A transient solution for vesicle electrode formation and relaxation

A transient analysis for vesicle deformation under direct-current electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the latter, both a membrane-charging and a membrane-mechanical model are supplied. The vesicle is assumed to remain spheroidal in shape for all times. The main result is an ordinary differential equation governing the evolution of the vesicle aspect ratio. The effects of initial membrane tension and pulse length are examined. The model prediction is extensively compared with experimental data, and is shown to accurately capture the system behavior in the regime of no or weak electroporation. More importantly, the comparison reveals that vesicle relaxation obeys a similarity law regardless of the means of deformation. The process is governed by a single time scale that is a function of the vesicle initial radius, the fluid viscosity, and the initial membrane tension. This similarity scaling law can be used to calculate membrane properties from experimental data.