Elasto-capillarity Simulations based on the Navier-Stokes-Cahn-Hilliard Equations

TL;DR

This paper develops a computational model for complex-fluid-solid interactions using diffuse-interface and hyperelastic models, validated by numerical simulations and experimental comparisons.

Contribution

It introduces a novel weak formulation combining Navier-Stokes-Cahn-Hilliard equations with hyperelastic solid models for accurate simulation of elasto-capillarity phenomena.

Findings

Numerical results match experimental data for droplet behavior on soft substrates.

The model captures complex fluid-solid interface dynamics.

The approach provides a robust framework for simulating elasto-capillarity effects.

Abstract

We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the incompressible Navier-Stokes-Cahn-Hilliard equations with preferential-wetting boundary conditions at the fluid-solid interface. The corresponding fluid traction on the interface includes a capillary-stress contribution, and the dynamic interface condition comprises the traction exerted by the non-uniform fluid-solid surface tension. We present a weak formulation of the aggregated complex-fluid-solid-interaction problem, based on an Arbitrary-Lagrangian-Eulerian formulation of the Navier-Stokes-Cahn-Hilliard equations and a proper reformulation of the complex-fluid traction and the fluid-solid surface tension. To validate the presented complex-fluid-solid-interaction model, we present numerical results and conduct a comparison to experimental data for a droplet on a soft substrate.