Self-similar breakup of polymeric threads as described by the Oldroyd-B model

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations

Self-similarity in the breakup of very dilute viscoelastic solutions

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.When pushed out of a syringe, polymer solutions form droplets attached by long and slender cylindrical filaments whose diameter decreases exponentially with time before eventually breaking. In the last stages of this process, a striking feature is the self-similarity of the interface shape near the end of the filament. This means that shapes at different times, if properly rescaled, collapse onto a single universal shape. A theoretical description based on the Oldroyd-B model was recently shown to disagree with existing experimental results. By revisiting these measurements and analysing the interface profiles of very diluted polyethylene oxide solutions at high temporal and spatial resolution, we show that they are very well described by the model. © 2020 Cambridge University Press

Evolutionary and Ecological Trees and Networks

Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations among which gene flow occurs. This flow can also be represented as a network. In this paper we briefly show some properties of these complex networks of evolutionary and ecological relationships. First, we characterize large scale evolutionary relationships in the Tree of Life by a degree distribution. Second, we represent genetic relationships between individuals of a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum Spanning Tree. Finally, relationships among plant shoots inside populations are represented as networks of genetic similarity.Comment: 6 pages, 5 figures. To appear in Proceedings of the Medyfinol06 Conferenc

Author Correction: Infuence of the surface viscous stress on the pinch‑of of free surfaces loaded with nearly‑inviscid surfactants [Corrección]

Correction to: Scientifc Reports https://doi.org/10.1038/s41598-020-73007-1, published online 30 September 2020. The original version of this Article contained errors

Enhancement of the stability of the flow focusing technique for low-viscosity liquids

Article number 115039We propose a modified flow focusing configuration to produce low-viscosity microjets at much smaller flow rates than those reached by the standard configuration. In the modified flow focusing device, a sharpened rod blocks the recirculation cell appearing in the tapering liquid meniscus for low flow rates, which considerably improves its stability. We measured the minimum flow rates attainable with the modified configuration and compared the results with the corresponding values for the standard technique. For moderate and large applied pressure drops, the minimum flow rate reached with the modified configuration was about five times smaller than its counterpart in the standard configuration. The Weber numbers of the jets produced with the modified flow focusing configuration were considerably smaller than those with the standard technique. Numerical simulations were conducted to show how the presence of the inner rod substantially changes the flow pattern in the liquid meniscus.Ministerio de Ciencia y Educación, Junta de Extremadura y Junta de Andalucía (España) DPI2010-21103, GR10047 y P08-TEP-0412

Global stability analysis of axisymmetric liquid-liquid flow focusing

Article number A10We analyse both numerically and experimentally the stability of the steady jetting tip streaming produced by focusing a liquid stream with another liquid current when they coflow through the orifice of an axisymmetric nozzle. We calculate the global eigenmodes characterizing the response of this configuration to small-amplitude perturbations. In this way, the critical conditions leading to the instability of the steady jetting tip streaming are determined. The unstable perturbations are classified according to their oscillatory character and to the region where they originate (convective and absolute instability). We derive and explain in terms of the velocity field a simple scaling law to predict the diameter of the emitted jet. The numerical stability limits are compared with experimental results, finding reasonable agreement. The experiments confirm the existence of the two instability mechanisms predicted by the global stability analysisMinisterio de Economía, Industria y Competitividad (España) DPI2016-78887Junta de Extremadura GR18175Junta de Andalucía P18-FR-362

Effect of an axial electric field on the breakup of a leaky-dielectric liquid filament

Article number 092114We study experimentally and numerically the thinning of Newtonian leaky-dielectric filaments subjected to an axial electric field. We consider moderately viscous liquids with high electrical permittivity. We analyze the influence of the electric field on the formation of satellite droplets from the breakup of the filaments in the experiments. The electric force delays the free surface pinching. Two electrified filaments with the same minimum radius are thin at the same speed regardless of when the voltage is applied. The numerical simulations show that the polarization stress is responsible for the pinching delay observed in the experiments. Asymptotically close to the pinching point, the filament pinching is dominated by the diverging hydrodynamic forces. The polarization stress becomes subdominant even if this stress also diverges at this finite-time singularity. © 2021 Author(s).Ministerio de Economía, Industria y Competitividad (España) PID2019–108278RBJunta de Extremadura GR1817