Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-02-12
Physics
Condensed Matter
Statistical Mechanics
18 pages
Scientific paper
10.1088/0305-4470/39/14/019
Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on the surface is determined completely by geometry. In equilibrium, its divergence is proportional to the Laplace pressure, normal to the surface, maintaining the constraint on the volume. It is shown that this source itself can be expressed as the divergence of a position-dependent surface stress. As a consequence, the equilibrium can be described in terms of a conserved `effective' surface stress. Various non-trivial geometrical consequences of this identification are explored. In a cylindrical geometry, the cross-section can be viewed as a closed planar Euler elastic curve. With respect to an appropriate centre the effective stress itself vanishes; this provides a remarkably simple relationship between the curvature and the position along the loop. In two or higher dimensions, it is shown that the only geometry consistent with the vanishing of the effective stress is spherical. It is argued that the appropriate generalization of the loop result will involve `null' stresses.
No associations
LandOfFree
Laplace pressure as a surface stress in fluid vesicles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Laplace pressure as a surface stress in fluid vesicles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Laplace pressure as a surface stress in fluid vesicles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-166799