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.Graphical abstract
Highlights
From a theoretical perspective, membranes can be treated as interfaces with specific elastic properties, namely a vanishing surface tension and resistance to bend
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 have two main goals: on the one hand, to show that the mechanic formalism of the classic theory of membranes [24,25] can be applied to phase-field models, allowing to sequentially recover the expressions of the stress tensor, lateral stress profile, and elastic moduli, in terms of the order parameter profile
Summary
Membranes can be treated as interfaces with specific elastic properties, namely a vanishing surface tension and resistance to bend. Provided that classic interfaces are much simpler than membranes, the understanding of the elastic properties of membrane phase-field models is essential for a precise control and interpretation of the subsequent studies. We have two main goals: on the one hand, to show that the mechanic formalism of the classic theory of membranes [24,25] can be applied to phase-field models, allowing to sequentially recover the expressions of the stress tensor, lateral stress profile, and elastic moduli, in terms of the order parameter profile. We aim to characterize and discuss two different dynamic models and show how the method can be applied to study relaxational processes of the membrane. The Helfrich theory has been the basis to explain an important number of membrane phenomena [5, 31, 32], and it remains largely valid in general problems in which the cytoskeleton or the balance between leaflets do not play a key role
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