Van der Waals interactions between planar substrate and tubular lipid membranes undergoing pearling instability
Abstract
In the current article we study the behavior of the van der Waals force between a planar substrate and an axisymmetric bilayer lipid membrane undergoing pearling instability, caused by uniform hydrostatic pressure difference. To do so, the recently suggested "surface integration approach" is used, which can be considered a generalization of the well known and widely used Derjaguin approximation. The static equilibrium shape after the occurrence of the instability is described in the framework of Helfrich's spontaneous curvature model. Some specific classes of exact analytical solutions to the corresponding shape equation are considered, and the components of the respective position vectors given in terms of elliptic integrals and Jacobi elliptic functions. The mutual orientation between the interacting objects is chosen such that the axis of revolution of the distorted cylinder be parallel to the plane bounding the substrate. Based on the discussed models and approaches we made some estimations for the studied force in real experimentally realizable systems, thus showing the possibility of pearling as an useful technique for reduction of the adhesion in variety of industrial processes using lipid membranes as carriers.
- Publication:
-
Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'17
- Pub Date:
- October 2017
- DOI:
- 10.1063/1.5007402
- Bibcode:
- 2017AIPC.1895i0002V