基于Navier-Stokes-Cahn-Hilliard方程的弹性毛细作用模拟
Elasto-capillarity Simulations based on the Navier-Stokes-Cahn-Hilliard Equations
AI总结：
本文提出基于Navier-Stokes-Cahn-Hilliard方程的复杂流-固相互作用模型，结合弹性材料模型，通过弱形式和任意拉格朗日-欧拉格式解决流固耦合问题，并通过实验数据验证了滴落行为。
摘要：
我们考虑了一个基于扩散界面模型的复杂流-固相互作用计算模型，该模型采用不可压缩的Navier-Stokes-Cahn-Hilliard方程和超弹性材料模型描述复杂流体和固体。扩散界面复杂流体模型在流-固界面处包含优先润湿边界条件，流体牵引力包括毛细应力贡献，动态界面条件包含非均匀流-固表面张力的牵引力。我们基于Navier-Stokes-Cahn-Hilliard方程的任意拉格朗日-欧拉格式和复杂流体牵引力与流-固表面张力的适当改写，提出了聚合的复杂流-固相互作用问题的弱形式。为了验证所提出的复杂流-固相互作用模型，我们展示了数值结果，并对软基质上的液滴进行了实验数据对比。
英文摘要：
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.
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