A Taylor cone refers to the cone observed in electrospinning, electrospraying and hydrodynamic spray processes from which a jet of charged particles emanates above a threshold voltage. Aside from electrospray ionization in mass spectrometry, the Taylor cone is important in field-emission electric propulsion (FEEP) and colloid thrusters used in fine control and high efficiency (low power) thrust of spacecraft.
This cone was described by Sir Geoffrey Ingram Taylor in 1964 before electrospray was "discovered". [1] This work followed on the work of Zeleny [2] who photographed a cone-jet of glycerine in a strong electric field and the work of several others: Wilson and Taylor (1925), [3] Nolan (1926) [4] and Macky (1931). [5] Taylor was primarily interested in the behavior of water droplets in strong electric fields, such as in thunderstorms.
When a small volume of electrically conductive liquid is exposed to an electric field, the shape of liquid starts to deform from the shape caused by surface tension alone. As the voltage is increased the effect of the electric field becomes more prominent. As this effect of the electric field begins to exert a similar magnitude of force on the droplet as the surface tension does, a cone shape begins to form with convex sides and a rounded tip. This approaches the shape of a cone with a whole angle (width) of 98.6°. [1] When a certain threshold voltage has been reached the slightly rounded tip inverts and emits a jet of liquid. This is called a cone-jet and is the beginning of the electrospraying process in which ions may be transferred to the gas phase. It is generally found that in order to achieve a stable cone-jet a slightly higher than threshold voltage must be used. As the voltage is increased even more, other modes of droplet disintegration are found. The term Taylor cone can specifically refer to the theoretical limit of a perfect cone of exactly the predicted angle or generally refer to the approximately conical portion of a cone-jet after the electrospraying process has begun.
Sir Geoffrey Ingram Taylor in 1964 described this phenomenon, theoretically derived based on general assumptions that the requirements to form a perfect cone under such conditions required a semi-vertical angle of 49.3° (a whole angle of 98.6°) and demonstrated that the shape of such a cone approached the theoretical shape just before jet formation. This angle is known as the Taylor angle. This angle is more precisely where is the first zero of (the Legendre function of order 1/2).
Taylor's derivation is based on two assumptions: (1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have azimuthal symmetry and have dependence to counter the surface tension to produce the cone. The solution to this problem is:
where (equipotential surface) exists at a value of (regardless of R) producing an equipotential cone. The angle necessary for for all R is a zero of between 0 and which there is only one at 130.7099°. The complement of this angle is the Taylor angle.
In chemistry, hydrophobicity is the physical property of a molecule that is seemingly repelled from a mass of water. In contrast, hydrophiles are attracted to water.
In geometry, a solid angle is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle at that point.
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects to float on a water surface without becoming even partly submerged.
An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.
In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, BL Lac objects, quasars, blazars and recently also in some galactic sources called microquasars. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion.
Electrospray ionization (ESI) is a technique used in mass spectrometry to produce ions using an electrospray in which a high voltage is applied to a liquid to create an aerosol. It is especially useful in producing ions from macromolecules because it overcomes the propensity of these molecules to fragment when ionized. ESI is different from other ionization processes since it may produce multiple-charged ions, effectively extending the mass range of the analyser to accommodate the kDa-MDa orders of magnitude observed in proteins and their associated polypeptide fragments.
Electrowetting is the modification of the wetting properties of a surface with an applied electric field.
The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane on which the material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. The morphology of the material affects the angle of repose; smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. The angle of repose can also be affected by additions of solvents. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase the angle of repose, and related quantities such as the soil strength.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.
In physics and engineering, a phasor is a complex number representing a sinusoidal function whose amplitude, angular frequency, and initial phase are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and sinor or even complexor.
Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not miscible with the first one. The degree of wetting (wettability) is determined by a force balance between adhesive and cohesive forces.
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour molecular interaction.
The name electrospray is used for an apparatus that employs electricity to disperse a liquid or for the fine aerosol resulting from this process. High voltage is applied to a liquid supplied through an emitter. Ideally the liquid reaching the emitter tip forms a Taylor cone, which emits a liquid jet through its apex. Varicose waves on the surface of the jet lead to the formation of small and highly charged liquid droplets, which are radially dispersed due to Coulomb repulsion.
Cassie's law, or the Cassie equation, describes the effective contact angle θc for a liquid on a chemically heterogeneous surface, i.e. the surface of a composite material consisting of different chemistries, that is non uniform throughout. Contact angles are important as they quantify a surface's wettability, the nature of solid-fluid intermolecular interactions. Cassie's law is reserved for when a liquid completely covers both smooth and rough heterogeneous surfaces.
In chemistry and materials science, ultrahydrophobic surfaces are highly hydrophobic, i.e., extremely difficult to wet. The contact angles of a water droplet on an ultrahydrophobic material exceed 150°. This is also referred to as the lotus effect, after the superhydrophobic leaves of the lotus plant. A droplet striking these kinds of surfaces can fully rebound like an elastic ball. Interactions of bouncing drops can be further reduced using special superhydrophobic surfaces that promote symmetry breaking, pancake bouncing or waterbowl bouncing.
Electrohydrodynamic droplet deformation is a phenomenon that occurs when liquid droplets suspended in a second immiscible liquid are exposed to an oscillating electric field. Under these conditions, the droplet will periodically deform between prolate and oblate ellipsoidal shapes. The characteristic frequency and magnitude of the deformation is determined by a balance of electrodynamic, hydrodynamic, and capillary stresses acting on the droplet interface. This phenomenon has been studied extensively both mathematically and experimentally because of the complex fluid dynamics that occur. Characterization and modulation of electrodynamic droplet deformation is of particular interest for engineering applications because of the growing need to improve the performance of complex industrial processes(e.g. two-phase cooling, crude oil demulsification). The primary advantage of using oscillatory droplet deformation to improve these engineering processes is that the phenomenon does not require sophisticated machinery or the introduction of heat sources. This effectively means that improving performance via oscillatory droplet deformation is simple and in no way diminishes the effectiveness of the existing engineering system.
Elasto-capillarity is the ability of capillary force to deform an elastic material. From the viewpoint of mechanics, elastocapillarity phenomena essentially involve competition between the elastic strain energy in the bulk and the energy on the surfaces/interfaces. In the modeling of these phenomena, some challenging issues are, among others, the exact characterization of energies at the micro scale, the solution of strongly nonlinear problems of structures with large deformation and moving boundary conditions, and instability of either solid structures or droplets/films.The capillary forces are generally negligible in the analysis of macroscopic structures but often play a significant role in many phenomena at small scales.
Optoelectrowetting (OEW) is a method of liquid droplet manipulation used in microfluidics applications. This technique builds on the principle of electrowetting, which has proven useful in liquid actuation due to fast switching response times and low power consumption. Where traditional electrowetting runs into challenges, however, such as in the simultaneous manipulation of multiple droplets, OEW presents a lucrative alternative that is both simpler and cheaper to produce. OEW surfaces are easy to fabricate, since they require no lithography, and have real-time, reconfigurable, large-scale manipulation control, due to its reaction to light intensity.
An ideal solid surface is flat, rigid, perfectly smooth, and chemically homogeneous, and has zero contact angle hysteresis. Zero hysteresis implies the advancing and receding contact angles are equal.
Moffatt eddies are sequences of eddies that develop in corners bounded by plane walls due to an arbitrary disturbance acting at asymptotically large distances from the corner. Although the source of motion is the arbitrary disturbance at large distances, the eddies develop quite independently and thus solution of these eddies emerges from an eigenvalue problem, a self-similar solution of the second kind.
