Cylindrical Fluid Film Statics And Dynamics Properties

Since eighties of the 20th century, membranes and vesicles as main parts of soft matter or soft condensed matter have aroused many interests of scientists, such as physicists, chemists and biologists, because of their attractive characteristics. The development of soft matter physics indicates the progress of condensed matter physics in the 21st century.Recognizing that the vesicle consisting of amphiphiles bilayer membrane is just like a nematic liquid crystal cell, Helfrich gave the elastic energy of the fluid membrane and the shape equation. In this paper, we give a brief introduction to the Helfrich elastic theory. To solve the Helfrich equation under the physical conditions of vesicles, a Taylor series method is introduced, which offers a unified method to reproduce the exact solution including the famous axisymmetrical constant-curvature surfaces and the biconcave shape solution.The equilibrium condition for the cylindrical configuration in fluid membrane is re-examined in this paper, using the direct and the indirect variational method and taking account of possible influences of its topology. Since the pure cylindrical vesicles without ends are unstable even non-existence, approximations of torus and cylinder with spherical ends are utilized. The result from the former approximation means the condition of infinite long cylinder, which gives us no useful information. By spherically topological approximation, we get a set of conditions, all of which specify the range of parameters. Evidently, spherically topological approximation is more usable than the other. When our result is used to examine a debate related to the integral constant C, a clean conclusion is reached, that Helfrich shape equation with C=0 is only valid for spherical topology vesicles.Applying laser tweezers to cylindrical vesicles of lipid bilayers induces an instability, which propagates down the vesicle leaving behind it a peristaltic state, which appears under the microscope as pearls on a string. We make up a simple model based on the microscopic mechanism of the membrane to investigate this phenomenon. The model proves reasonable after we quantify the velocity of the pearls drift slowly towards the laser trap.