On the stress and torque tensors in fluid membranes

Details On the stress and torque tensors in fluid membranes On the stress and torque tensors in fluid membranes

2007-02-12

arxiv.org/abs/cond-mat/0702279v1

Physics

Condensed Matter

Soft Condensed Matter

7 pages, 5 figures

Scientific paper

We derive the membrane elastic stress and torque tensors using the standard Helfrich model and a direct variational method in which the edges of a membrane are infinitesimally translated and rotated. We give simple expressions of the stress and torque tensors both in the local tangent frame and in projection onto a fixed frame. We recover and extend the results of Capovilla and Guven [J. Phys. A, 2002, \textbf{35}, 6233], which were obtained using covariant geometry and Noether's theorem: we show that the Gaussian rigidity contributes to the torque tensor and we include the effect of a surface potential in the stress tensor. Many interesting situations may be investigated directly using force and torque balances instead of full energy minimization. As examples, we consider the force exerted at the end of a membrane tubule, membrane adhesion and domain contact conditions.

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