Stability and bifurcation of dynamic contact lines in two dimensions

Keeler, Jack S. ORCID: https://orcid.org/0000-0002-8653-7970, Lockerby, Duncan A., Kumar, Satish and Sprittles, James E. (2022) Stability and bifurcation of dynamic contact lines in two dimensions. Journal of Fluid Mechanics, 945. ISSN 0022-1120

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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, above which no steady-state solution can be found. Below, both stable and unstable steady-state solutions exist and if some appropriate measure of these solutions is plotted against, 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, we show that the trajectories in phase space closely follow the unstable branch.

Item Type: Article
Additional Information: Data availability statement: The data that support the findings of this study are openly available in figshare at https://doi.org/10.6084/m9.figshare.17277812. Funding Information: The authors acknowledge funding from EPSRC grants EP/N016602/1, EP/P020887/1, EP/S029966/1 and EP/P031684/1. This material is also based upon work supported by the National Science Foundation under grant no. CBET-1935968.
Uncontrolled Keywords: bifurcation,computational methods,contact lines,condensed matter physics,mechanics of materials,mechanical engineering,applied mathematics ,/dk/atira/pure/subjectarea/asjc/3100/3104
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: LivePure Connector
Date Deposited: 27 Jul 2022 15:30
Last Modified: 24 Sep 2022 20:35
URI: https://ueaeprints.uea.ac.uk/id/eprint/86950
DOI: 10.1017/jfm.2022.526

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