Showing papers on "Knudsen number published in 1977"

Brownian coagulation of aerosols in rarefied gases

Abstract: The kinetics of coagulation of aerosols is well understood when the particle radius is much larger or much smaller than the mean free path of the surrounding gas (very small or very large Knudsen numbers). However, no adequate theory is available in the so‐called transition regime between these limiting cases. This is an experimental investigation of Brownian coagulation in the transition regime. Monodisperse aerosol [di(2‐ethylhexyl)sebacate, particle radius 0.2 μm] was produced in a falling‐film condensation aerosol generator. The evolution of the size distribution, and hence the rate of coagulation, was monitored as the aerosol flowed through a series of light scattering cells. Measurements were performed at five different pressures, ranging from atmospheric pressure to 67 Torr, thereby scaling the Knudsen number from 1 to 12. The influence of diffusional deposition, sedimentation, and gradient coagulation in vaporization was kept to a minimum, and the uniqueness of the inversion technique was demonstr...

Slightly rarefied gas flow over a specularly reflecting body

Abstract: The asymptotic behavior (for small Knudsen number) of the steady flow of a rarefied gas over a specularly reflecting body with arbitrary but smooth shape is investigated on the basis of the linearized Boltzmann–Krook–Welander equation. As applications of the theory, a sphere in a uniform flow of gas and that in a gas at rest with a uniform temperature gradient are considered. The velocity and temperature fields around the spheres and the drag and thermal forces acting on the sphere are obtained. The formulae of the forces are compared with those given by various approximate methods and those for other types of boundary conditions.

Generalized hydrodynamics of thermal transpiration, thermal force and friction force

Abstract: Transport processes in a rarefied gas are treated phenomenologically by means of generalized hydrodynamics with appropriate boundary conditions. The integral mass and heat flows through a capillary of arbitrary width are calculated from the differential constitutive laws and boundary conditions. The coefficients connecting these flows with the driving forces - pressure and temperature differences - automatically fulfil the well-known integral second law requirements and Onsager symmetry which de facto had been incorporated in the basic generalized hydrodynamics and boundary conditions. The formula obtained for thermal transpiration can account for the experimental data over a wide pressure range. Furthermore, expressions for the frictional and thermal forces on a spherical particle suspended in a gas are derived. These expressions have the correct behavior all the way from the ordinary hydrodynamical to the Knudsen regime. In particular, thermal force data are well represented, with suitably chosen surface coefficients, for small and large ratios of the particle/gas heat conductives.

Knudsen forces in vacuum microbalance

Abstract: The problem of transverse and longitudinal Knudsen forces in typical vacuum microbalance measurements is studied by the use of the BGK model and diffuse reflection at the surfaces of the inner and outer cylinders. The forces are expressed in terms of appropriate quadratures of the macroscopic velocity profiles which in turn are obtained by numerical solutions of relevant integral equations. Detailed results for several values of the Knudsen number (Kn) spanning all regimes of interest are reported and the Knudsen forces are seen to exhibit maximum in the transition regime. These results are found in good qualitative, as well as quantitative, agreement with the experimental data (on helium) of Massen et al.

Kinetic theory analysis of rarefied gas flow through finite length slots

Abstract: A kinetic theory analysis is made of the flow of a rarefied monatomic gas through a two‐dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete ordinate methods. The former method portrays the transition regime characteristics well, but has limitations in the free molecule regime. The latter method gives accurate results in the free molecule and slip regime and bolsters confidence in the accuracy of the transition regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytic solution of the moment equations for length‐to‐width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.

The high temperature vaporization and thermodynamics of the titanium oxides. XII. The temperature coefficient of the vapor pressure of TiO

Abstract: Knudsen vapor pressure measurements over the temperature range 1921–1998 K are reported for stoichiometric titanium monoxide contained in a molybdenum crucible The pressures are consistent with that obtained in the preceding paper at 1806 K with the same material in a tungsten crucible The combined results are given by logPE(atm) = (−1292±17) ×103/4576T+(3925±086)/4576 The uncertainties should be increased by about a factor of 3 to recognize the uncertainties in the mass spectrometric ionization cross sections This equation together with the Knudsen equation allows the calculation of the equilibrium rate of mass loss of incongruently vaporizing stoichiometric TiO over the range zero to about 8% mass loss

The solvability of stationary problems for Boltzmann's equation at large Knudsen numbers

Abstract: THE UNIQUE solvability of internal stationary problems (in particular, Couette's problem) for the non-linear Boltzmann equation at large Knudsen numbers is proved.

