Eur. Phys. J. E (2017) 40: 77
https://doi.org/10.1140/epje/i2017-11566-8

Regular Article

Elastic and dynamic properties of membrane phase-field models

¹ Martin Fisher School of Physics, Brandeis University, 02454, Waltham, MA, USA
² Departament de Fisica de la Matèria Condensada, Universitat de Barcelona, Av. Diagonal 645, E08028, Barcelona, Spain
³ Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain
⁴ CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne, Batochime, Avenue Forel 2, 1015, Lausanne, Switzerland
⁵ Institute of Nanoscience and Nanotechnology (IN2UB), University of Barcelona, Barcelona, Spain

^* e-mail: grolazaro@gmail.com

Received: 18 April 2017
Accepted: 22 August 2017
Published online: 19 September 2017

Abstract

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.