Linear oscillations of axisymmetric viscous liquid bridges

Small amplitude free oscillations of axisymmetric capillary bridges are considered for varying values of the capillary Reynolds number C-1 and the slenderness of the bridge Λ . A semi-analytical method is presented that provides cheap and accurate results for arbitrary values of C-1 and Λ ; several asymptotic limits (namely, C>> 1, C>>1, Λ >> 1 \ {and} \ |π -Λ |>> 1 ) are considered in some detail, and the associated approximate results are checked. A fairly complete picture of the (fairly complex) spectrum of the linear problem is obtained for varying values of C and Λ . Two kinds of normal modes, called capillary and hydrodynamic respectively, are almost always clearly identified, the former being associated with free surface deformation and the latter, only with the internal flow field; when C is small the damping rate associated with both kind of modes is comparable, and the hydrodynamic ones explain the appearance of secondary (steady or slowly-varying) streaming flow

A note on the effect of surface contamination in water wave damping

Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film

Dynamics of nearly unstable axisymmetric liquid bridges

The dynamics of a noncylindrical, axisymmetric, marginally unstable liquid bridge between two equal disks is analyzed in the inviscid limit. The resulting model allows for the weakly nonlinear description of both the (first stage of) breakage for unstable configurations and the (slow) dynamics for stable configurations. The analysis is made for both slender and short liquid brides. In the former range, the dynamics breaks reflection symmetry on the midplane between the supporting disks and can be described by a standard Duffing equation, while for short bridges reflection symmetry is preserved and the equation is still Duffing-like but exhibiting a quadratic nonlinearity. The asymptotic results compare well with existing experiments

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

Weakly nonlinear nonaxisymmetric oscillations of capillary bridges at small viscosity

Weakly nonlinear nonaxisymmetric oscillations of a capillary bridge are considered in the limit of small viscosity. The supporting disks of the liquid bridge are subjected to small amplitude mechanical vibrations with a frequency that is close to a natural frequency. A set of equations is derived for accounting the slow dynamics of the capillary bridge. These equations describe the coupled evolution of two counter-rotating capillary waves and an associated streaming flow. Our derivation shows that the effect of the streaming flow on the capillary waves cannot be a priori ignored because it arises at the same order as the leading (cubic) nonlinearity. The system obtained is simplified, then analyzed both analytically and numerically to provide qualitative predictions of both the relevant large time dynamics and the role of the streaming flow. The case of parametric forcing at a frequency near twice a natural frequency is also considere

On the steady streaming flow due to high-frequency vibration in nearly inviscid liquid bridges

The steady streaming flow due to vibration in capillary bridges is considered in the limiting case when both the capillary Reynolds number and the non-dimensional vibration frequency (based on the capillary time) are large. An asymptotic model is obtained that provides the streaming flow in the bulk, outside the thin oscillatory boundary layers near the disks and the interface. Numerical integration of this model shows that several symmetric and non-symmetric streaming flow patterns are obtained for varying values of the vibration parameters. As a by-product, the quantitative response of the liquid bridge to high-frequency axial vibrations of the disks is also obtained

Permutas financieras y mercados secundarios

Dentro del marco del comercio internacional, han hecho su aparición nuevos instrumentos de financiación de las empresas. Entre ellos destaca la operación conocida como permuta financiera o “swap”. La innovación financiera comprende un complejo proceso que abarca desde la creación de nuevos mercados e instituciones hasta el desarrollo de múltiples técnicas operativas instrumentadas en los denominados contratos financieros, terminando con un amplio juego de garantías para todas esas nuevas operaciones. Todos estos exponentes son los que se han dado en llamar, Nuevos Instrumentos Financieros. El contrato de permuta financiera se justifica porque presta determinadas funciones económicas respecto a operaciones financieras principales pasivas o activas de las empresas y en relación con la gestión y flexibilización de ciertos riesgos propios de tales operaciones principales, concretamente con el tipo de interés y con los tipos de cambio de las divisas. La reducción de costes de transacciones, el eludir barreras legales al libre movimiento internacional de los capitales, el estar consideradas como operaciones fuera de balance o la pura especulación financiera son otros de los atractivos de las permutas financieras. Para ello se realiza una aproximación conceptual, un análisis de la naturaleza jurídica del contrato de permuta financiera y de su negociabilidad, así como un estudio sobre la posibilidad de organización de los mercados financieros oficiales de permutas financieras.Within the framework of international trade, have appeared new financing instrument companies. These include the operation known as "swap". Financial innovation comprises a complex process from the creation of new markets and institutions to the development of multiple operational techniques implemented in the so-called financial contracts, ending with a broad set of guarantees for all these new operations.These exponents are those who have been called, New Financial Instruments. The swap contract is justified because it provides certain economic functions with respect to major financial operations, passive or active companies and in relation to the management and flexibility of certain inherent risks such major operations, particularly with the interest rate and the types exchange of currencies. Reducing transaction costs, the bypass legal barriers to international free movement of capital are other attractions of the swaps. For this, a conceptual approach, an analysis of the legal nature of the swap agreement and its marketability as well as a study on the possibility of organizing an official financial markets swap is performed

