Boundary slip phenomena in a binary gas mixture

The slip phenomena in gas mixtures are of fundamental significance in the specification of boundary conditions for flows in the slip regime. In a recent paper, new explicit results for the slip coefficients appropriate to binary gas mixtures were reported. The present work being reported extends the previous work to a higher level of accuracy by involving a higher order Chapman-Enskog expansion. In particular, new expressions for the slip coefficients are presented which are applicable for arbitrary models of the intermolecular interaction. Limiting expressions for the slip coefficients are given (for a simple gas) and the accuracy of the theory is discussed. Numerical calculations of the slip coefficients for different binary gas mixtures using the first and second order Chapman-Enskog approximations and the rigid sphere and Lennard-Jones (12-6) potential models have been carried out. The thermal creep and diffusion slip coefficients are found to be sensitive to the order of the approximation and to the potential model used. A comparison of the new higher order results with some of our previously obtained experimental data for the thermal transpiration effect has also been carried out and shows excellent agreement between the theory and the experiments which confirms the accuracy of the theory.     

Adsorption on Heterogeneous Regular Surfaces

Quantifying the role of surface shape and physicochemical surface conditions on the interfacial reactivity of particles and substrates is fundamental to a multitude of natural and engineered surface adsorption phenomena. We consider continuum/jump regime adsorption at the gas or liquid interface of arbitrary regular solid surfaces with heterogeneous surface features. In particular, the 3-D boundary value problem (based on Laplace's diffusion equation) is converted into a 2-D integral equation for the adsorbate concentration at the particle surface. This accommodates numerical descretization via the implementation of 2-D Gauss-Legendre quadratures on an arrangement of high- and low-adsorption patch trace sites constructed to completely cover the particle surface. A generalized computer program is developed to solve the resulting linear algebra problem for the unkown local adsorption current densities. We investigate the role of various distributions of high- and low-adsorption sites for a generalized class of spheres which includes the DNA-like shaped twisted spheres. The biological implications of the role of surface curvature on interfacial adsorption/reactivity at particle surfaces are also discussed. Copyright 2001 Academic Press.     

Gold,silver, and palladium nanoparticle/nano-agglomerate generation,collection, and characterization

Generation, collection, and characterization of gold, silver, and palladium nanoparticles and nano-agglomerates (collectively “nanoparticles”) have been explored. The nanoparticles were generated with a spark aerosol generator (Palas GFG-1000). They were collected using a deposition cell under diffusion and thermophoresis. The shapes and sizes of the deposited particles were measured using transmission electron microscopy (TEM). TEM images showed that the particles were in the range of 8–100 nm in diameter, and their shapes varied from nearly spherical to highly non-spherical. Thermophoresis enhanced the deposition of nanoparticles (over the diffusive or the isothermal deposition) in all cases. Further, the size distributions of the nanoparticles generated in the gas phase (aerosol) were measured using a scanning mobility particle sizer (SMPS 3080, TSI) spectrometer. The SMPS results show that an increase in the spark frequency of the generator shifted the size distributions of the nanoparticles to larger diameters, and the total particle mass production rate increased linearly with increase in the spark frequency. The computational fluid dynamics code Fluent (Ansys) was used to model the flow in the deposition cell, and the computed results conform to the observations.     

Magnetic structure of NdB6

Neutron diffraction measurements were made on a polycrystalline sample of NdB₆ at 78 and 4.2 K. This material orders antiferromagnetically with a Neel temperature of 8.6 K. The magnetic structure inferred from the diffraction data indicates a simple antiferromagnetic doubling of the unit cell in one direction. Based on this structure a profile analysis of the data gives a magnetic moment at 4.2 K of 1.74 Bohr magnetons per neodymium ion.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

The velocity slip problem: Accurate solutions of the BGK model integral equation

The velocity slip problem (also known as the Kramers problem) in the kinetic theory has been solved by a variety of techniques, and some accurate numerical as well as general variational results are available for both simple gases and gas mixtures. For the model equations, reasonably accurate solutions (within about 1% of the exact results) have been obtained by solving the related integral equations, but such techniques have not previously been pushed far enough to explore the possibilities of obtaining benchmark solutions. Some of the reasons for not further pursuing these techniques were limitations on the efficiencies and accuracies of the computer routines that could be constructed for the needed Abramowitz functions and limitations in terms of computational resources with respect to available precision and storage capabilities. These limitations have now effectively been removed with modern advances in computer technology and the computational tools that have become available, and it is the purpose of the present paper to report on our explorations in this regard within the specific context of the velocity slip problem as based on the BGK model which we have approached using the singularity subtraction technique in conjunction with numerical quadratures.     

