@inbook{74509d0aaef1481b99578058f6398a01,
title = "Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations",
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. ",
author = "{van Brummelen}, E.H. and {Shokrpour Roudbari}, M. and {Simsek - Senel}, G. and {van der Zee}, K.G.",
year = "2017",
doi = "10.1515/9783110494259-008",
language = "English",
isbn = "978-3-11-049527-0",
series = "Radon Series on Computational and Applied Mathematics",
publisher = "Walter de Gruyter GmbH",
pages = "283--323",
editor = "Stefan Frei and B{\"a}rbel Holm and Thomas Richter and Thomas Wick and Huidong Yang",
booktitle = "Fluid-structure interaction",
address = "Germany",
}