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：生物细胞利用膜和被称为生物分子凝聚物的液滴状结构来组织其内部环境。尽管液滴与膜的相互作用涉及多个关键生物学过程，但目前对此了解甚少。本文提出了一种首次数值方法，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与任意拉格朗日-欧拉（ALE）方法对弹性表面进行显式描述的优点。该模型具有热力学一致性，将流体动力学与毛细力以及薄膜的弯曲、张力和拉伸耦合。通过将单液滴的模拟结果与形状方程的理论结果进行对比，验证了该方法的有效性，并在二维和三维轴对称场景中展示了其能力。