### Abstract

We consider a computational model for binary-fluid-solid interaction based on an arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes-Korteweg equations, and we assess the predictive capabilities of this model. Due to the presence of two distinct fluid components, the stress tensor in the binary-fluid exhibits a capillary component in addition to the pressure and viscous-stress components. The distinct fluid-solid surface energies of the fluid components moreover lead to preferential wetting at the solid substrate. Compared to conventional FSI problems, the dynamic condition coupling the binary-fluid and solid subsystems incorporates an additional term associated with the binary-fluid-solid surface tension. We consider a formulation of the Navier-Stokes-Korteweg equations in which the free energy associated with the standard van-der Waals equation of state is replaced by a polynomial double-well function to provide better control over the diffuse-interface thickness and the surface tension. For the solid subsystem, we regard a standard hyperelastic model. We explore the main properties of the binary-fluid-solid interaction problem and establish a dissipation relation for the aggregated system. In addition, we present numerical results based on a fully monolithic approach to the complete nonlinear system. To validate the computational model, we consider the elasto-capillary interaction of a sessile droplet on a soft solid substrate and compare the numerical results with a corresponding solid model with fabricated fluid loads and with experimental data.

Original language | English |
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Pages (from-to) | 995-1036 |

Number of pages | 42 |

Journal | Mathematical Models & Methods in Applied Sciences |

Volume | 29 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2 Apr 2019 |

### Keywords

- binary-fluid-solid interaction
- elasto-capillarity
- monolithic methods
- Navier-Stokes-Korteweg equations
- Elastocapillarity
- Binary-fluid-solid interaction
- Monolithic methods

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## Cite this

*Mathematical Models & Methods in Applied Sciences*,

*29*(5), 995-1036. https://doi.org/10.1142/S0218202519410069