Abstract

Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature consider the dependence of surface energy only on mean curvature with an added linear term for Gauss curvature. Therefore, for closed surfaces the Gauss curvature term can be eliminated because of the Gauss–Bonnet theorem. Rosso and Virga (Proc. Roy. Soc. Lond. A 455:1992 (1999), 4145–4168) considered the dependence on the mean and Gaussian curvatures in statics and under a restrictive assumption of the membrane inextensibility. The authors derived the shape equation as well as two scalar boundary conditions on the contact line.

In this paper — thanks to the principle of virtual working — the equations of motion and boundary conditions governing the fluid membranes subject to general dynamical bending are derived without the membrane inextensibility assumption. We obtain the dynamic “shape equation” (equation for the membrane surface) and the dynamic conditions on the contact line generalizing the classical Young–Dupré condition.

Keywords

Physics and Astronomy Classification Scheme 2010

Mathematical Subject Classification 2010

Milestones

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