Dynamics of a slowly evaporating solvent-polymer mixture with a deformable upper surface

Matthew G. Hennessy*, Andreas Münch

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)

Abstract

This paper examines how surface deformations affect the stability of a slowly evaporating solvent-polymer mixture. The destabilizing effect of surface-tension variations arising from evaporation-induced concentration gradients and the counteracting influence of mean gravity and surface tension are incorporated into the mathematical model. A linear stability analysis that takes advantage of the separation between the characteristic time scales of the slowly evolving base state and the perturbations is carried out in combination with numerical solutions of the linearized system. It is shown that the onset of instability can occur for Marangoni numbers that are much lower than the critical value for a non-deformable surface. Moreover, two types of Marangoni instabilities appear in the system: one is associated with the traditional stationary instability, and the other is an oscillatory instability that is not present for a non-deformable liquid surface. A region of the parameter space where the oscillatory instability dominates is identified and used to formulate appropriate conditions for future experiments.

Original languageEnglish
Pages (from-to)681-720
Number of pages40
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume79
Issue number4
DOIs
Publication statusPublished - Aug 2014

Bibliographical note

Funding Information:
This work was supported by the King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04].

Keywords

  • evaporating films
  • multiple scales
  • oscillatory Marangoni instability
  • WKB approximation

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