Steady rimming flows with surface tension

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder’s bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones

Modelling and experimental evidence of the cathode erosion in a plasma spray torch

The lifetime of tungsten cathodes used in plasma spray torches is limited by processes leading to a loss of cathode material. It was reported in the literature that the mechanism of their erosion is the evaporation. A model of the ionization layer of a cathode is developed to study the diffusive transport of evaporated tungsten atoms and tungsten ions produced due to ionization by electron impact in a background argon plasma. It is shown that the Stefan-Maxwell equations do not reduce to Fick law as one could expect for the transport of diluted species, which is due to significant diffusion velocities of argon ions. The ionization of tungsten atoms occurs in a distance of a few micrometers from the cathode surface and leads to a strong sink, which increases the net flux of tungsten atoms far beyond that obtained in absence of tungsten ions. This shows that the tungsten ions are driven by the electric field towards the cathode resulting in no net diffusive flux and no removal of tungsten species from the ionization layer even if convection is accounted for. A possible mechanism of removal is found by extending the model to comprise an anode. The extended model resolves the inter-electrode region and provides the plasma parameters for a current density corresponding to the value at the center of the cathode under typical arc currents of 600 A and 800 A. The presence of the anode causes a reversal of the electric field on the anode side, which pulls the ions away from the ionization layer of the cathode. The net flux of tungsten ions can be further fortified by convection. This model allows one to evaluate the loss of cathode material under realistic operating conditions in a quantitative agreement with measured values

High-dimensional interior crisis in the Kuramoto-Sivashinsky equation

An investigation of interior crisis of high dimensions in an extended spatiotemporal system exemplified by the Kuramoto-Sivashinsky equation is reported. It is shown that unstable periodic orbits and their associated invariant manifolds in the Poincaré hyperplane can effectively characterize the global bifurcation dynamics of high-dimensional systems.A. C.-L. Chian, E. L. Rempel, E. E. Macau, R. R. Rosa, and F. Christianse

Semiphenomenological model for gas-liquid phase transitions

We examine a rarefied gas with inter-molecular attraction. It is argued that the attraction force amplifies random density fluctuations by pulling molecules from lower-density regions into high-density regions and thus may give rise to an instability. To describe this effect, we use a kinetic equation where the attraction force is taken into account in a way similar to how electromagnetic forces in plasma are treated in the Vlasov model. It is demonstrated that the instability occurs when the temperature T is lower than a certain threshold value T-s depending on the gas density. It is further shown that, even if T is only marginally lower than T-s, the instability generates clusters with density much higher than that of the gas. These results suggest that the instability should be interpreted as a gas-liquid phase transition, with T-s being the temperature of saturated vapor and the high-density clusters representing liquid droplets

Peculiar property of noble gases and its explanation through the Enskog-Vlasov model

An observation is presented that the ratio of the critical and triple-point temperatures T-cr/T-tp of neon, argon, krypton, and xenon fit within a narrow interval, T-cr/T-tp = 1.803 +/- 0.5%, and the same applies to the density ratio, n(cr)/n(tp) = 0.3782 +/- 1.7% (of the two remaining noble gases, helium does not have a triple point and, for radon, n(tp) is unknown). We explain this peculiar property by the fact that the molecules of noble gases are nearly spherical, as a result of which they satisfy the Enskog-Vlasov (EV) kinetic model based on the approximation of hard spheres. The EV model has also allowed us to identify two more parameter combinations which are virtually the same for all noble gases

On the theory of structures in near-electrode plasma regions

SIGLEAvailable from TIB Hannover: RO 9159(11-A1-91) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Self-Consistent Model of HID Lamp for Design Applications

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