Electrical Conductivity of a Stretching Viscoelastic Filament

Long polymeric chains highly stretched and aligned with the flow confer a strong mechanical anisotropy on a viscoelastic solution. The electrically-driven transport of free ions under such conditions is far from being understood. In this paper, we determine experimentally whether the above-mentioned deviation from isotropy affects the electric charge transport across the liquid. To this end, we measure the electrical conductivity in the flow (stretching) direction of the cylindrical liquid filament formed in the elasto-capillary thinning that arises during the breakup of a viscoelastic liquid bridge. First, we examine the behavior of monodisperse solutions of polyethylene oxide (PEO) in a mixture of glycerine and water. For all the concentrations and molecular weights considered, the filament conductivity remains practically the same as the isotropic conductivity measured under hydrostatic conditions. However, we observe a decrease in the electric current at the end of elasto-capillary regime which may partially be attributed to the reduction of the liquid conductivity. Then, we measure the conductivity of bidisperse solutions of PEO with very different molecular weights. In this case, a significant decrease in conductivity is observed as the filament radius decreases. This constitutes the first experimental evidence of ion mobility reduction in stretching viscoelastic filaments, a relevant effect in applications such as electrospinning.

Thermal fluctuations in capillary thinning of thin liquid films

Thermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry are, however, non-planar. Thinning of such films not just results from the interplay between stabilizing surface tension forces and destabilizing van der Waals forces, but also from drainage due to curvature differences. This work explores the influence of thermal fluctuations on the dynamics of thin non-planar films subjected to drainage, with their dynamics governed by two parameters: the strength of thermal fluctuations, $\unicode[STIX]{x1D703}$, and the strength of drainage, $\unicode[STIX]{x1D705}$. For strong drainage ($\unicode[STIX]{x1D705}\gg \unicode[STIX]{x1D705}_{tr}$), we find that the film ruptures due to the formation of a local depression called a dimple that appears at the connection between the curved and flat parts of the film. For this dimple-dominated regime, the rupture time, $t_{r}$, solely depends on $\unicode[STIX]{x1D705}$, according to the earlier reported scaling, $t_{r}\sim \unicode[STIX]{x1D705}^{-10/7}$. By contrast, for weak drainage ($\unicode[STIX]{x1D705}\ll \unicode[STIX]{x1D705}_{tr}$), the film ruptures at a random location due to the spontaneous growth of fluctuations originating from thermal fluctuations. In this fluctuations-dominated regime, the rupture time solely depends on $\unicode[STIX]{x1D703}$ as $t_{r}\sim -(1/\unicode[STIX]{x1D714}_{max})\ln (\sqrt{2\unicode[STIX]{x1D703}})^{\unicode[STIX]{x1D6FC}}$, with $\unicode[STIX]{x1D6FC}=1.15$. This scaling is rationalized using linear stability theory, which yields $\unicode[STIX]{x1D714}_{max}$ as the growth rate of the fastest-growing wave and $\unicode[STIX]{x1D6FC}=1$. These insights on if, when and how thermal fluctuations play a role are instrumental in predicting the dynamics and rupture time of non-flat draining thin films.