VTS-100 oscillator, and G. Swan, B. Land, D. Hartino, S.J. Weinstein, M.Y. Louge, A.T. Zehnder, W.H. Sachse, K. Boettcher, C. Cohen, and D. Lee for assistance and helpful discussions. C.T.C. thanks P. Ehrhard for sponsoring his research stay at Technical University Dortmund. The authors also thank the reviewers for their numerous helpful suggestions. Finally, the authors thank NASA (Grant No. NNX09AI83G), the National Science Foundation (Grant No. CBET-1236582), and Xerox Corporation for financial support.