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.
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
StatePublished - 2017

Publication series

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

Fingerprint

fluid-solid interactions
binary fluids
traction
fluids
interfacial tension
formulations
wetting
dissipation
boundary conditions

Cite this

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. DOI: 10.1515/9783110494259-008
van Brummelen, E.H. ; Shokrpour Roudbari, M. ; Simsek - Senel, G. ; van der Zee, K.G./ Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations. Fluid-structure interaction: modeling, adaptive discretizations and solvers. editor / Stefan Frei ; Bärbel Holm ; Thomas Richter ; Thomas Wick ; Huidong Yang. Walter de Gruyter GmbH, 2017. pp. 283-323 (Radon Series on Computational and Applied Mathematics).
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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.",
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van Brummelen, EH, Shokrpour Roudbari, M, Simsek - Senel, G & van der Zee, KG 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. 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.

Fluid-structure interaction: modeling, adaptive discretizations and solvers. ed. / Stefan Frei; Bärbel Holm; Thomas Richter; Thomas Wick; Huidong Yang. Walter de Gruyter GmbH, 2017. p. 283-323 (Radon Series on Computational and Applied Mathematics; Vol. 20).

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

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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 -

van Brummelen EH, Shokrpour Roudbari M, Simsek - Senel G, van der Zee KG. Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations. In Frei S, Holm B, Richter T, Wick T, Yang H, editors, Fluid-structure interaction: modeling, adaptive discretizations and solvers. Walter de Gruyter GmbH. 2017. p. 283-323. (Radon Series on Computational and Applied Mathematics). Available from, DOI: 10.1515/9783110494259-008