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Evaporation excites temporal sequence of resonant modes in a sessile droplet perturbed at constant frequency - Insights into the universal dynamics of mode transitions

Sanyal, Apratim and Basu, Saptarshi (2018) Evaporation excites temporal sequence of resonant modes in a sessile droplet perturbed at constant frequency - Insights into the universal dynamics of mode transitions. In: CHEMICAL ENGINEERING SCIENCE, 176 . pp. 294-305.

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Official URL: http://dx.doi.org/10.1016/j.ces.2017.10.053

Abstract

A sessile droplet excited at a constant frequency exhibits a temporal sequence of interface modes when allowed to evaporate. Evaporation tunes the droplet to resonate at different modes in a descending order. The life of each mode spans over a transition stage from the onset of its own resonance to that of the next lower order mode. Mode lifetime during the evaporation period of any droplet has been found to decrease in a power law fashion both theoretically and experimentally when higher driving frequencies are considered. Such dynamics are driven by both evaporation and interface oscillations, the latter being governed by the dispersion relation of one dimensional capillary wave. The natural excitation of sequential mode resonances in the present case is governed by a tuning parameter. Variation of this parameter by evaporation is analogous to external frequency sweep in non evaporating droplets to detect similar mode resonances. The dynamics of transition stage corresponding to each mode is characterized by a second parameter denoted as mode transition parameter. The transition stage (higher to lower order) is initially fast but slows down close to the resonance of lower order mode. Theoretical expressions of mode lifetimes and the tuning parameter have been derived based on reasonably valid assumption of constant static contact angle (a measure of the contact angle of the unperturbed hypothetical droplet shape in an oscillation cycle). An approximate linear relation has been established between detuning (complement of the tuning parameter) and mode transition parameters which governs the dynamics of the transition stage. The experimental data corresponding to the detuning and mode transition parameters show universal merging for all excitation frequencies. The experimental data also follows the proposed theoretical linear trend but deviates towards the later part of the transition stage. Such deviations have been attributed to neglecting higher order terms and possible viscous damping from boundary layer at the substrate. Even then the universality of mode transition across all frequencies is maintained throughout the evaporative lifetime. (C) 2017 Elsevier Ltd. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Depositing User: review EPrints Reviewer
Date Deposited: 12 Jan 2018 09:35
Last Modified: 12 Jan 2018 09:35
URI: http://eprints.iisc.ac.in/id/eprint/58643

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