Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany.
Center of Systems Biology Dresden, Pfotenhauerstr. 108, 01307 Dresden, Germany.
J R Soc Interface. 2024 Jul;21(216):20240056. doi: 10.1098/rsif.2024.0056. Epub 2024 Jul 31.
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic processes. We here consider wrinkling of fluid deformable surfaces. In contrast with thin elastic sheets, with in-plane and out-of-plane elasticity, these surfaces are characterized by in-plane viscous flow and out-of-plane elasticity and have been established as model systems for biomembranes and cellular sheets. We use this hydrodynamic theory and numerically explore the formation of wrinkles and their coarsening, either by a continuous reduction of the enclosed volume or by the continuous increase of the surface area. Both lead to almost identical results for wrinkle formation and the coarsening process, for which a scaling law for the wavenumber is obtained for a broad range of surface viscosity and rate of change of volume or area. However, for large Reynolds numbers and small changes in volume or area, wrinkling can be suppressed and surface hydrodynamics allows for global shape changes following the minimal energy configurations of the Helfrich energy for corresponding reduced volumes.
薄弹性片的起皱不稳定性可用于在广泛的长度尺度上生成周期性结构。薄弹性片或其周围介质的粘性已被证明是导致动力学过程的原因。我们在这里考虑可变形流体表面的起皱。与具有面内和面外弹性的薄弹性片不同，这些表面的特征在于面内粘性流动和面外弹性，并且已经确立为生物膜和细胞片的模型系统。我们使用这种流体动力学理论并通过连续减小封闭体积或连续增加表面积来数值探索皱纹的形成及其粗化。这两种方法对于褶皱的形成和粗化过程都产生了几乎相同的结果，对于宽范围的表面粘性和体积或面积的变化率，获得了波数的标度定律。然而，对于大雷诺数和体积或面积的小变化，起皱可以被抑制，并且表面流体动力学允许根据对应于减小的体积的 Helfrich 能量的最小能量配置进行全局形状变化。
