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

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this work, we present an extensive analytical, numerical and experimental analysis of confined capillary jets extending previous studies. We propose an extended, accurate analytic model in the limit of low Reynolds flows, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show a remarkable accuracy with results from the extensive experimental exploration provided.Comment: Submitted to the Physical Review E (20-March-2008

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

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier–Stokes equations for diferent values of the shear and dilatational surface viscosities. This comparison shows the small but measurable efect of the surface viscous stresses for sufciently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the efect of the surface viscosities on the last stage of temporal evolution of the neck radius.Ministerio de Economía y Competitividad DPI2016-78887Junta de Extremadura GR1817

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

Spatial structure of shock formation

The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening and eventual overturning of a wave. Using self-similar variables in two space dimensions and a power series expansion based on powers of , being the singularity time, we show that the spatial structure of this process, which starts at a point, is equivalent to the formation of a caustic, i.e. to a cusp catastrophe. The lines along which the profile has infinite slope correspond to the caustic lines, from which we construct the position of the shock. By solving the similarity equation, we obtain a complete local description of wave steepening and of the spreading of the shock from a point. The shock spreads in the transversal direction as and in the direction of propagation as , as also found in a one-dimensional model problem