Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations

E.H. van Brummelen, M. Shokrpour Roudbari, G. Simsek - Senel, K.G. van der Zee

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

We consider amodel for binary-fluid-solid interaction based on a diffuse-interface model for the binary fluid and a hyperelastic-materialmodel for the solid. The diffuse-interface binary-fluidmodel is described by the quasi-incompressible Navier-Stokes-Cahn-Hilliard equations with preferential-wetting boundary conditions at the fluid-solid interface. The fluid traction on the interface includes a capillary-stress contribution in addition to the regular viscous-stress and pressure contributions. The dynamic interface condition comprises the traction exerted by the nonuniform solid-fluid surface tension in accordance with the Young-Laplace law for the solid-fluid interface. The solid is modeled as a hyperelastic material. We present a weak formulation of the aggregated binary-fluid-solid interaction problem, based on an arbitrary Lagrangian-Eulerian formulation of theNavier-Stokes-Cahn-Hilliard equations and a properweak evaluation of the binary-fluid traction and of the solid-fluid surface tension. We also present an analysis of the essential properties of the binary-fluid-solid interaction problem, including a dissipation relation for the complete fluid-solid interaction problem. To validate the presented binary-fluid-solid interactionmodel, we consider numerical simulations for the elasto-capillary interaction of a droplet with a soft solid substrate and present a comparison to corresponding experimental data.
Original languageEnglish
Title of host publicationFluid-structure interaction
Subtitle of host publicationmodeling, adaptive discretizations and solvers
EditorsStefan Frei, Bärbel Holm, Thomas Richter, Thomas Wick, Huidong Yang
PublisherWalter de Gruyter GmbH
Chapter8
Pages283-323
Number of pages41
ISBN (Electronic)978-3-11-049258-3, 978-3-11-049425-9
ISBN (Print)978-3-11-049527-0
DOIs
Publication statusPublished - 2017

Publication series

NameRadon Series on Computational and Applied Mathematics
PublisherDe Gruyter
Volume20
ISSN (Print)1865-3707

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van Brummelen, E. H., Shokrpour Roudbari, M., Simsek - Senel, G., & van der Zee, K. G. (2017). Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations. In S. Frei, B. Holm, T. Richter, T. Wick, & H. Yang (Eds.), Fluid-structure interaction: modeling, adaptive discretizations and solvers (pp. 283-323). (Radon Series on Computational and Applied Mathematics; Vol. 20). Walter de Gruyter GmbH. https://doi.org/10.1515/9783110494259-008