论文标题
具有大量表面相互作用的两相流：具有动态边界条件的热力学上一致的Navier-Stokes-Cahn-Hilliard模型
Two-phase flows with bulk-surface interaction: thermodynamically consistent Navier-Stokes-Cahn-Hilliard models with dynamic boundary conditions
论文作者
论文摘要
我们得出了一种具有动态边界条件的新型热力学一致的Navier -Stokes-cahn--Hilliard系统。该模型描述了具有不同密度的粘性不可压缩二元流体的运动。与文献中的先前模型相反，我们的新模型允许表面扩散，扩散界面和边界之间的可变接触角以及散装和表面之间的质量转移。特别是，这种材料的转移受到大规模保护法的约束，包括批量和表面贡献。该推导是通过局部耗能法则和拉格朗日乘数方法进行的。接下来，在具有匹配密度的流体的情况下，我们在两个维度和三个维度上显示了全球弱解的存在，以及在二维中弱解的唯一性。
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the diffuse interface and the boundary, and mass transfer between bulk and surface. In particular, this transfer of material is subject to a mass conservation law including both a bulk and a surface contribution. The derivation is carried out by means of local energy dissipation laws and the Lagrange multiplier approach. Next, in the case of fluids with matched densities, we show the existence of global weak solutions in two and three dimensions as well as the uniqueness of weak solutions in two dimensions.
