Equilibrium electrodeformation of a spheroidal vesicle in an ac electric field

Abstract

In this work, we develop a theoretical model to explain the equilibrium spheroidal deformation of a giant unilamellar vesicle (GUV) under an alternating (ac) electric field. Suspended in a leaky dielectric fluid, the vesicle membrane is modeled as a thin capacitive spheroidal shell. The equilibrium vesicle shape results from the balance between mechanical forces from the viscous fluid, the restoring elastic membrane forces, and the externally imposed electric forces. Our spheroidal model predicts a deformation-dependent transmembrane potential, and is able to capture large deformation of a vesicle under an electric field. A detailed comparison against both experiments and small-deformation (quasispherical) theory showed that the spheroidal model gives better agreement with experiments in terms of the dependence on fluid conductivity ratio, permittivity ratio, vesicle size, electric field strength, and frequency. The spheroidal model also allows for an asymptotic analysis on the crossover frequency where the equilibrium vesicle shape crosses over between prolate and oblate shapes. Comparisons show that the spheroidal model gives better agreement with experimental observations.

Integral equation methods for vesicle electrohydrodynamics in three dimensions

“…The tension is uniformly higher for high Ca case as shown in Figure 4. Finally, note that if the conductivity of the interior fluid is higher compared to the exterior, the equilibrium shapes are in form of prolates as supported by previous theoretical predictions [33].…”

“…Using small deformation theory, they were able to obtain the experimentally observed prolate-to-oblate shape transitions [1] that depend on the interior-to-exterior fluid conductivity ratio (see [52] for a review on the dynamics of vesicles in electric fields). A spheroidal model has been developed in [33,55] that can handle large deformations (as long as the shape remains spheroidal). While the aforementioned models offered key insights in some settings, they cannot, however, be applied to general three-dimensional EHD flows.…”

Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method

“…For a DC electric field, theoretical models have been developed for a slightly deformed vesicle [10,11,16,37] and a spheroidal vesicle [35,46,47]. The extension to a vesicle under an AC (alternative current) electric field can be found in [6,12,32,43]. These theoretical results are limited by the model assumptions such as small deformation from a nearly spherical vesicle and the vesicle can only take a spheroidal shape.…”

Vesicle dynamics in uniform electric fields: squaring and breathing

“…6 Electric fields have also been used to modulate the phase transitions in tri-component membranes (made of neutral lipids), and found to decrease the miscibility temperature. 3,5,[8][9][10][11][12][13][14][15] These models, however, are limited to nearly spherical 3,5,[8][9][10][11][12] or strictly spheroidal shapes, [13][14][15] and cannot explain the peculiar drum-like shapes observed in the experiments with quasi-spherical vesicles. 3,5,[8][9][10][11][12][13][14][15] These models, however, are limited to nearly spherical 3,5,[8][9][10][11][12] or strictly spheroidal shapes, [13][14][15] and cannot explain the peculiar drum-like shapes observed in the experiments with quasi-spherical vesicles.…”