R.V. Tompson

Viscosity and velocity slip coefficients for gas mixtures: Measurements with a spinning rotor gauge

A selection of experimental measurements for He-Ar, He-N2, and He-Ne binary gas mixtures which were made with a spinning rotor gauge (SRG) are reported. All of the experiments were conducted in the slip regime. Theoretical results from a previous paper on the SRG are used to extract values of the viscosity and the velocity slip coefficient from the experimentally obtained data for each of the gas mixtures. The measured viscosities are in excellent agreement with existing literature values. Slip coefficients for binary gas mixtures have not previously been reported. An important issue here is whether the velocity slip coefficients for binary gas mixtures can be predicted accurately using separately measured tangential momentum accommodation coefficients. The calculation of slip coefficients from theory requires a knowledge of the accommodation coefficients of each constituent of the mixture. The dependence of these coefficients on the gas composition is not known and the simplest assumption is to regard th...

The spinning rotor gauge: Measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients

A set of experimental measurements with a spinning rotor gauge (SRG) with 3.85, 4.00, and 4.50 mm nominal diameter steel spheres in He, Ar, and Kr is reported. The experiments covered the continuum and the slip regimes for all three gases. Theoretical results from a companion paper on the SRG, together with a calibration based on known viscosity for helium, are used to extract values of the viscosity, the velocity slip coefficient, and the tangential momentum accommodation coefficient for each of the gases. The measured viscosities are in good agreement with existing literature values.

Isothermal condensation on a spherical particle

The problem of isothermal condensation onto a spherical particle for a vapor diffusing through a background gas is considered. Accurate numerical results for the condensation rate and density profile in the Knudsen layer, for arbitrary mass ratio (background/vapor) and Knudsen number, are obtained by use of the SN method and the resulting theoretical values are compared with recent experimental data. The present theoretical results correspond to an assumption of rigid sphere molecular interactions, but the development is sufficiently general that results for other molecular force laws could also be obtained.

Measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients using a modified spinning rotor gauge

A selection of experimental viscosity and slip measurements are reported for He and Ar. The measured values have been made with a modified spinning rotor gauge (SRG-2; MKS Instruments, Inc.) where the sphere is coaxially rotated in the cylindrical tube housing. All of the experiments were conducted in the slip regime in accordance with the theory previously developed [S. K. Loyalka, J. Vac. Sci. Technol. A 14, 2940 (1996)]. The theoretical results from this previous article allow one to extract values of the viscosity, the velocity slip coefficient, and the tangential momentum accommodation coefficient from the experimentally obtained angular retardation data for each gas without a need for calibration of the system against a known gas viscosity. Since the existing manufactured SRGs mount horizontally with the rotor angular momentum vector oriented vertically, the required SRG modifications were necessarily limited to the interior of the mounting tube. Here, an insert was developed for the mounting tube in which was bored a short, vertically oriented, cylindrical hole in which the rotor could turn coaxially. Measurements made with this modified version of the SRG are compared with previous experimental results and a discussion of the errors associated with both wall and end effects is included.

Rotatory oscillations of arbitrary axi-symmetric bodies in an axi-symmetric viscous flow: Numerical solutions

The problem of the rotatory oscillation of an axi-symmetric body in an axi-symmetric, viscous, incompressible flow at low Reynolds number has been studied. In contrast to the steady rotation of a body, which involves solving the Laplace equation, the study of an oscillating body requires solution of the Helmholtz equation which results from the simplification of the unsteady Stokes equations. In the present work, we have numerically evaluated the local stresses and torques on a selection of free, oscillating, axi-symmetric bodies in the continuum regime in an axi-symmetric viscous incompressible flow. The Helmholtz equation was solved by a Green’s function technique. The accuracy of the technique is tested against known solutions for a sphere, a prolate spheroid, a thin disk, and an infinitely long cylinder. Good agreements have been obtained. Finite cylinders have been studied and the edge correction factors for the circular disk geometry, that are basic to oscillating disk viscometers, have been calculated. It has been found that the calculated edge correction factors, based on the ratios of the real parts of the actual torques (calculated from this work) to the ideal torques, agree to within 1% to 10% with the reported values obtained by Clark et al. [Physica A 89, 539 (1977)] using the theory of Kestin and Wang [J. Appl. Mech. 24, 197 (1957)]. However, since the ratios of the real parts and the ratios of the imaginary parts of the torques do not coincide, the edge correction factors depend upon which ratio is used.

Computation of electric fields and particle motion in electrodynamic balances

Abstract A numerical method based on the Greens function (the potential theory) approach is adapted for computation of the electric fields in electrodynamic balances. The accuracy of the method is checked against analytical solutions for the case of a single torus and excellent agreement is found. Explicit numerical results for a typical double-ring balance are obtained. The method is an improvement over the existing “charge simulation technique” which, although often adequate, is not rigorously founded. Additionally, the equations of particle motion are solved using the numerically precise electric fields (rather than the linearized fields). Overall, the rigor of potential theory is combined with the computational /display power of Mathematica® to provide accurate descriptions of the electric fields and the particle motion. Use of Mathematica® also leads to the simple computation of particle stability diagrams.

Isothermal condensation on a plane surface

The half‐space problem of isothermal condensation of a vapor diffusing through a background gas is considered. Accurate numerical results for the jump distance and density profile in the Knudsen layer for arbitrary mass ratio (background/vapor) are obtained via the use of the SN method. The results correspond to the assumption of rigid sphere molecular interaction, but the development is sufficiently general that results for other molecular force laws could also be obtained. Finally, a correlation for the jump coefficient as a function of the mass ratio is given.

Chapman–Enskog solution for diffusion: Pidduck’s equation for arbitrary mass ratio

In several studies of rarefied gas dynamics and particle transport, not only the diffusion coefficient, but also a detailed description of the Chapman–Enskog solution for diffusion is required. The case of diffusion of a trace species in a background gas is considered for arbitrary molecular mass ratio, and accurate results are reported for the Chapman–Enskog solution obtained by solving numerically an integral equation of Pidduck.

Condensational growth of a spherical droplet: Free molecular limit

Abstract Previously reported variational results on the problem of condensation onto a spherical droplet are studied in the free molecular limit. The Mellin transform is used to evaluate certain integrals, and it is noted that the derivative of the variational expression for the condensation rate is quite erroneous. The need for improved trial functions is pointed out.

Condensation on a spherical droplet—III

Abstract The condensation rate for a spherical droplet in a vapor-gas mixture is studied for all Knudsen numbers. The boundary conditions method is used to derive a simple expression for the condensation rate where the jump coefficient is expressed in terms of the Chapman-Enskog solution for diffusion. Numerical results for a range of Knudsen numbers and mass ratios are obtained assuming rigid sphere interactions between the vapor and gas molecules. It is found that the normalized condensation rate has a weak but interesting dependence on the mass ratio.