### Abstract

Language | English |
---|---|

Title of host publication | Fluid-structure interaction |

Subtitle of host publication | modeling, adaptive discretizations and solvers |

Editors | Stefan Frei, Bärbel Holm, Thomas Richter, Thomas Wick, Huidong Yang |

Publisher | Walter de Gruyter GmbH |

Chapter | 8 |

Pages | 283-323 |

Number of pages | 41 |

ISBN (Electronic) | 978-3-11-049258-3, 978-3-11-049425-9 |

ISBN (Print) | 978-3-11-049527-0 |

DOIs | |

State | Published - 2017 |

### Publication series

Name | Radon Series on Computational and Applied Mathematics |
---|---|

Publisher | De Gruyter |

Volume | 20 |

ISSN (Print) | 1865-3707 |

### Fingerprint

### Cite this

*Fluid-structure interaction: modeling, adaptive discretizations and solvers*(pp. 283-323). (Radon Series on Computational and Applied Mathematics; Vol. 20). Walter de Gruyter GmbH. DOI: 10.1515/9783110494259-008

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*Fluid-structure interaction: modeling, adaptive discretizations and solvers.*Radon Series on Computational and Applied Mathematics, vol. 20, Walter de Gruyter GmbH, pp. 283-323. DOI: 10.1515/9783110494259-008

**Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations.** / van Brummelen, E.H.; Shokrpour Roudbari, M.; Simsek - Senel, G.; van der Zee, K.G.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations

AU - van Brummelen,E.H.

AU - Shokrpour Roudbari,M.

AU - Simsek - Senel,G.

AU - van der Zee,K.G.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

U2 - 10.1515/9783110494259-008

DO - 10.1515/9783110494259-008

M3 - Chapter

SN - 978-3-11-049527-0

T3 - Radon Series on Computational and Applied Mathematics

SP - 283

EP - 323

BT - Fluid-structure interaction

PB - Walter de Gruyter GmbH

ER -