Thermal Casimir effect in lipid bilayer tubules

We calculate the thermal Casimir effect for a dielectric tube of radius R and thickness delta formed from a membrane in water. The method uses a field-theoretic approach in the grand canonical ensemble. The leading contribution to the Casimir free energy behaves as -k(B)TL kappa(c)/R giving rise to an attractive force which tends to contract the tube. We find that kappa(c)similar to 0.3 for the case of typical lipid membrane t tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilize such tubes against the bending stress which tends to increase the radius.