The Library
Stability and bifurcation of dynamic contact lines in two dimensions
Tools
Tools
Tools
Keeler, J. S., Lockerby, Duncan A., Kumar, S. and Sprittles, J. E. (2022) Stability and bifurcation of dynamic contact lines in two dimensions. Journal of Fluid Mechanics, 945 . A34. doi:10.1017/jfm.2022.526 ISSN 0022-1120.
|
PDF
WRAP-stability-bifurcation-dynamic-contact-lines-two-dimensions-Keeler-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (4Mb) | Preview |
|
|
PDF
WRAP-Stability-bifurcation-dynamic-contact-lines-two-dimensions-2022.pdf - Accepted Version - Requires a PDF viewer. Download (6Mb) | Preview |
Official URL: https://doi.org/10.1017/jfm.2022.526
Abstract
The moving contact line between a fluid, liquid and solid is a ubiquitous phenomenon, and determining the maximum speed at which a liquid can wet/dewet a solid is a practically important problem. Using continuum models, previous studies have shown that the maximum speed of wetting/dewetting can be found by calculating steady solutions of the governing equations and locating the critical capillary number, Cacrit , above which no steady-state solution can be found. Below Cacrit , both stable and unstable steady-state solutions exist and if some appropriate measure of these solutions is plotted against Ca , a fold bifurcation appears where the stable and unstable branches meet. Interestingly, the significance of this bifurcation structure to the transient dynamics has yet to be explored. This article develops a computational model and uses ideas from dynamical systems theory to show the profound importance of the unstable solutions on the transient behaviour. By perturbing the stable state by the eigenmodes calculated from a linear stability analysis it is shown that the unstable branch is an ‘edge’ state that is responsible for the eventual dynamical outcomes and that the system can become transient when Ca<Cacrit due to finite-amplitude perturbations. Furthermore, when Ca>Cacrit , we show that the trajectories in phase space closely follow the unstable branch.
| Item Type: | Journal Article | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics Q Science > QD Chemistry T Technology > TA Engineering (General). Civil engineering (General) |
||||||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Bifurcation theory , Fluid mechanics , Interfaces (Physical sciences) -- Mathematics , Solid-liquid interfaces | ||||||||||||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||||||||||||
| Publisher: | Cambridge University Press | ||||||||||||||||||
| ISSN: | 0022-1120 | ||||||||||||||||||
| Official Date: | 25 August 2022 | ||||||||||||||||||
| Dates: |
|
||||||||||||||||||
| Volume: | 945 | ||||||||||||||||||
| Article Number: | A34 | ||||||||||||||||||
| DOI: | 10.1017/jfm.2022.526 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2022.526. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | ||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
| Date of first compliant deposit: | 13 June 2022 | ||||||||||||||||||
| Date of first compliant Open Access: | 14 October 2022 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
|
||||||||||||||||||
| Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
