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In this paper, we develop a new boundary integral equation formulation that describes the coupled electro- and hydro-dynamics of a vesicle suspended in a viscous fluid and subjected to external flow and electric fields. The dynamics of the vesicle are characterized by a competition between the elastic, electric and viscous forces on its membrane. The classical Taylor–Melcher leaky-dielectric model is employed for the electric response of the vesicle and the Helfrich energy model combined with local inextensibility is employed for its elastic response. The coupled governing equations for the vesicle position and its transmembrane electric potential are solved using a numerical method that is spectrally accurate in space and first-order in time. The method uses a semi-implicit time-stepping scheme to overcome the numerical stiffness associated with the governing equations. [ABSTRACT FROM AUTHOR]

Using a rod theory formulation, we derive equations of state for a thin elastic membrane subjected to several different boundary conditions--clamped, simply supported, and periodic. The former is applicable to membranes supported on a softer substrate and subjected to uniaxial compression. We show that a wider family of quasistatic equilibrium shapes exist beyond the previously obtained analytical solutions. In the latter case of periodic membranes, we were able to derive exact solutions in terms of elliptic functions. These equilibria are verified by considering a fluid-structure interaction problem of a periodic, length-preserving bilipid membrane modeled by the Helfrich energy immersed in a viscous fluid. Starting from an arbitrary shape, the membrane dynamics to equilibrium are simulated using a boundary integral method. [ABSTRACT FROM AUTHOR]