Modeling the electrohydrodynamics of three-dimensional vesicles
Kolahdouz, Mohammad Ebrahim
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In this work a numerical method is presented to model the electrohydrodynamics of a three-dimensional vesicle. The objective of this study is to develop robust numerical algorithms to solve the physical governing equations of the vesicle in the presence of fluid flow and DC electric fields. Furthermore the model will be able to predict the fast dynamics of the vesicle exposed to strong fields for a wide range of material properties and deformations that cannot be easily captured in experimental settings. The vesicle membrane is modeled as an infinitesimally thin capacitive interface. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which computes the electric potential field and the trans-membrane potential simultaneously. The interface is tracked through the use of a semi-implicit, gradient-augmented level set method. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The valdiation of the hydrodynamic model was examined in the light of experimental data and observations. The two major modes of the vesicle motion in the linear shear flow namely the tank-treading and tumbling regimes, were studied. Simulation results show a very good agreement between the present results and the experimental data. The electrohydrodynamic results also match well with previously published experimental, analytic and two-dimensional computational works and the model is capable of capturing the type of topological changes previously observed in experiments. A parameter study of different important material properties is carried out for the transition between oblate and prolate ellipsoidal shapes in order to estimate the critical parameter tresholds for this transition to happen. In addition, investigation of the vesicle behavior under the combined effects of shear flow and weak DC electric fields reveals the remarkable influence of the electric field in changing the standard behaviors of tank-treading and tumbling vesicles. If the electric field is strong enough the induced resistance caused by the electric field may alter the behavior of a tumbling vesicle into a tank-treading motion.