Electrospray cone-jet mode for weakly viscoelastic liquids

Breakup of an electrified viscoelastic liquid bridge

We study both numerically and experimentally the breakup of a viscoelastic liquid bridge formed between two parallel electrodes. The polymer solutions and applied voltages are those commonly used in electrospinning and near-field electrospinning. We solve the leaky-dielectric finitely extensible nonlinear elastic-Peterlin (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 elastocapillary balance in the filament. As a consequence, the extensional relaxation times measured from the filament exponential thinning approximately coincides with the stress relaxation time prescribed in the FENE-P model. The above results allow us to interpret correctly the experiments. In the experiments, we measure the filament electrical conductivity and extensional relaxation time for polyethylene oxide (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 in 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. These deviations may be attributed to the heat transferred to the ambient, which is neglected in the calculation of the filament temperature. We measure the extensional relaxation time from the images acquired during the filament thinning. The relaxation times obtained in the first stage of the exponential thinning hardly depend on the applied voltage. Little but measurable influence of the applied voltage is found in the last phase of the filament thinning.

Dripping, jetting and tip streaming

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.