Scattering by small defects in the neighbourhood of a fluid-solid interface

The scattering of incident plane elastic waves by a varietyof different defects that lie upon a fluid-solid interface isconsidered here using matched asymptotic expansions. The expansionscheme is developed in terms of a parameter , the ratio of typicaldefect length scale to a typical wavelength of the incidentfield, taken to be small. Three different canonical situations occur and these are illustratedvia three specific examples treated here: a rigid strut, anedge crack, and a rigid strip. In each case the leading-ordermatching is performed to identify the leading-order contributionof the defect to the acoustic field in the far field. In particular,each defect is identified with a source of dipole response ininterfacial stress of displacement. It is shown in the limit as s<<s1 that in the inner problemsthe fluid and solid pieces uncouple in a particularly convenientmanner allowing analytical solutions to be deduced. These arethen matched with appropriate outer solutions.     

A numerical study of two coaxial axi-symmetric particles undergoing steady equal rotation in the slip regime

The problem of two axi-symmetric particles (separated by a certain distance) that rotate about their common axis of symmetry in an infinite viscous fluid with slip boundary conditions at their surfaces have been studied numerically. Aerosol particles are usually nonspherical with the exception of liquid droplets in certain cases, and the shape of particles has a significant impact on frictional drag (for particle translation) and torque (for particle rotation), and, hence, on Brownian motion, and the deposition, sampling and coagulation of particles. The effects of the rotation of particles prior to their collision and coagulation have usually been ignored in favor of simpler calculations. The study of two-particle systems should give more information about the interaction between particles that cannot be understood from the study of single particles alone. In this work, the Laplace equation (resulting from the steady Stokes equation) with slip boundary conditions is converted into a Fredholm integral equation of the second kind via the use of Green's function. The integral equations are then solved by the singularity subtraction method. The local stresses are calculated at each nodal point and the torques are then calculated from the summation of the local stresses. Explicit numerical results for the local stresses and torques are reported for three systems of two axi-symmetric particles, i.e. sphere-sphere, sphere-spheroid, and spheroid-spheroid. While the formulation of the problem is quite general, the results reported here have been limited to calculations for systems in which both particles have identical angular velocities. The numerical method is, however, valid for arbitrary axi-symmetric particles and its modification to systems containing other shaped particles or differing angular velocities is straightforward. Numerical results of the torques for each system studied show in every case that the presence of slip results in a reduction in the torques. As a consequence, the impact of the slip on the torques and local stresses is substantial and cannot be ignored. The distance between the centers of the particles (the separation distance) also plays an important role in determining the values of the torques and local stresses. In the systems that have been studied here, as the particles get further apart, the torques on both particles increase.     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials III: Diffusion,thermal diffusion,and thermal conductivity in a binary,rigid-sphere,gas mixture

The Chapman–Enskog solutions of the Boltzmann equation provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper (I), for simple, rigid-sphere gases (i.e. single-component, monatomic gases) we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are free of numerical error and, in a second paper (II), we have extended our initial simple gas work to modeling the viscosity in a binary, rigid-sphere, gas mixture. In this latter paper we reported an extensive set of order 60 results which are believed to constitute the best currently available benchmark viscosity values for binary, rigid-sphere, gas mixtures. It is our purpose in this paper to similarly report the results of our investigation of relatively high-order (order 70), standard, Sonine polynomial expansions for the diffusion- and thermal conductivity-related Chapman–Enskog solutions for binary gas mixtures of rigid-sphere molecules. We note that in this work, as in our previous work, we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. For rigid-sphere gases, all of the relevant omega integrals needed for these solutions are analytically evaluated and, thus, results to any desired precision can be obtained. The values of the transport coefficients obtained using Sonine polynomial expansions for the Chapman–Enskog solutions converge and, therefore, the exact diffusion and thermal conductivity solutions to a given degree of convergence can be determined with certainty by expanding to sufficiently high an order. We have used Mathematica® for its versatility in permitting both symbolic and high-precision computations. Our results also establish confidence in the results reported recently by other authors who used direct numerical techniques to solve the relevant Chapman–Enskog equations. While in all of the direct numerical methods more-or-less full calculations need to be carried out with each variation in molecular parameters, our work has utilized explicit, general expressions for the necessary matrix elements that retain the complete parametric dependence of the problem and, thus, only a matrix inversion at the final step is needed as a parameter is varied. This work also indicates how similar results may be obtained for more realistic intermolecular potential models and how other gas-mixture problems may also be addressed with some additional effort.