Electrodispersion of a liquid of finite elcetrical conductivity in an immiscible dielectric liquid

Order-of-magnitude estimates and numerical computations are used to analyze an electrospray operating in the cone-jet mode in a bath of an immiscible dielectric liquid. In agreement with experimental results in the literature, the analysis predicts that the electric current carried by the jet increases as the square root of the flow rate of dispersed liquid in a wide range of conditions of the flow. The characteristics of the current transfer region determining the electric current are estimated taking into account the viscous drag of the dielectric liquid that surrounds the jet. The electric current is predicted to depart from the square root law for small flow rates, when charge relaxation effects become important in the current transfer region, and also when the flow rate increases to values of the order of QM = ϵ0γ2a/μ22K, where ϵ0 and μ2 are the permittivity and viscosity of the dielectric liquid, K is the electrical conductivity of the dispersed liquid, a is the radius of the capillary needle through which this liquid is injected, and γ is the interfacial tension of the liquid pair. When the flow rate becomes of order QM, the meniscus at the tip of the capillary ceases to resemble a Taylor cone, the current transfer region ceases to be short compared to the size of the meniscus, the electric current levels to a constant value, and the stationary jet cannot extend very far downstream of the meniscus

Numerical computation of the domain of operation of an electrospray of a very viscous liquid

A numerical study is carried out of the injection of a very viscous liquid of small electrical conductivity at a constant flow rate through an orifice in a metallic plate under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet emanating from its tip are investigated by computing the flow, the electric field and the transport of electric charge in the meniscus and a leading region of the jet. A stationary solution is found only for values of the flow rate above a certain minimum. At moderate values of the applied field, this minimum flow rate decreases when the applied field or the conductivity of the liquid increase. The electric shear stress acting on the surface of the liquid is not able to drive the liquid into the jet at flow rates smaller than the minimum while, for any flow rate higher than the minimum, the transfer of electric current to the surface may occur in a slender region of the jet where charge relaxation effects are small and the field induced by the electric charge of the jet is important. At high values of the applied field, the flow rate must be higher than another minimum, which increases with the applied field, in order for the viscous stress to balance the strong electric stress acting on the meniscus. The two conditions taken together determine lower and upper bounds for the applied field at a given flow rate, but the value of the applied field at which a stationary jet is first established when this parameter is gradually increased is higher than the lower bound, leading to hysteresis. When the liquid is electrosprayed in a surrounding dielectric fluid, the viscous shear stress that this fluid exerts on the surface of the jet eventually balances the electric shear stress and stops the continuous stretching of the jet. A fraction of the conduction current is left in the jet when the effect of the outer liquid comes into play in the region where this current is transferred to the surface, and no stationary solution is found above a maximum flow rate that decreases when the viscosity of the outer liquid increases or the applied field decreases. Order of magnitude estimates of the electric current and the conditions in the current transfer region are worked out

Effects of fresh gas velocity and thermal expansion on the structure of a Bunsen flame tip

Numerical computations and order-of-magnitude estimates are used to describe the tip region of a Bunsen flame where the flame departs from a planar flame at an angle to the incoming fresh gas flow. A single irreversible Arrhenius reaction with high activation energy is assumed. The well-known linear relation between flame velocity and curvature is recovered in the thermodiffusive limit, when the thermal expansion of the gas is left out, for velocities of the fresh gas (U0) only slightly larger than the velocity of a planar flame (UL), provided this flame is stable. For large values of the velocity ratio U0/UL, the tip region becomes slender and the curvature of the reaction sheet at the tip increases proportionally to U0/UL. The thermal expansion of the gas across the flame reduces the aspect ratio of the tip region. A qualitative analysis of the structure of the tip region for very exothermic reactions shows that this region ceases to be slender when the burnt-to-fresh gas temperature ratio becomes of the order of the velocity ratio U0/UL. For even larger values of the temperature ratio, the tip region becomes a cap of characteristic size not very different from the thickness of a planar flam

Bubble growth by injection of gas into viscous liquids in cylindrical and conical tubes.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall

Multi-fluid Eulerian model of an electrospray in a host gas.

An Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray

Electrospray of a very viscous liquid in a dielectric liquid bath

Numerical computations and order-of-magnitude estimates are used to analyze a jet of a very viscous liquid of finite electrical conductivity that is injected at a constant flow rate in an immiscible dielectric liquid under the action of an electric field. The conditions under which the injected liquid can form an elongated meniscus with a thin jet issuing from its apex (a cone-jet) are investigated by computing the flow, the electric field, and the transport of electric charge in the meniscus and a leading region of the jet. The boundaries of the domain of operation of the cone-jet mode are discussed. The current transfer region determining the electric current carried by the jet is analyzed taking into account the viscous drag of the dielectric liquid surrounding the jet. Conditions under which the electric current/flow rate characteristic follows a square root law or departs from it are discussed

