Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Interfacial instabilities of a fluid annulus in a rotating Hele-Shaw cell

We have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele-Shaw cell rotating with angular velocity Omega. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.

The influence of the symmetry energy on the giant monopole resonance of neutron-rich nuclei analyzed in Thomas-Fermi theory

We analyze the influence of the density dependence of the symmetry energy on the average excitation energy of the isoscalar giant monopole resonance (GMR) in stable and exotic neutron-rich nuclei by applying the relativistic extended Thomas-Fermi method in scaling and constrained calculations. For the effective nuclear interaction, we employ the relativistic mean field model supplemented by an isoscalar-isovector meson coupling that allows one to modify the density dependence of the symmetry energy without compromising the success of the model for binding energies and charge radii. The semiclassical estimates of the average energy of the GMR are known to be in good agreement with the results obtained in full RPA calculations. The present analysis is performed along the Pb and Zr isotopic chains. In the scaling calculations, the excitation energy is larger when the symmetry energy is softer. The same happens in the constrained calculations for nuclei with small and moderate neutron excess. However, for nuclei of large isospin the constrained excitation energy becomes smaller in models having a soft symmetry energy. This effect is mainly due to the presence of loosely-bound outer neutrons in these isotopes. A sharp increase of the estimated width of the resonance is found in largely neutron-rich isotopes, even for heavy nuclei, which is enhanced when the symmetry energy of the model is soft. The results indicate that at large neutron numbers the structure of the low-energy region of the GMR strength distribution changes considerably with the density dependence of the nuclear symmetry energy, which may be worthy of further characterization in RPA calculations of the response function.

Scaling calculation of isoscalar giant resonances in relativistic Thomas-Fermi theory

We derive analytical expressions for the excitation energy of the isoscalar giant monopole and quadrupole resonances in finite nuclei, by using the scaling method and the extended ThomasFermi approach to relativistic mean-field theory. We study the ability of several nonlinear σω parameter sets of common use in reproducing the experimental data. For monopole oscillations the calculations agree better with experiment when the nuclear matter incompressibility of the relativistic interaction lies in the range 220260 MeV. The breathing-mode energies of the scaling method compare satisfactorily with those obtained in relativistic RPA and time-dependent mean-field calculations. For quadrupole oscillations, all the analyzed nonlinear parameter sets reproduce the empirical trends reasonably well.

Scaling in relativistic Thomas-Fermi approach for nuclei

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the ThomasFermi approach. The ThomasFermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use.

Perturbing Hele-Shaw flow with a small gap gradient

A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changed by the perturbation.

Muerte en Venecia de Thomas Mann o la via plutarquea hacia Eros

En Muerte en Venecia Thomas Mann se refiere explícitamente al Simposio y al Fedro de Platón para explicar la relación entre Gustav von Aschenbach y Tadzio, pero oculta que su novela se inspira también en el Erótico de Plutarco. ¿Por qué? El objetivo de este artículo es justamente revelar las razones de este proceder. En efecto, Plutarco elogia el amor matrimonial en el Erótico y éste no es el camino que sigue Mann, pero, al mismo tiempo, el escritor alemán halla en el diálogo plutarqueo todo lo necesario para construir su historia de amor masculino y decide no prescindir de él.

Thomas Mann's Death in Venice or Plutarch's way towards Eros

In Death in Venice Thomas Mann refers explicitly to Plato's Symposium and Phaedrus in order to explain the relationship between Gustav von Aschenbach and Tadzio but he hides that his novel also depends on Plutarch's Eroticus. Why? The aim of this article is precisely to reveal the different reasons for such an attitude. Indeed, Plutarch speaks highly of conjugal love in his Eroticus and this way is not followed by Mann in Death in Venice but, at the same, the German writer finds in this Plutarch's philosophical dialogue all the necessary elements to build his story of masculine love and decides not to manage without it.

La mort a Venècia de Thomas Mann o la via plutarquea vers Eros

A Mort a Venècia Thomas Mann es refereix explícitament al Simposi i al Fedre de Plató per explicar la relació entre Gustav von Aschenbach i Tadzio, però amaga que la seva novel·la s'inspira també en l'Eròtic de Plutarc. Per què? L'objectiu d'aquest article és justament revelar les raons d'aquest capteniment. En efecte, Plutarc elogia l'amor matrimonial a l'Eròtic i aquest no és el camí que segueix Mann, però, alhora, l'escriptor alemany troba en el diàleg plutarqueu tot el que necessita per bastir la seva història d'amor masculí i decideix no prescindir-ne.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

The effect of lattice defects on Hele-Shaw flow over an etched lattice

We examine the patterns formed by injecting nitrogen gas into the center of a horizontal, radial Hele-Shaw cell filled with paraffin oil. We use smooth plates and etched plates with lattices having different amounts of defects (010 %). In all cases, a quantitative measure of the pattern ramification shows a regular trend with injection rate and cell gap, such that the dimensionless perimeter scales with the dimensionless time. By adding defects to the lattice, we observe increased branching in the pattern morphologies. However, even in this case, the scaling behavior persists. Only the prefactor of the scaling function shows a dependence on the defect density. For different lattice defect densities, we examine the nature of the different morphology phases.

El Pigmalión de Shaw, manifiesto teatral de la lingüística

La comedia Pigmalión, que Bernard Shaw escribió en 1912 y estrenó al año siguiente, es una proclamación artística de la lingüística. A pesar de la popularidad de la obra, es un acontecimiento que se conoce como una anécdota extravagante. El extraordinario mérito de Pigmalión ha pasado desapercibido para la historia de la lingüística. Su mérito estriba en la calidad teatral, la capacidad prospectiva de Shaw y la intención social de su mensaje. Shaw anuncia la utilidad de la lingüística en facetas que, décadas después, se conocerán como sociolingüística, planificación lingüística y logopedia. Por otra parte, se ha relacionado de modo simplista el personaje del profesor Higgins al fonetista H. Sweet. The play Pygmalion, that Bernard Shaw wrote in 1912 and released the following year, is an artistic proclamation of Linguistics. Despite the popularity of the play, this event is known as an extravagant story. The History of Linguistics does not recognize the extraordinary merit of Pygmalion. Its merit lays in the theatrical quality ant the social intention of the message. Shaw announces the usefulness of Linguistics in facets that will be known as Sociolinguistics, Language Planning and Speech Therapy. And furthermore, in a simplistic way, the character of Professor Higgins has been linked to the phonetician H. Sweet.

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme inter-actions and from relativistic mean field theory. VWK consist s of the Thomas-Fermi part plus a pure, perturbative h 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total en energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of h 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g.208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an adhoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

Radial displacement of a fluid annulus in a rotating Hele-Shaw cell

The radial displacement of a fluid annulus in a rotating circular HeleShaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy"s law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interfacemotion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film left by the inner interface is obtained as a function of Ca.