Composite solutions to a liquid bilayer model

Composite solutions to a liquid bilayer model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Composite solutions to a liquid bilayer model Georgy Kitavtsev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4772314/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Nov, 2024 Read the published version in Journal of Nonlinear Science → Version 1 posted 7 You are reading this latest preprint version Abstract This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an intermolecular potential depending on both layer heights. The found solutions are composed of the repeated elementary blocks (bulk, contact line and ultra-thin film ones) being consistently asymptotically matched together. We show that once considered on a finite interval with Neumann boundary conditions these stationary solutions are either dynamically stable or weakly translationally unstable. Other composite solutions are found to be numerically unstable and rather exhibit complex coarsening dynamics. stationary solutions bilayer systems intermolecular potential coarsening. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 23 Nov, 2024 Read the published version in Journal of Nonlinear Science → Version 1 posted Editorial decision: Revision requested 21 Sep, 2024 Reviews received at journal 20 Sep, 2024 Reviewers agreed at journal 29 Jul, 2024 Reviewers invited by journal 21 Jul, 2024 Editor assigned by journal 20 Jul, 2024 Submission checks completed at journal 20 Jul, 2024 First submitted to journal 20 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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