Instability and Deformation of a Spherical Vesicle by Pressure

Abstract

The infinitesimal stability of a spherical vesicle (closed membrane) is studied as a function of the pressure difference between the outer and inner media. It is found that above some threshold pressure the spherical vesicle can be deformed into a shape associated with $l\mathrm{th}$-order spherical harmonics. The comparison with numerical examples calculated previously by Deuling and Helfrich shows good agreement. Some applications to red blood cells are discussed.