Department of Civil Engineering, Duke University, Durham, NC 27708, USA.
Biomech Model Mechanobiol. 2013 Jun;12(3):597-615. doi: 10.1007/s10237-012-0428-1. Epub 2012 Aug 21.
A chemo-mechanical model is used to capture the formation and evolution of microdomains on the deforming surface of giant unilamellar vesicles. The model is intended for the regime of vesicle dynamics characterized by a distinct difference in time scales between shape change and species transport. This is achieved by ensuring that shape equilibrium holds away from chemical equilibrium. Conventional descriptions are used to define the curvature and chemical contributions to the vesicle energetics. Both contributions are consistently non-dimensionalized. The phase-field framework is used to cast the coupled model in a diffuse-interface form. The resulting fourth-order nonlinear system of equations is discretized using the finite- element method with a uniform cubic spline basis, which satisfies global higher-order continuity. Two-dimensional and axisymmetric numerical examples of domain evolution coupled to vesicle shape deformation are presented. Curvature-dependent domain sorting and shape deformation dominated by line tension are also considered.
采用化学-力学模型来捕捉在变形的巨大单层囊泡表面上微域的形成和演化。该模型针对的是囊泡动力学的范围，其特征在于形状变化和物种输运之间的时间尺度有明显的差异。这是通过确保远离化学平衡来实现的。常规描述用于定义曲率和化学对囊泡能量学的贡献。这两个贡献都被一致地无量纲化。相场框架用于将耦合模型表示为扩散界面形式。所得的四阶非线性方程组使用具有一致三次样条基的有限元方法离散化，该基满足全局高阶连续性。呈现了与囊泡形状变形相耦合的域演化的二维和轴对称数值示例。还考虑了依赖于曲率的域分类和由线张力主导的形状变形。
