Grandmaison Nicolas, Brancherie Delphine, Salsac Anne-Virginie
Biomechanics and Bioengineering Laboratory (UMR 7338), Université de technologie de Compiègne - CNRS, CS 60319, 60203 Compiègne cedex, France.
Roberval Laboratory (FRE 2012), Université de technologie de Compiègne - CNRS, CS 60319, 60203 Compiègne cedex, France.
J Fluid Mech. 2021 Mar 5;914. doi: 10.1017/jfm.2020.652. eCollection 2021 May 10.
Capsules, composed of a liquid core protected by a thin deformable membrane, offer high-potential applications in many fields of industry such as bioengineering. One of their limitations comes from the absence of models of capsule damage and/or rupture when they are subjected to an external flow. To assess when rupture is initiated, we develop a fluid-structure interaction (FSI) numerical model of a capsule in Stokes flow that accounts for potential damage of the capsule membrane. We consider the framework of Continuum Damage Mechanics and model the membrane with an isotropic brittle damage model, in which the membrane damage state depends on the history of loading. The FSI problem is solved by coupling the finite element method, to solve for the membrane deformation, with the boundary integral method, to solve for the inner and outer fluid flows. The model is applied to an initially spherical capsule subjected to a simple shear flow. Damage initiates at a critical value of the capillary number, ratio of the fluid viscous forces to the membrane elastic forces, and rupture at a higher capillary number, when it reaches a threshold value. The material parameters introduced in the damage model do not influence the mode of damage but only the values of the critical and threshold capillary numbers. When the capillary number is larger than the critical value, damage develops in the two symmetric central regions containing the vorticity axis. It is indeed in these regions that the internal tensions are the highest on the membrane.
胶囊由一层薄的可变形膜保护的液芯组成，在生物工程等许多工业领域具有很高的应用潜力。它们的局限性之一在于，当受到外部流动作用时，缺乏胶囊损坏和/或破裂的模型。为了评估破裂何时开始，我们开发了一个斯托克斯流中胶囊的流固耦合（FSI）数值模型，该模型考虑了胶囊膜的潜在损坏。我们采用连续介质损伤力学框架，并用各向同性脆性损伤模型对膜进行建模，其中膜的损伤状态取决于加载历史。通过将求解膜变形的有限元方法与求解内外流体流动的边界积分方法相结合，解决了FSI问题。该模型应用于一个初始为球形的胶囊，使其受到简单剪切流作用。当达到临界值时，在毛细管数（流体粘性力与膜弹性力之比）的临界值处开始损伤，在更高的毛细管数达到阈值时发生破裂。损伤模型中引入的材料参数不影响损伤模式，只影响临界和阈值毛细管数的值。当毛细管数大于临界值时，损伤在包含涡度轴的两个对称中心区域发展。实际上，正是在这些区域，膜上的内部张力最高。
