Robert J. Turnbull

Effect of transonic flow in the ablation cloud on the lifetime of a solid hydrogen pellet in a plasma

A knowledge of solid hydrogen pellet lifetimes in a plasma is critical to the design of devices to refuel tokamak fusion reactors. When the pellet is injected into the plasma, the ablated material from the pellet undergoes a transonic flow since it is heated while it expands. Calculations are done on the behavior of the transonic flow for various plasma conditions and pellet sizes. From these calculations, the ablation rate and lifetimes of the pellet are determined. A scaling law is given which allows pellet lifetimes to be easily calculated for any plasma conditions. The results of these calculations give good agreement when compared with experiments.

Generation of charged drops of insulating liquids by electrostatic spraying

Development of a new method for the generation of microparticles of controlled size and charge is reported. The method, which is particularly suited for insulating liquids, is to generate stable fine jets through electrostatic spraying. Charge in the liquid is produced by placing a sharp electrode inside the liquid and raising it to a high potential. High electric fields then disrupt the liquid to form fine jets which later break up into small drops. A theoretical explanation of these phenomena is presented and compared with experimental results with a qualitatively good agreement. Among the possible applications of this work is generation of cryogenic droplets for refueling fusion reactors and for laser fusion targets.

Electrohydrodynamic Rayleigh‐Taylor Bulk Instability

A stability criterion is found for an initially static, stratified fluid subject to an electric stress. The equilibrium fluid density, permittivity, viscosity, and space charge distributions are functions of the vertical spatial coordinate, with gradients directed parallel to the imposed electric field intensity and gravitational acceleration. In the limit where the fluid is perfectly insulating, sufficient conditions for stability are found; the principle of exchange of stabilities is shown, and variational principles derived for the eigenfrequencies and, in the case of no space charge, for the critical field strength. An experiment demonstrates instability in the dielectrophoretic limit of no bulk free charge. The property gradients are induced thermally, and incipience of instability, as measured by the Schmidt‐Milverton heat‐transfer technique, is successfully predicted by the theoretical criterion.

Effect of Dielectrophoretic Forces on the Bénard Instability

When a fluid is heated from below, there is a critical temperature gradient above which the fluid becomes unstable and convection results. The effect of dielectrophoretic forces on this critical temperature gradient is studied. Dielectrophoretic forces are caused by an electric field and a gradient in dielectric constant. The principle of exchange of stabilities is shown to hold for a certain set of boundary conditions. Variational principles are derived for various boundary conditions. These variational principles and the Galerkin method are then used to find approximate solutions for the critical temperature gradient as a function of the wavelength and the electric field.

Field injection electrostatic spraying of liquid hydrogen

Uniform charged liquid‐hydrogen drops are produced using the method of field injection electrostatic spraying. This method consists of forming a meniscus of liquid hydrogen at the end of a glass nozzle and injecting charge into the liquid using a sharp electrode raised to a high voltage. A small pressure drop across the nozzle results in a constant volume flow rate of liquid through the nozzle allowing a drop to form and drip off. As the amount of charge injection increases with the raised needle electrode voltage, the drop size decreases due to the increased electrostatic forces compensating for the surface tension forces. As a result, the drops drip off at an increased frequency. Eventually a charged jet forms which in turn breaks up into small uniform charged drops. A detailed description of the experimental apparatus is presented. Experimental results are presented and discussed.

Electrostatic Spraying of Liquid Insulators

A method for generating drops of liquid insulators using electrostatic spraying is reported. This method differs from normal electrostatic spraying in the method of charging the liquid. A sharp needle placed in the liquid near the end of a capillary is raised to a high potential, thus injecting charge into the liquid. As the voltage is raised, a jet is formed electrostatically with the size of the jet decreasing with increasing voltage. A theoretical prediction of the jet radius as a function of current is obtained by finding the amount of electrical energy which goes into mechanical energy. Experimental results of the spraying of silicone oils are given and compared with the theory.

Free Convection from a Heated Vertical Plate in a Direct‐Current Electric Field

A theoretical study is made of the convection near a heated vertical plate in a dc electric field. Electrical forces are produced by a bulk charge density in an electric field. This charge density occurs because the temperature gradients produce gradients in conductivity in a fluid with Ohmic electrical properties. To find the effect of the electrical forces, a set of boundary‐layer equations is developed and then integrated over the boundary layer. This integration produces ordinary differential equations when profiles are assumed for the temperature, velocity, and electric field. These profiles each have the same boundary‐layer thickness. Both numerical and analytical solutions are found for these equations. The analytical solutions are for special cases and approximate the numerical solutions. The results are approximate expressions for the temperature, velocity, electric field, and heat transfer from the plate.

Self-acceleration of a charged jet

When insulators are sprayed electrostatically, charges are injected into the liquid, resulting in the formation of a charged jet. Mutual repulsion between these charges, which reside on the jet surface, causes the jet to accelerate. This acceleration is opposed by surface tension and inertial forces. As the jet accelerates, its radius decreases until it reaches a minimum radius. When the minimum jet size is achieved, the rate of acceleration decreases to zero. Equations are derived which allow this minimum radius to be calculated. In addition to the accelerating jet, the equations have another solution with the jet decelerating. In the experiments the acceleration is observed but not the deceleration. Rather, drops form on the end of the jet, indicating that it becomes unstable before it can decelerate. The values for minimum jet radius calculated from the equations are compared with experimental measurements of the minimum jet size in electrostatic spraying of insulators, and good correlation is obtained. >

Techniques for generating uniform charged particles of hydrogen isotopes

Abstract An apparatus has been built which is capable of generating uniform charged particles of hydrogen isotopes. Two unrelated physical processes are used to produce charged jets of controlled size and current. The jets later break up into uniform sized charged droplets. In both processes, charging of the liquid is accomplished by placing a sharp electrode inside the liquid and by raising it to a high potential. The first process is to electrostatistically spray the charged liquid to form a fine jet of controlled size and current, whereas the second process is Rayleighs method of uniform droplet production. This method consists of breaking up a smooth jet of predetermined size into uniform drops using an externally excited acoustic wave. Uniform charged particles with charges up to one-third of the Rayleigh limit were generated through the first process, while in the second process the maximum charge was approximately one-quarter of the Rayleigh limit. A wide range of sizes can be produced using either process.

Theory of electrohydrodynamic behaviour of nematic liquid crystals in a constant field

A theory is suggested for predicting the threshold voltage for dynamic scattering in nematic liquid crystals subject to a constant electric field. Because of experimental results showing similar instabilities in isotropic liquids, an isotropic model is used. The electrical behaviour of the liquid is assumed to have a charge carrier dissociation-recombination process in equilibrium. Under these assumptions, typical ion density curves are obtained and a non-zero charge density is found near the electrodes. The resulting electrical forces result in an instability. Calculations are performed to predict the threshold voltage for the instability. Order-of-magnitude calculations give results consistent with experimental data in liquid crystals.