Breakup of an electrified viscoelastic liquid bridge

Abstract

We study both numerically and experimentally the breakup of a viscoelastic liquid bridge between two parallel electrodes. We solve the leaky-dielectric FENE-P model to describe the dynamical response of the liquid bridge under isothermal conditions. The results show that the surface charge screens the inner electric field perpendicular to the free surface over the entire dynamical process. The liquid bridge deformation produces a normal electric field on the outer side of the free surface that is commensurate with the axial one. The surface conduction does not significantly affect the current intensity in the time interval analyzed in the experiments. The force due to the shear electric stress becomes comparable to both the viscoelastic and surface tension forces in the last stage of the filament. However, it does not alter the elasto-capillary balance in the filament. The extensional relaxation times approximately coincides with the stress relaxation time prescribed in the FENE-P model. We measure experimentally the filament electrical conductivity and extensional relaxation time for PEO dissolved in deionized water and in a mixture of water and glycerine. We compare the filament electrical conductivity with the value measured in hydrostatic conditions for the same estimated temperature. Good agreement was found for PEO dissolved in water+glycerine, which indicates that the change of the filament microscopic structure due to the presence of stretched polymeric chains does not significantly alter the ion mobility in the stretching direction. Significant deviations are found for PEO dissolved in deionized water that may be attributed to the heat transferred to the ambient, neglected in the calculation of the filament temperature. The extensional relaxation time measured from the images acquired during the filament thinning hardly depends on the applied voltage.