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Stability and instability of axisymmetric droplets in thermocapillary-driven thin films

Nicolaou, Zachary G. (2018) Stability and instability of axisymmetric droplets in thermocapillary-driven thin films. Nonlinearity, 31 (3). pp. 1009-1044. ISSN 0951-7715. https://resolver.caltech.edu/CaltechAUTHORS:20180213-102506132

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Abstract

The stability of compactly supported, axisymmetric droplet states is considered for driven thin viscous films evolving on two-dimensional surfaces. Stability is assessed using Lyapunov energy methods afforded by the Cahn–Hilliard variational form of the governing equation. For general driving forces, a criterion on the gradient of profiles at the boundary of their support (their contact slope) is shown to be a necessary condition for stability. Additional necessary and sufficient conditions for stability are established for a specific driving force corresponding to a thermocapillary-driven film. It is found that only droplets of sufficiently short height that satisfy the contact slope criterion are stable. This destabilization of droplets with increasing height is characterized as a saddle-node bifurcation between a branch of tall, unstable droplets and a branch of short, stable droplets.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1361-6544/aa999cDOIArticle
http://iopscience.iop.org/article/10.1088/1361-6544/aa999c/metaPublisherArticle
ORCID:
AuthorORCID
Nicolaou, Zachary G.0000-0003-4542-4256
Additional Information:© 2018 IOP Publishing Ltd & London Mathematical Society. Received 12 July 2016; Accepted 10 November 2017; Published 12 February 2018.
Issue or Number:3
Record Number:CaltechAUTHORS:20180213-102506132
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180213-102506132
Official Citation:Zachary G Nicolaou 2018 Nonlinearity 31 1009
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84811
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Feb 2018 18:38
Last Modified:03 Oct 2019 19:23

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