Showing papers on "Knudsen number published in 1978"

Kinetic Theory of Evaporation and Condensation : Hydrodynamic Equation and Slip Boundary Condition

Abstract: The steady behavior of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The Knudsen number of the system (the mean free path of the gas molecules divided by the characteristic length of the system) being assumed to be fairly small, the hydrodynamic equations for the macroscopic quantities, the velocity, temperature, and pressure, of the gas and their boundary conditions on the interface of the gas and its condensed phase are derived, and two simple examples (evaporation from a sphere, two-surface problem of evaporation and condensation) are worked out.

Angular distribution of molecular beams from modified Knudsen cells for molecular-beam epitaxy

Abstract: The molecular‐beam epitaxy (MBE) method is an important tool which can provide new and different types of semiconductor films. The effusion ovens used in MBE studies were not an ideal Knudsen‐type design that had employed small orifices. We have measured the beam intensity distribution of an effusion oven that had 240 small channels. Applying the theory of Clausing, who derived the angular distribution from a small hole of radius r and length L, and using the superposition principle, we have compared the calculation with experimental data and found good agreement. Intensity distributions from an oven with a single large opening are also measured. This geometry cannot be calculated but actually provides a useful method of collimating molecular beams.

One‐dimensional outgassing problem

Abstract: A predominantly numerical study, using the direct simulation Monte Carlo method, of the flow from outgassing surfaces with plane, cylindrical, or spherical geometry is presented. The numerical results for the plane flow case are compared with existing theoretical and experimental results, and also with a new formulation of the jump conditions across the Knudsen layer between the surface and the continuum outflow. This outflow is sonic for the free expansion case, but subsonic in the presence of back‐pressure effects. The self‐scattered return flux is 19% of the outgassed flux in the sonic outflow case and increases at lower Mach numbers. Thermal accomodation and reflection of this return flux produces an outgassing cooling effect. The cylindrical and spherical geometries introduce an additional Knudsen number defined by the ratio of the mean free path in the effusing gas to the radius. The plane flow results apply when this Knudsen number is less than 0.001 and, when it is of order unity or above, the return flux is inversely proportional to it.

Recondensation of a monatomic gas at low Knudsen numbers

Abstract: THE PROBLME of the one-dimensional motion of a gas between infinite plane-parallel evaporating and absorbing surfaces is considered on the basis of model kinetic equation for a monatomic gas. A specially developed numerical method makes it possible to obtain a solution of the problem for the whole range of Knudsen numbers and trace the gas flow right up to the continuous medium mode.

Capillary models for porous media. VIII. A study of gaseous flow in the transition from the Knudsen to the Poiseuille flow regimes

Abstract: For pt.VII see ibid., vol.10, p.2423 (1977). The capillary network model has been used to examine the effects of connectivity and radius distribution on the minimum in the transition from Knudsen to Poiseuille flow. It was found that, using formulae for infinitely long capillaries, the minimum persisted in two-dimensional random networks for all the structures examined. When short-tube formulae were used to describe the flow in network elements minima were absent even when the length to (mean) radius ratio was as large as 20. It is concluded that the limitation of diffusion path lengths, rather than network topology, is the significant factor influencing the Knudsen minimum. On the other hand, information about network structure can be obtained from structure factors at low- and high-pressure limits.

Optimization of a Knudsen Cs--Ba thermionic converter

Abstract: The performance of a thermionic converter that operates in the Knudsen regime is optimized The potential distribution with surface-ionization is studied, with particular attention being paid to the region near the transition from the overneutralized state to the underneutralized state The saturation current is optimized and the maximum converter current is compared with the random current in an isothermal equilibrium cavity The concept of a generalized voltage--current characteristic is introduced for power optimization This characteristic is used to determine the anode work function and to calculate the output power The experimental data agree with the calculated results and indicate a high efficiency for a cesium--barium thermionic converter

Wind-Tuimel Simulation of High-Altitude Rocket Plumes

Abstract: R plumes at altitudes above 150 km are among the largest man-made phenomena. As rocket speed and altitude increase, the description of plume features systematically varies from continuum through transitional to rarefied flow. Despite the vast size of these structures, this progressive rarefaction of high-altitude plumes can be reasonably simulated in the wind tunnel. The high-altitude regime is that region wherethe rocket body dimensions are small relative to the plume scale. In this region, vehicle Mach numbers are usually very supersonic. The fully continuum, high-altitude plume flowfield has been summarized in a model by Jarvinen and Hill. l The plume dimensional analysis has been developed by Moran. The Jarvinen and Hill plume scaling has been put into nomogram form by Draper and Sutton. Jarvinen and Hill based the scaling of their plume model upon the hypersonic plume scale L and the engine drag to thrust ratio D/F. Here, L — lF/q^ where q^ is freestream dynamic pressure. In the Jarvinen and Hill model inviscid limit, freestream and exhaust gases would be separated by a contact surface. At high altitudes, a laminar mixing layer exists in which transport phenomena are important. The parameter controlling viscous plume features is a Knudsen number KnL based on plume scale L. The KnL values also indicate the extent to which the plume is in the transitional flow regime. Consequently, this Knudsen number is the major parameter in the wind-tunnel fluid-mechanical simulation of high-altitude rocket plumes.

Effect of rotational degrees of freedom of molecules on energy flux in attenuated gas

Abstract: On the basis of model kinetic equations a solution is obtained by a numerical method for the flow of attenuated gas around a sphere. The effect of rotational degrees of freedom on the energy flux to the body is investigated. Values of the ratio between the energy flux Q and its free-molecular value Q* for monatomic and diatomic gases are compared; for the comparison, the dimensionless temperature of the body, the gas velocity at infinity, and the law of viscosity must be the same in the two cases. For sufficiently cold bodies (when the body temperature is below the equilibrium temperature for a diatomic gas) the difference between Q/Q* for monatomic and diatomic gases is insignificant. For a diatomic gas when the body temperature is close to equilibrium, the ratio Q/Q* is found to have a nonmonotonic dependence on the Knudsen force.

The Measurement of Membrane Filter Pore Size by a Gas Permeability Technique

Abstract: A differential low pressure gas flow technique has been developed for the measurement of the mean pore size of membrane filters. The method is here applied to the pore size determination in a range of commercial micro-porous polymer films with pore diameters ranging from 0.03 to 0.8 μm (‘Nuclepore’). The polymer films were also examined using scanning electron microscopy so that structural and physical parameters could be evaluated. Two flow regimes could be demonstrated for the permeability data with clear separation between diffusional (Knudsen) flow and viscous or transitional flow occurring at a pore size of 0.2 μm. Alternative theoretical treatments are required for the two regimes but mean pore diameters could be calculated with reasonable precision and agreed with the results obtained by microscopy. In the case of viscous flow it is necessary to assume that the membranes have a tortuosity of less than unity and this is shown to be justified from a consideration of the structure of the pore ...