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Sharp Interface Three-Dimensional Electrohydrodynamic Vesicle Simulations: Formulation and Numerical Methods

David Salac (University at Buffalo SUNY), Mohammad Kolahdouz (University at Buffalo SUNY), Prerna Gera (University at Buffalo SUNY)

Computational Mechanics of Biomembranes

Mon 10:45 - 12:15

Barus-Holley 160

The behavior of vesicles in electric fields is of interest due to biomedical applications such directed drug delivery and micro-scale bio-reactors. The controlled application of electric fields can induced large shape deformations and even induce the formation of pores in the vesicle membrane. In this talk a sharp-interface computational model of the electrohydrodynamic response of vesicles in the presence of electric fields is outlined. The formulation is based on the level set method coupled to an immersed interface method solver. The physical jump conditions for the fluid pressure and velocity are developed. Closed-form solutions for the Stokes equations with an embedded, inextensible interface are created and used to test the fluids solver. The immersed interface method is also used to evaluate the electric potential field due to the embedded vesicle membrane. The time-evolution of the voltage jump due to the capacitive interface is solved for implicitly. A closed-form solution for the electric potential field is created to verify the accuracy of the electric potential solver. The algorithms are implemented in parallel the PETSc library and a custom three-dimensional mesh generation algorithm. The methods are demonstrated to be second-order accurate. Time permitting examples of vesicles in both fluid flow and electric fields will be presented.