Breakup of a supported drop of a viscous, conducting liquid in a uniform field

Numerical computations and order-of-magnitude estimates are used to describe the time evolution of a drop of a very viscous liquid of finite electrical conductivity attached to a metallic plate which is suddenly subject to a uniform electric field. Under the action of the electric stresses induced at its surface, the drop elongates in the direction of the field, and charged droplets are emitted when the strength of the field is higher than a certain critical value. A stationary emission mode exists in which the attached drop develops a conical tip and a thin jet, with small droplets emitted from the end of the jet in a process that involves the formation of a long ligament. The flow rate and the electric current carried by the stream of droplets emitted in this mode are determined by the flow and the transfer of charge in the attached drop, in particular in a small region around its tip and in a leading stretch of the jet, where the solution is nearly stationary despite the transient character of the jet further downstream. A simplified analysis of the stationary regions is carried out to elucidate the effects of the physical properties of the liquid _electrical conductivity, permittivity, viscosity, and surface tension_, the volume of the drop, and the strength of the applied field. For high electrical conductivities and applied fields well above its critical value, the electrical and viscous stresses are large compared to surface tension stresses, and their balance gives a flow rate proportional to the square of the applied field. The electric current is then that of a stationary electrified jet fed with this flow rate

Laminar flow of a gas in a tube with large temperature differences.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wal

On super free fall.

Villermaux & Pomeau (J. Fluid Mech., vol. 642, 2010, p. 147) analysed the motion of the interface of an inviscid liquid column released from rest in a vertical tube whose area expands gradually downwards, with application to an inverted conical container for which experimental measurements were carried out. An error in the analysis is found and corrected in the present investigation, which provides the new governing equation for the super-accelerated interface motion down gradually varying tubes in general, and integrated results for interface trajectories, velocities and accelerations down a conical tube in particular. Interestingly, the error does not affect any of the conclusions given in the 2010 paper. Further new results are reported here such as the equation governing the centre of mass and proof that the end point acceleration is exactly that of gravit

El lenguaje educativo en una metafísica no ontológica

En el presente artículo se reflexiona sobre el papel del lenguaje educativo en una metafísica no ontológica. El texto se divide en tres partes. En la primera parte, se realiza un recorrido en el que se recuerdan las principales posiciones filosóficas desarrolladas a lo largo de la historia de Occidente. Aquello evidencia que el lenguaje constituye un “problema”, desde la filosofía griega pre-aristotélica hasta nuestros días. El paradigma metafísico no ontológico acepta la existencia de una dimensión metafísica en la persona humana; pero aquella no se estructura a partir del on, ontos tradicional. Esta nueva forma paradigmática de comprender a la persona humana reconoce su dignidad extraordinaria a partir de la categoría metafísica de Otro. En este nuevo horizonte de comprensión metafísica, el lenguaje se presenta como presupuesto de mi/la relación con el Otro. En la segunda parte, se recuerda que el docente tiene dos alternativas de uso del lenguaje, o como medio de dominación o como canal de apertura al Otro: en el primer caso, el docente desarrolla una relación asimétrica que conduce al dominio de los estudiantes; en el segundo, el docente enfatiza la dimensión de reconocimiento y de respeto del Otro. En la tercera parte, se discute si el lenguaje puede ser considerado como categoría metafísica, dentro de un paradigma metafísico no ontológico. La respuesta a esta pregunta es afirmativa, pues es el lenguaje constituye el único medio y canal que permite mi/la relación con el Otro. Por ello, se reconoce que el lenguaje es presupuesto y condición de apertura al Otro. De ese modo, Otro y lenguaje se relacionan y condicionan, hasta llegar a reclamarse mutuamente; y de llegar a constituir como categorías metafísicas del presente paradigma metafísico no ontológico. // In this article it reflects on the role of language education in a non ontological metaphysics. The text is divided into three parts. In the first part, a journey in which the main philosophical positions developed throughout Western history are remembered is performed. It evidences that language constitutes a “problem” from the pre-Aristotelian Greek philosophy to this day. The non ontological metaphysical paradigm accept the existence of a metaphysical dimension of the human person; but that is not structured on from traditional ontos. This new paradigmatic way of understanding the human person recognizes his extraordinary dignity from the metaphysical category of Other. In this new horizon of metaphysical understanding, language is presented as budget for my / the relationship with the Other. In the second part, it is recalled that the teacher has two alternative language uses, or as mean of domination or as channel for opening to the Other. In the first case, the teacher develops an asymmetrical relationship that leads to the domain of students; in the second, the teacher emphasizes the dimension of recognition and respect for the Other. In the third part, we discuss whether language can be considered as a metaphysical category, within a non ontological metaphysical paradigm. The answer to this question is yes, because language constitutes the only means and channel that allows me/the relationship with the Other. Therefore, it is recognized that language is budget and open condition to the Other. Thus, Other and language are interrelated and interdependent, up to claim from each other; and become to constitute as metaphysical categories of this not ontological metaphysical paradigm