Eur. Phys. J. B 29, 317-322 (2002)
https://doi.org/10.1140/epjb/e2002-00308-5

Elasticity and shape equation of a liquid membrane

Institute of Solid State Physics, Bulgarian Academy of Sciences, Laboratory of Liquid Crystals, 72 Tzarigradsko chaussee blvd., Sofia 1784, Bulgaria

Corresponding author: ^a bivas@issp.bas.bg

Received: 4 February 2002
Revised: 15 April 2002
Published online: 2 October 2002

Abstract

The density of the elastic energy of a deformed membrane in a liquid state is calculated. The thermodynamic equilibrium of its different parts is taken into account. The shape equation of a closed membrane is deduced. The quantity which keeps its value, when the variations of the energy of the system are calculated, is not the area of the deformed membrane, but its area in the flat tension free state. Because of this, additional terms appear in the second variation around the stable state. The case of a lipid bilayer and its fluctuations is examined for both free and blocked exchange of molecules between the monolayers, comprising the bilayer.