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Notes: A three-dimensional axially symmetric model for a liquid ion source is used to obtain the shape and critical potential for breakdown of a conducting fluid at the onset of instability. A set of electromechanical equations is obtained for the first-order deformation of the fluid surface from the Taylor cone which is used as the zeroth-order configuration. The equations are evaluated in both the quasihydrostatic and hydrodynamic limits. These analyses yield the angle deformation ξ=(r/a)sε, for r〈a, and the associated critical voltage VC=V(0)TC1 ×[(a/r)s+C2]−0.5, where a is a boundary-matching parameter, r0 is the distance between the cone apex and the counterelectrode, and ε contains the time dependence of the first-order angle deformation. Here, V(0)T is the potential needed for formation of the purely hydrostatic Taylor cone and C1 and C2 are constants dependent upon boundary-matching conditions. The hydrodynamic analysis predicts that the shape of the surface is concave at the onset of instability. The results obtained in both limits are (i) that the instability is localized in the apex region, and (ii) the values of the critical voltages VC, are in good agreement with experiment for Ga.

Notes: Liquid metal ion sources are of interest in diverse areas of technology since they provide a high brightness, quasipoint source of ions and droplets for microfabrication, surface analysis, ultrathin film deposition, and other potential applications. N. M. Miskovsky, M. Chung, P. H. Cutler, T. E. Feuchtwang, and E. Kazes [J. Vac. Sci. Technol. A 6, 2992 (1988)] have developed an electrohydrodynamic capillary wave theory for ion and droplet emission in electrically stressed conducting viscous fluids based on a mathematical formalism introduced by J. R. Melcher and C. V. Smith [Phys. Fluids 12, 778 (1969)] and S. Grossmann and A. Muller [Z. Phys. B 57, 161 (1984)]. As the simplest analytical application of this theory they chose a model consisting of a planar fluid of thickness "a'' supported on a rigid electrode. A parallel planar counter electrode is at a distance "b'' from the unperturbed surface. The Navier–Stokes equation was solved subject to a dynamical Laplace–Young stress boundary condition (which includes the frictional tensor) to obtain the dispersion relation used to investigate the stability of the system.In earlier work the effect of viscosity and gravity on the spectrum of unstable wavelengths for the case of a thick film (i.e., λ(very-much-greater-than)a) was investigated within the planar surface capillary wave model. In this limit, it was found that viscosity plays a significant role in determining the growth rate and the dominant mode, suggesting that it should be included in studies of the instabilities in liquid metal ion sources. It was also found that the local electric field is much larger than the average field of the perturbed fluid surface, implying that nonlinear effects can be important. In the present study the same formalism is used to investigate the case of a thin (i.e., λ〈a) liquid metal film. For thin films, that is, 〈1 μm, the effect of the boundary conditions at the supporting electrode can produce significant changes in the maximum growth rate (∼20%), the dominant mode (∼10%), and the maximum value of Re(ω2) (∼40%). For both the thick- and thin-film regimes viscous damping is found to have an important role increasing the stability of the fluid film. In addition, an increase in viscosity shifts the most unstable mode to longer wavelengths. This shift competes with the effect of decreasing the film thickness.

Notes: An electrohydrodynamic surface capillary wave theory has previously been developed for ion and droplet formation in electrically stressed conducting viscous fluids. In this paper the formalism has been used to derive the dispersion relation for the simplest model, a planar liquid-metal ion source, which includes both gravitational and viscous effects. The calculation required the simultaneous solution of the linearized Navier–Stokes equation, the Maxwell equation, and the time-dependent Laplace–Young stress condition. The critical field necessary for the onset of instability of the fluid surface is obtained, as well as its dependence on surface tension, viscosity, and gravity. In addition, the effects of viscosity and gravity on the growth and decay rates of particle emission are investigated. It is found that, as a function of applied field, the effects of viscosity and gravity on the dominant capillary wave mode and growth rate range from a few percent for liquid Li to about 20%–40% for liquid Ga and Au, respectively. However, for the liquid metals Li, Al, Ga, Sn, and Au viscosity dominates gravity: a factor of 3 larger for Li to more than an order of magnitude greater for the heavier liquid metals. Finally, it is found that the field above a model protrusion on the perturbed surface is significantly larger than the average field over the liquid surface.

Notes: We report on the specific heats of type E thermocouple wires, constantan (55% Cu–45% Ni) and chromel (10% Cr–90% Ni), measured using ac calorimetry in the temperature range 18–290 K. Data were normalized to values at 200 K determined by differential scanning calorimetry. The constantan values are close to those of other Cu/Ni alloys, while this is the first reported low-temperature result for chromel.

Notes: The rate of convergence of the Karhunen–Loève expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers' equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority of the Karhunen–Loève expansion, especially for high Reynolds number flows.

Notes: Conditional averages of turbulent flow quantities can be approximated in terms of unconditional correlation data by means of stochastic estimation. The validity and accuracy of this procedure are investigated by comparing stochastic estimates to conditional averages measured in four turbulent flows: grid turbulence, the axisymmetric shear layer of a round jet, a plane shear layer, and pipe flow. Comparisons are made for quantities that are separated from the conditional data in time or space, and for turbulent pressures, as well as turbulent velocities. In each case, the linear estimate accurately represents large scale structure. Nonlinear quadratic estimation shows little improvement over linear estimation, because the second-order terms are small for probable values of the turbulent fluctuations.

Notes: A direct numerical simulation was made of instability in a spatially evolving channel flow. A local surface suction/blowing was imposed at the upper wall (x/h=20). A Tollmien–Schlichting (TS) wave was superimposed on the laminar channel flow at the inflow. At the outflow, the buffer domain technique was applied to suppress the reflection of outgoing waves. The influence of the local suction/blowing on the linear and nonlinear instabilities of the flow was examined. It was found that the local suction/blowing increases the disturbance energy significantly in the interaction zone for subcritical (Re=5000) and supercritical (Re=10 000) cases. The effects of the blowing strength (0≤AS≤0.1) and the initial TS wave amplitude (0≤ATS≤2.0) on the subcritical channel flow were scrutinized. Two regimes of the wave/flow interaction were found by varing AS, i.e., "monotonic" and "vortex splitting" regimes. © 1997 American Institute of Physics.