摘要:

A numerical method of calculating the correct stable equilibrium shape of a conducting drop subject to electrical forces is described. Its application to the problem of the stability of an isolated water drop of undistorted radiusRand surface tensionTsituated in an electric fieldEindicates that a drop is unstable ifE(R/T)12exceeds a value of 1.603 and its maximum stable deformation expressed asa/b, the ratio of the major to minor axes is 1.83. The numerical method is also applied to a study of the stability of drop pairs. The results show that the critical value ofE(R/T)12depends upon the initial separationXof the drops. ForX = 0, E(R/T)12is zero and its value increases asXincreases, tending to a value of 1.603. Finally, the relevance of these results to the behavior of drops in the atmosphere is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1693258

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Gilman and Benton have demonstrated the existence of composite Ekman‐Hartmann layer flow in rotating, electrically conducting fluids permeated by a magnetic field normal to the boundary. This flow was shown to evolve smoothly from a pure Ekman layer to a pure Hartmann layer as the parameter&agr; ≡ (2&mgr;&rgr;&lgr;&OHgr;0)−1/2 B0increases (&mgr; is magnetic permeability,&rgr;is density,&lgr;is magnetic diffusivity,&OHgr;0is the rotation rate, andB0is the imposed magnetic field). Here, it is shown that in the Cartesian, low magnetic Prandtl number limit, this flow exhibits the two instabilities to two‐dimensional rolls characteristic of the pure Ekman layer, but at Reynolds numbers that increase rapidly as&agr;increases. Both rolls decrease in horizontal scale, orient more nearly parallel to the flow far from the boundary, and acquire smaller phase velocities. Coriolis forces are seen to give a parallel roll instability of the Hartmann layer, at much lower Reynolds numbers than given by Roberts for Hartmann layer instability in the absence of rotation.

ISSN:0031-9171    

DOI:10.1063/1.1693290

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

An investigation is made of the stability to infinitesimal disturbances of a horizontal layer of dissociating fluid, heated from above or below. A modification of mathematical model due to Lighthill is employed. The results of the linear perturbation analysis of the normal mode resolution of the disturbances show that: (1) there is a slight departure in the onset of convective instability from the classical Be´nard problem for a nonreactive fluid layer heated from below; (2) for the case of heating from above, which is stable for a nonreactive fluid, there is also an onset of instability. Such a flow situation which is stable if the fluid is not chemically reactive but can exhibit an instability if the fluid is chemically reactive (i.e., in this case a dissociating fluid) is referred to as achemical instability.

ISSN:0031-9171    

DOI:10.1063/1.1693263

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

An analysis of the dispersion of a solute in a channel flow of fluid with couple stresses has been carried out. It is observed that couple stresses are more effective for&agr; < 20where&agr;is a nondimensional parameter. When&agr; > > 20, the effects of couple stresses on the dispersion of a solute are negligibly small. For&agr; → ∞, the dispersion of the solute is not affected by the couple stresses.

ISSN:0031-9171    

DOI:10.1063/1.1693276

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A simple and accurate expression for slip in the thermal creep problem is obtained via the use of the Roussopolous variational principle. The linearized Boltzmann equation is used and it is shown that, contrary to the results obtained by Yalamov, Ivchenko, and Deryagin, the Bhatnagar‐Gross‐Krook model, and the Maxwell molecules give essentially the same numerical values for the slip coefficient. Interestingly, the result for the rigid sphere molecules is about 12% lower than these values. Further, it is shown that some variational principles used previously in the kinetic theory are, in fact, only a special case of the Roussopolous principle.

ISSN:0031-9171    

DOI:10.1063/1.1693284

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The problem of wave propagation in one‐component systems is treated using the discrete ordinate method. Forced and free oscillations in a monatomic gas and longitudinal electrostatic oscillations in a one‐component plasma are considered. The governing equation is the linearized ellipsoidal model of the Boltzmann equation. When the ratio of collision frequency to a characteristic frequency of the wave is greater than one, the present technique yields results which are in excellent agreement with other theories and experimental data. For values of this ratio less than one, the present theory is very similar to the polynomial expansion theories.

ISSN:0031-9171    

DOI:10.1063/1.1693285

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Solutions to the problems of forced and free wave propagation in binary gas mixtures are presented which were obtained using the discrete ordinate method. The governing equations for the mixtures are the model equations proposed by Hamel. The solution is in excellent agreement with existing experimental data.

ISSN:0031-9171    

DOI:10.1063/1.1693286

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The time‐dependent problem of piston and shock wave formation in a low density (collision‐free) magnetized plasma has been experimentally studied in a high voltage theta pinch. The applied field strongly interacts with the plasma: either exciting instabilities that cause a fast resistive penetration and very low force density, or exerting a sufficiently large force density to produce high Mach number (5‐20) shock waves. The data on piston formation is discussed in terms of a magnetic field‐dependent resistivity such as might be expected from an ion plasma drift wave instability. The piston ejects ions possibly by the interaction of ions with ion plasma waves. The shock wave is seen to evolve from an initially one‐dimensional disturbance.

ISSN:0031-9171    

DOI:10.1063/1.1693287

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The collapse phase of a dense plasma focus gun operating in deuterium was studied using streak photography and time resolved x‐ray and neutron measuring techniques. The streak photographs, showing the radial motion of the luminous front at various axial positions, indicate a collapsing luminous front at the time of the current collapse followed by an expanding front and a recompression. The luminosity then disappears for a period of several hundred nanoseconds, during which time the neutrons are emitted. Estimates of shock heating and magnetic compressional heating were made from the streak pictures, and a calculation of plasma heating due to viscous forces arising from axial motion of the plasma was carried out. The effects of shock heating, magnetic compressional heating, and viscous heating are shown to be sufficient to produce an ion temperature of several kilovolts.

ISSN:0031-9171    

DOI:10.1063/1.1693288

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The asymptotic structure of the far‐wake behind a charged body in a rarefied plasma flow is investigated under the assumption of small ion‐to‐electron temperature ratio and of flow speed hypersonic with respect to the ions but not with respect to the electrons. It is found that waves are excited even if the flow is subacoustic (flow velocity less than the ion‐acoustic speed). For both superacoustic and subacoustic velocities a steep wave front develops separating the weakly perturbed, quasineutral plasma ahead, from the region behind where ion waves appear. Near the axis a trailing front develops; the region between this and the axis is quasineutral for superacoustic speeds. The decay laws in all of these regions, the self‐similar structure of the fronts and the general character of the waves are determined. The damping of the waves and special flow detail for bodies large and small compared with the Debye length are discussed. A nonlinear analysis of the leading wave front in superacoustic flow is carried out. A hyperacoustic equivalence principle is presented.

ISSN:0031-9171    

DOI:10.1063/1.1693289

出版商:AIP    

年代:1971

数据来源: AIP