We consider two-phase fluid deformable surfaces as model systems for biomembranes. Such surfaces are modeled by incompressible surface Navier-Stokes-Cahn-Hilliard-like equations with bending forces. We derive this model using the Lagrange-D'Alembert principle considering various dissipation mechanisms. The highly nonlinear model is solved numerically to explore the tight interplay between surface evolution, surface phase composition, surface curvature and surface hydrodynamics. It is demonstrated that hydrodynamics can enhance bulging and furrow formation, which both can further develop to pinch-offs. The numerical approach builds on a Taylor-Hood element for the surface Navier-Stokes part, a semi-implicit approach for the Cahn-Hilliard part, higher order surface parametrizations, appropriate approximations of the geometric quantities, and mesh redistribution. We demonstrate convergence properties that are known to be optimal for simplified sub-problems.

翻译：我们考虑两相流体可变形表面作为生物膜的系统模型。这类表面通过包含弯曲力的不可压缩表面Navier-Stokes-Cahn-Hilliard型方程进行建模。我们利用拉格朗日-达朗贝尔原理，结合多种耗散机制推导出该模型。为探究表面演化、表面相组成、表面曲率与表面流体动力学之间的紧密耦合关系，我们对这一高度非线性模型进行了数值求解。研究表明，流体动力学可增强凸起和沟槽的形成，这两种形变均可能进一步演化为颈缩断裂。数值方法基于表面Navier-Stokes部分的Taylor-Hood单元、Cahn-Hilliard部分的半隐式格式、高阶表面参数化、几何量适当逼近以及网格重分布技术。我们展示了已知对简化子问题具有最优性的收敛性特征。