Abstract
We consider a computational model for complex-fluid–solid interaction (CSFI) 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 (NSCH) 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 CSFI problem, based on an arbitrary-Lagrangian–Eulerian formulation of the NSCH equations and a proper reformulation of the complex-fluid traction and the fluid–solid surface tension. To validate the presented CSFI model, we present numerical results and conduct a comparison to experimental data for a droplet on a soft substrate.
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The admissible solid deformations must in fact satisfy auxiliary conditions at the interface to ensure that the surface-tension contributions are well-defined. Detailed treatment of this aspect is beyond the scope of this work.
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This work is supported by NanoNextNL, a micro and nanotechnology consortium of the Government of the Netherlands and 130 partners.
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van Brummelen, E.H., Shokrpour-Roudbari, M., van Zwieten, G.J. (2016). Elasto-Capillarity Simulations Based on the Navier–Stokes–Cahn–Hilliard Equations. In: Bazilevs, Y., Takizawa, K. (eds) Advances in Computational Fluid-Structure Interaction and Flow Simulation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40827-9_35
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DOI: https://doi.org/10.1007/978-3-319-40827-9_35
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