Lázaro Guillermo R, Pagonabarraga Ignacio, Hernández-Machado Aurora
Martin Fisher School of Physics, Brandeis University, 02454, Waltham, MA, USA.
Departament de Fisica de la Matèria Condensada, Universitat de Barcelona, Av. Diagonal 645, E08028, Barcelona, Spain.
Eur Phys J E Soft Matter. 2017 Sep;40(9):77. doi: 10.1140/epje/i2017-11566-8. Epub 2017 Sep 19.
Phase-field models have been extensively used to study interfacial phenomena, from solidification to vesicle dynamics. In this article, we analyze a phase-field model that captures the relevant physical features that characterize biological membranes. We show that the Helfrich theory of elasticity of membranes can be applied to phase-field models, allowing to derive the expressions of the stress tensor, lateral stress profile and elastic moduli. We discuss the relevance and interpretations of these magnitudes from a phase-field perspective. Taking the sharp-interface limit we show that the membrane macroscopic equilibrium equation can be derived from the equilibrium condition of the phase-field interface. We also study two dynamic models that describe the behaviour of a membrane. From the study of the relaxational behaviour of the membrane we characterize the relevant dynamics of each model, and discuss their applications.
相场模型已被广泛用于研究界面现象，从凝固到囊泡动力学。在本文中，我们分析了一个相场模型，该模型捕捉了表征生物膜的相关物理特征。我们表明，膜的赫尔弗里希弹性理论可以应用于相场模型，从而能够推导出应力张量、横向应力分布和弹性模量的表达式。我们从相场的角度讨论了这些量的相关性和解释。取尖锐界面极限，我们表明膜的宏观平衡方程可以从相场界面的平衡条件推导出来。我们还研究了两个描述膜行为的动力学模型。通过对膜的弛豫行为的研究，我们表征了每个模型的相关动力学，并讨论了它们的应用。