La protección de la propiedad intelectual

De todas las formas jurídicas de protección de la propiedad intelectual, la penal es la más enérgica y eficaz, ya que la índole de las sanciones y el carácter público del Ordenamiento actúan como resortes intimidatorios y represores contra los posibles infractores de la legalidad en la materia. Por elo, cuando se habla de protección debemos referirnos a esta forma de tutela ya que, en muchos casos, la tutela civil va a la zaga y sin duda ninguna es siempre la protección punitiva la que eligen las posibles víctimas para buscar amparo contra las infracciones de sus derechos.Of all the legal forms of protection of intellectual property, the criminal justice system is the strongest and most effective, because the nature of the sanctions and the public nature of the Order act as springs intimidating and repressive against potential violators of the law in the matter. So when we talk about protection, we should refer to this form of make it because, in many cases, civil protection lags behind and is always the punitive one what potential victims choose to seek protection against violations of their rights

El comercio de compensación en períodos de crisis

El comercio de compensación consiste en operaciones internacionales o nacionales en las que las empresas se comprometen a aceptar el pago en forma de bienes o servicios. Hay muchas formas de intercambio compensatorio, que van desde simples a complejos acuerdos de trueque, incluidas ofertas que implican acuerdos de compensación en relación con el comprador. El comercio de compensación usualmente se lleva a cabo entre las empresas privadas en los países desarrollados y los gobiernos de los países en desarrollo, aunque también se produce el intercambio compensatorio entre los países desarrollados. Se ha extendido como una forma de financiar operaciones comerciales para reducir los riesgos o superar los problemas relacionados con las divisas. Históricamente, el comercio de compensación ha tenido más éxito en periodos de crisis económica.Countertrade is a category of international or national trade in which an enterprise agrees to accept payment in the form of goods or services. The number of alternatives being used as mechanisms for the exchange of goods and services has grown in volume and acceptance. There are many forms of countertrading, ranging from simple barter agreements to complex offset deals that involve the exporter agreeing to compensatory practices with respect to the buyer. Countertrading commonly takes place between private companies in developed nations and the governments of developing countries, although countertrading also occurs between developed nations. It has become popular as a means of financing international trade to reduce risks or overcome prob¬lems associated with various national currencies. Historically, countertrading has expanded when international economies have been sluggish or in periods of recession.peerReviewe

Tendencias actuales en la responsabilidad del empresario

En los últimos tiempos la noción de empresario ha sufrido una ampliación conceptual, motivada por la necesidad de extender sus obligaciones profesionales con el fin de regular su actuación en el mercado incrementando la protección a los sujetos débiles como los usuarios y consumidores. Consecuencia de unos planteamientos más acordes con la “teoría de la culpa" en la responsabilidad, incluso patrimonial, ha hecho que, desde el ámbito de la jurisprudencia, primero, y después desde la propia normativa legal, en casi todos los ámbitos de actuación del empresariado, se concierte una responsabilidad ilimitada para aquellos agentes que hayan actuado de una forma negligente en la gestión empresarial. De ahí que la teoría del levantamiento del velo, o las más recientes normativas sobre responsabilidad tributaria o frente a la Seguridad Social, hayan perfilado un sistema de responsabilidad que incide en que los gestores o responsables de Ia gestión social no queden indemnes a los perjuicios económicos que puedan causar a terceros, en general.In recent times the notion of employer wins a conceptual expansion, motivated by the need to extend their professional obligations to regulate their conduct on the market increasing the weak subjects protection as users and consumers. As a consequence of a more consistent approach to the " theory of guilt " on responsibility, including equity, it's defined from the field of jurisprudence and from the legal rules themselves unlimited liability for those agents who have acted in a way defined slothful in business management