Stability and instability of axisymmetric droplets in thermocapillary-driven thin films
- Creators
- Nicolaou, Zachary G.
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.
Additional Information
© 2018 IOP Publishing Ltd & London Mathematical Society. Received 12 July 2016; Accepted 10 November 2017; Published 12 February 2018.Additional details
- Eprint ID
- 84811
- Resolver ID
- CaltechAUTHORS:20180213-102506132
- Created
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2018-02-13Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field