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We develop an analytical theory to explain the experimentally-observedmorphological transitions of giant vesicles induced by AC electric fields (1).The model treats the inner and suspending media as lossy dielectrics, while themembrane as an ion-impermeable flexible incompressible-fluid sheet. The vesicleshape is obtained by balancing electric, hydrodynamic, and bending stressesexerted on the membrane. Considering a nearly spherical vesicle, the solutionto the electrohydrodynamic problem is obtained as a regular perturbationexpansion in the excess area.  The theory predicts that stationary vesicle deformation depends on fieldfrequency and conductivity conditions. If the inner fluid is more conductingthan the suspending medium, the vesicle always adopts a prolate shape. In theopposite case, the vesicle undergoes a transition from a prolate to oblateellipsoid at a critical frequency, which the theory identifies with the inversemembrane charging time. At frequencies higher than the inverse Maxwell-Wagnerpolarization time, the electrohydrodynamic stresses become too small to alterthe vesicle's quasi-spherical rest shape. The analysis shows that the evolutiontowards the stationary vesicle deformation strongly depends on membraneproperties such as viscosity. The model can be applied to rationalize thetransient and steady deformation of biological cells in electric fields.

Electrohydrodynamic model of vesicle deformation in alternating electric fields