The relationship between viscoelasticity and elasticity

Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability

Nonparallel local spatial stability analysis of pipe entrance swirling flows

A spatial local viscous stability analysis of a swirling flow developing in a cylindrical pipe has been carried out numerically. Even at moderately low swirl strengths, we have found the existence of centrifugal modes in addition to the shear ones found in previous stability analysis of nonswirling flows developing in pipes. It is found that these centrifugal instabilities develop at Reynolds numbers that are much lower than those required for the growing of the shear instability. Moreover, the extent of the region where centrifugal instabilities appear is much larger than that where the shear layer instability grows. We have found from the analysis that the most unstable mode was the counter-rotating one (n = -1). The critical Reynolds number for which linear analysis predicts the growth of the convective instabilities is for the centrifugal modes one hundred times smaller than for the shear layer ones

Factores que influyen en los consumidores para no exigir su comprobante de pago de sus transacciones en el mercado de Piura

Este estudio tuvo como objetivo, describir los factores que influyen en los consumidores para no exigir comprobante de pago en sus transacciones comerciales, en el distrito de Piura. Para contrastar la hipótesis, se realizó una encuesta a 384 consumidores del mercado Modelo de Piura. Una vez aplicado el cuestionario, se analizaron los datos, lo cual permitió confirmar la hipótesis planteada; asimismo, las causas que conllevan a que los consumidores no exijan comprobante de pago de sus transacciones en el distrito de Piura, entre las cuales tenemos: 1) La falta de cultura tributaria, 2) El bajo nivel de comportamiento tributario, 3) Los inadecuados sistemas de comunicación e información que no permiten una buena orientación a los contribuyentes del mercado del distrito de Piura, lo que origina que cada día la evasión tributaria sea mayor

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

Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses.We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.Ministerio de Economía y Competitividad DPI2013-46485-C3-1-R, TRA2013- 45808-RJunta de Extremadura GR1004

Vortex breakdown in a water-spout flow

The numerical study of the steady axisymmetric air-water flow in a vertical sealed cylinder, driven by the rotating top disk, describes topological transformations as the rotation intensifies. The air meridional flow (AMF) and swirl induce meridional motions of opposite directions in water. For slow (fast) rotation, the effect of AMF (swirl) dominates. For very fast rotation, large-scale regions of clockwise meridional circulation in air and water are separated by a thin layer of anticlockwise circulation adjacent to the interface in water. This pattern develops for other fluids as well. Physical reasoning behind the flow evolution is provided