| The work presented here falls into three categories. First, the dynamics of a closed lipid bilayer vesicle in a linear viscous flow is investigated. The effects of membrane fluidity, incompressibility and resistance to bending are taken in account, as well as the transport of lipid molecules along the monolayer surfaces and intermonolayer friction. Assuming a nearly spherical vesicle, the leading-order perturbation analysis for small excess lipids on the surface results in a nonlinear system of coupled ordinary differential equations for the dynamics of the vesicle shape, and the density of lipids on the monolayers. Multiple solution states are found as a function of problem parameters. The dynamics and stability of these solutions is discussed.;Next, the dynamics of a lipid bilayer membrane subjected to a DC electric pulse is studied. The thin lipid membrane is impermeable to ions and thus acts as a capacitor. The model consists of Maxwells equations, conservation of current, and the Stokes equations. Small amplitude perturbations of a planar membrane are considered. First, the electrohydrodynamics of a Helfrich interface is sought. A coupled system of time dependent ODEs is found for the interfacial height, and perturbations to the electric field. Perturbations are enhanced by an increasing mismatch in the bulk fluid conductivities, and the applied electric field strength. The electrohydrodynamics of a bilayer interface is also examined. Similar physical processes arising from the electric properties of the system drive a fluid flow whose tangential components at the interface create regions of increasing and decreasing lipid density.;In the last part, a vesicles response to an combined uniform DC electric field and shearing flow is investigated. For a Helfrich interface, numerical integration of the resulting system of non-autonomous ODEs yields transient dynamics which depend on the material properties of the fluids. Assuming constant coefficients, multiple solution states are found as a function of material properties. The stability of these solutions states is discussed. For the lipid bilayer, regions of varying lipid density difference are found when the electric field is applied. The presented theoretical findings are relevant to understanding the physical mechanisms of electroporation. |