On an integral equation of viscous flow theory

Abstract: The integral equation encountered by van de Vooren and Veldman [1] in their study of the Knudsen region near the leading edge of a flat plate is solved by the method of Wiener and Hopf. This exact solution yields the values of certain arbitrary constants which were not determined in [1].

Capillary models for porous media. VII. Study of gaseous flow in the transition from the Knudsen to the counter-diffusion regimes

Abstract: For pt.VI see ibid., vol.10, p.1911 (1977). Structure factors have been calculated for the interdiffusion of two gases in random capillary networks over the region of the transition from Knudsen to gaseous diffusion. Parallel bundle and serial models were also investigated as the extremes for high and low connectivity. Certain limits on the magnitude of the structure factors have been demonstrated and these indicate that strong variation of kappa g with pressure would only be evident for non-random network structures.

On the analysis of rarefied gas transition flow in a circular tube based on the locally uniform velocity distribution functions

Abstract: An analytical method is proposed for the problem of rarefied gas channel flow, on the basis of the concept of locally-uniform velocity distribution, and the flow in a circular tube is analyzed. The solution is in good agreement with the experimental results over the whole range of Knudsen number. From the derived results, a new expression of the slip coefficient is also proposed.

Theory of electrostatic stagnation point probes in a low-density flowing continuum plasma. II. The effects of the Knudsen number

Abstract: For pt.I see ibid., vol.9, p.2349 (1976). The continuum stagnation point electrostatic probe theory of pt.I has been extended for a finite-charged-particle mean free path under continuum neutral flow conditions. The numerical results show that: (1) an effective Knudsen number smaller than 10-2 is required for continuum conditions; (2) the influence of effective Knudsen number increases with diffusion Reynolds number; (3) the influence of effective Knudsen number increases with retarding surface potentials and decreases with increasing attracting surface potential; (4) the usual retarding potential method for temperature determination will lead to an increasing overestimate of Te as the effective Knudsen number decreases; (5) the effect of effective Knudsen number is to smooth the 'knee' of the probe characteristic and to render more imprecise the determination of space potential.

Spherical expansion of vapor during evaporation of a droplet

Abstract: The problem of the evaporation of a spherical particle is solved by a numerical finnite-difference method for the stationary and nonstationary cases on the basis of the generalized Krook kinetic equation [1] Evaporation into a vacuum and into a flooded space are considered taking into account the reduction in size and cooling of the droplet The minimum mass outflow is determined for stationary evaporation into a vacuum at small Knudsen numbers The results are compared with those of other authors for both the spherical and plane problems Most previous studies have used different approximations which reduce either to linearizing the problem [2, 3] or to use of the Hertz-Knudsen equation [4] The inaccurate procedure of matching free molecular and diffusive flows at some distance from the surface of the droplet [5] is completely unsuitable in the absence of a neutral gas Equations for the rate of growth of a droplet in a slightly supercooled vapor were obtained in [6] from a solution of the ellipsoidal kinetic model by the method of (expansion of) moments

Thermal Conductivity of Liquid-Liquid Emulsions

Abstract: Correlations for predicting thermal conductivity of liquid-liquid emulsions are reviewed, and tested for their usefulness for oil-water and water-oil emulsions. Selected data from the literature are taken to evaluate the models. For the three systems tested, the Maxwell-Eucken equation gives the best results, with the idealized model of Wang and Knudsen being nearly as good.

Knudsen layers - Some problems and a solution technique

Abstract: Some problems are listed which can be investigated by solving half space boundary value problems for the linearized Boltzmann equation, and it is shown how the solution of these problems may, in principle, be obtained in a closed form. The basic contribution is a technique for solving systems of coupled singular integral equations which arise in the process of solving such Knudsen layer problems. After reducing the solution of the system to a problem in analytic function theory, a related matrix problem is shown to be solvable with a diagonalization technique. The particular case of the temperature Jump problem with the BGK model is discussed in some detail.

Gas flow in cylindrical capillaries under intermediate conditions

Abstract: At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn ∼ 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn ∼ 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.

Brownian coagulation of aerosols in the transition regime

Abstract: Earlier experimental studies of Brownian coagulation of aerosols have been extended into the transition regime, i.e. Knudsen number values 0.8–1.6. This was done by working with the same range of particle size as earlier, but at a reduced pressure. A number of modifications were made in the experimental technique, including the use of diethylhexylsebacate instead of dibutylphthalate in order to avoid the possibility of loss to the walls by evaporation. The rate of coagulation at Kn = 0.2 agreed closely with that predicted, using Smoluchowski's coagulation constant for the continuum regime as modified by the Cunningham correction. The rate at higher Knudsen numbers (Kn = 0.8–1.6) was somewhat lower (about 20%) than that predicted by Fuchs' formula for interpolation between the continuum and free molecule regimes.