Mathematics Colloquia and Seminars

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Giant unilamellar vesicles (GUVs), on the order of tens of micrometers in diameter, present an interesting analogy with living cells due both to their size and to the structural similarity between synthetic lipid bilayers and biological membranes. Many applications require GUVs of a proscribed size, but monodisperse suspensions are difficult to produce. The most widely used approach for synthesizing GUVs is electroformation, in which a low frequency electric field destabilizes planar hydrated lipid bilayers and ultimately produces a widely polydisperse suspension. Here we discuss two new phenomena observed when electric fields are applied to polydisperse vesicle suspensions near electrodes. First, we demonstrate an electrohydrodynamic (EHD) technique for separating GUVs by size in polydisperse suspensions. An oscillatory electric field generates EHD flow around each vesicle. Nearby vesicles are entrained in the flow and the vesicles move toward one another. Upon aggregation, smaller vesicles are pulled underneath the larger vesicles, ultimately lifting them off of the electrode. By appropriate modulation of the electric field, we can remove more than 90% of the smallest vesicles from a suspension of electroformed giant lipid vesicles. In contrast to the ‘lifting’ behavior, we also observe ‘orbiting’ behavior in which small vesicles orbit around larger vesicles in preferred orientations. Viewed from above, the vesicles appear to form dynamic ‘bands’ at prescribed angles, separated by regions devoid of vesicles. We interpret the angular segregation in terms of induced dipolar interactions, and we propose a minimalist model based on point dipoles rotating in a circular flow field. We demonstrate that this minimalist model yields a surprisingly diverse phase diagram of vesicle trajectories, including Cassini ovals and epitrochoids, and we show that a three-dimensional extension of the model yields vesicle bands qualitatively consistent with the experimental observations.