Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far little understood. Here, we present a first numerical method to simulate the continuum dynamics of droplets interacting with deformable membranes via wetting. The method combines the advantages of the phase-field method for multi-phase flow simulation and the arbitrary Lagrangian-Eulerian (ALE) method for an explicit description of the elastic surface. The model is thermodynamically consistent, coupling bulk hydrodynamics with capillary forces, as well as bending, tension, and stretching of a thin membrane. The method is validated by comparing simulations for single droplets to theoretical results of shape equations, and its capabilities are illustrated in 2D and 3D axisymmetric scenarios.

翻译：生物细胞利用膜和液态液滴（称为生物分子凝聚体）来构建其内部结构。尽管液滴与膜的相互作用涉及多个关键生物过程，但迄今仍知之甚少。本文提出首个数值方法，用于模拟液滴通过润湿与可变形膜相互作用的连续介质动力学。该方法结合了相场法在多相流模拟中的优势，以及任意拉格朗日-欧拉法（ALE）对弹性表面的显式描述。模型满足热力学一致性，将体相流体动力学与毛细力、薄膜的弯曲、张力和拉伸相耦合。通过将单液滴模拟结果与形状方程的理论结果进行对比验证了该方法，并展示了其在二维和三维轴对称场景中的应用能力。