AIP Publishing

An expression for the energy exchange between two Maxwellian gases at different temperatures is derived. The resultant formula contains an integral in which the scattering cross section for momentum transfer appears. If the cross section for hard-sphere collisions is used, the expression reduces to an expression obtained by Cravath for this case. If the cross section for screened Coulomb interactions is used, the results agree with results for the same case obtained by Spitzer and others.

The one-dimensional Cartesian model for the resistive diffusion of a force-free magnetic field in a plasma of negligible inertia is treated for the case of confinement between rigid walls made of perfect electrical conductors. An exact analysis is given of the general initial-boundary value problem. The field evolution is driven by a competition between Ohmic loss and the induction effects arising from the tenuous plasma moving to adjust with the diffusing magnetic field. The process is nonlinear and nonlocal. It is shown that the field topology determines whether electrical currents will decay away everywhere or else grow at isolated locations to infinite values in a finite period of time.

The steady-state energy loss of a homogeneous and isothermal spherical plasma due to de-excitation radiation of impurity ions, assumed to have two energy levels only, is investigated without making the assumption that this radiation is thermal. A method developed by R. N. Thomas is adopted which consists in solving simultaneously the equation of radiative transfer and the equations for the rate of change of the occupation numbers of the energy levels. Analytical methods for calculating the source function obtained in this way are indicated.

A generalization of previously existing theories of fluctuations in dilute monotonic gases is obtained which describes nonequilibrium states with spatial gradients. A kinetic description of the fluctuations is first derived, and the reduction to the fluid limit is then carried out. The theory can be used to describe the enhanced fluctuations which are expected to occur near the onset of hydrodynamic instabilities.

Experimental results are presented of the behavior of droplets, falling in water at Reynolds numbers ranging from 138–971. The location of flow separation and the wake configuration were studied with a shadowgraph optical system. The measured drag coefficients were found to be higher than predicted by Chao, who assumed complete internal circulation and negligible flow separation. The agreement was improved when a correction for the pressure drag was introduced. The latter was found to be essentially due to flow separation but not to the pressure differences across the boundary layer as asserted by Moore. In the nonoscillating range the viscous drag remains predominant, and there exists a systematic dependence of the drag coefficient on a property parameter associated with the propensity of the droplet to develop internal circulation. That parameter is also a significant group in correlating droplet deformation in pure systems. The onset of sustained droplet oscillation was observed to coincide with the onset of the periodic shedding of vortices. The transition to oscillation occurs at a critical Weber number of approximately 4, at which point there is a sharp increase of the drag coefficient.

Nonlinear equations describing the state of a weakly ionized plasma in an unstable positive column are derived from a set of hydrodynamic equations, the Poisson equation, and the ionization frequency equation for the direct ionization process. In order to find the solution of the initial value problem, an iterative method is applied. Numerically solved examples show that unstable ionization waves develop into high amplitude relaxation waves—striations. From the calculated distributions of the governing physical quantities particle-like properties of high amplitude striations are established. A nonlinear interaction between striations leading to their collision is noted. The explosive nature of ionization instability is found to be most pronounced at low ionization losses of electron energy. A quantitative, as well as qualitative agreement between calculated and experimental data is obtained.

The stability of an electrically charged droplet with respect to mechanical deformations is studied under the assumptions that the liquid is perfectly conducting, the medium devoid of external fields of force, and the sum of the electrical and mechanical energies in the system conserved. Unlike Rayleigh's case, which dealt with small perturbations of spherical drops, the deformations considered in the present case are allowed to be large in size but confined in shape to ellipsoids of revolution. The energy of the deformed droplet is expressed as a function of a geometrical parameter and the ratio α between the electrical and surface energies of the corresponding spherical shape. Likewise, the dependence of the extremal points on α is investigated. Conforming with Rayleigh, the spherical droplet is shown to be unstable for α > 4 and stable for α < 4. However, for a certain range of α in the latter case, it is found to be only in a metastable state. In addition, both one prolate and one oblate ellipsoid of minimal energy are shown to exist for every α > 4.

Strong electric potential double layers (eφ/Te≳10) are produced in the University of Iowa’s triple plasma device. The electron beam which results from acceleration by the double layer maintains its identity with little heating until it reaches the end of the chamber. Structure of the double layers is seen to depend upon the characteristics of the free and trapped particle species. A three-dimensional mapping for double layers is shown. A density criterion model for the stability of double layers is also presented.

The effect of polyethyleneoxide (Polyox grade WSR 301) on grid-generated turbulence was investigated using laser anemometry and flow-visualization techniques. It was found that the polymer additive reduced both the turbulent intensity and the rate of decay behind the grid. At typical drag-reducing concentrations, turbulent energy spectra were qualitatively the same as those in water, in agreement with the results of other investigations. However, at higher additive concentrations, the dissipation-range spectra showed noticeable attenuation. This seemed to be a threshold effect with onset at a polymer concentration between 100 and 250 ppm. This result was supported by photographs of dye-injection tracer but in this case the onset concentration for small-eddy suppression was between 50 and 100 ppm.

Earlier models for flows with drag reduction are reviewed and compared with a new energy-dissipation closure which describes the observed effects of drag reduction on the mean velocity, turbulent energy, and turbulent length-scale distributions, and suggests a new maximum drag reduction law related to the onset of drag reduction.