Volume 23, Issue 3, March 2011

Rinsing flows are common processes where a jet of one liquid impinges upon a layer of a second liquid for the purpose of removing the second liquid. An imaging setup has been developed to obtain both qualitative and quantitative data on the rinsing flow of a jet of water impinging on either layers of Newtonian or elastic fluids. Three classes of test fluids have been investigated: a Newtonian glycerolwater solution, a semidilute aqueous solution of high molecular weight polyacrylamide solution displaying both elasticity and shear thinning, and an elastic but nonshear thinning Boger fluid. The fluids were designed to have approximately equal zeroshear viscosities. For all cases, a circular hydraulic jump occurs and Saffman–Taylor instabilities were observed at the interface between the low viscosity jet and the higher viscosity coating liquids. Results show that the elasticity (extensional viscosity) of the samples influences the pattern of the instabilities and contributes to dampening surface disturbances in the vicinity of the hydraulic jump. Quantitative measurements of liquid layer thicknesses were obtained using a laser triangulation technique. We observed that shear thinning contributes to increasing the velocity of the hydraulic jump circle growth, and the growth profile appears to be linear instead of logarithmiclike as in the Newtonian fluids. Shear thinning characteristics of the samples also contribute to a larger vertical height of the hydraulic jump and an undercutting phenomenon. The elasticity of the fluids contributes to a “recoil” of the hydraulic jump circle, causing the circle, after initial expansion, to shrink in size before expanding again.
 SPECIAL TOPIC: A TRIBUTE TO CARLO CERCIGNANI (1939–2010)


Preface to Special Topic: A Tribute to Carlo Cercignani (1939–2010)
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Investigation of the ellipsoidalstatistical Bhatnagar–Gross–Krook kinetic model applied to gasphase transport of heat and tangential momentum between parallel walls
View Description Hide DescriptionThe ellipsoidalstatistical Bhatnagar–Gross–Krook (ESBGK) kinetic model is investigated for steady gasphase transport of heat, tangential momentum, and mass between parallel walls (i.e., Fourier, Couette, and Fickian flows). This investigation extends the original study of Cercignani and Tironi, who first applied the ESBGK model to heat transport (i.e., Fourier flow) shortly after this model was proposed by Holway. The ESBGK model is implemented in a moleculargasdynamics code so that results from this model can be compared directly to results from the full Boltzmann collision term, as computed by the same code with the direct simulation Monte Carlo (DSMC) algorithm of Bird. A gas of monatomic molecules is considered. These molecules collide in a pairwise fashion according to either the Maxwell or the hardsphere interaction and reflect from the walls according to the Cercignani–Lampis–Lord model with unity accommodation coefficients. Simulations are performed at pressures from nearfreemolecular to nearcontinuum. Unlike the BGKmodel, the ESBGK model produces heatflux and shearstress values that both agree closely with the DSMC values at all pressures. However, for both interactions, the ESBGK model produces molecularvelocitydistribution functions that are qualitatively similar to those determined for the Maxwell interaction from Chapman–Enskog theory for small wall temperature differences and momenthierarchy theory for large wall temperature differences. Moreover, the ESBGK model does not produce accurate values of the mass selfdiffusion coefficient for either interaction. Nevertheless, given its reasonable accuracy for heat and tangentialmomentum transport, its sound theoretical foundation (it obeys the Htheorem), and its available extension to polyatomic molecules, the ESBGK model may be a useful method for simulating certain classes of singlespecies noncontinuum gas flows, as Cercignani suggested.

Stochastic models in kinetic theory
View Description Hide DescriptionThe paper is concerned with some aspects of stochastic modeling in kinetic theory. First, an overview of the role of particle models with random interactions is given. These models are important both in the context of foundations of kinetic theory and for the design of numerical algorithms in various engineering applications. Then, the class of jump processes with a finite number of states is considered. Two types of such processes are studied, where particles change their states either independently of each other (monomolecular processes) or via binary interactions (bimolecular processes). The relationship of these processes with corresponding kinetic equations is discussed. Equations are derived both for the average relative numbers of particles in a given state and for the fluctuations of these numbers around their averages. The simplicity of the models makes several aspects of the theory more transparent.

Steady flows of a highly rarefied gas induced by nonuniform wall temperature
View Description Hide DescriptionSteady behavior of a rarefied gas between parallel plates with sinusoidal temperature distribution is investigated on the basis of the Boltzmann equation. The Cercignani–Lampis (CL) model or the Lord model for diffuse scattering with incomplete energy accommodation is adopted as the boundary condition on the plates. Most of the analysis is carried out numerically with special interest in the freemolecular limit. In the case of the CL model, the nonuniform temperature distribution of the plates may induce a steady freemolecular flow, which is in contrast with the earlier results for the Maxwelltypemodel [Y. Sone, J. Méc. Théor. Appl.3, 315 (1984); J. Méc. Théor. Appl.4, 1 (1985)]. This fact is confirmed through an accurate deterministic computation based on an integral equation. In addition, computations for a wide range of parameters by means of the direct simulation Monte Carlo method reveal that the flow field changes according to the accommodation coefficients and is classified into four types. The effect of intermolecular collisions on the flow is also examined. In the case of the Lord model, no steady flow of the freemolecular gas is induced as in the case of the Maxwelltypemodel. This result is extended to the case of a more general boundary condition that gives the cosine law (Lambert’s law) for the reflected molecular flux.

Sonine approximation for collisional moments of granular gases of inelastic rough spheres
View Description Hide DescriptionWe consider a dilute granular gas of hard spheres colliding inelastically with coefficients of normal and tangential restitution and , respectively. The basic quantities characterizing the distribution function of linear and angular velocities are the seconddegree moments defining the translational and rotational temperatures. The deviation of from the Maxwellian distribution parameterized by and can be measured by the cumulants associated with the fourthdegree velocity moments. The main objective of this paper is the evaluation of the collisional rates of change of these second and fourthdegree moments by means of a Sonine approximation. The results are subsequently applied to the computation of the temperature ratio and the cumulants of two paradigmatic states: the homogeneous cooling state and the homogeneous steady state driven by a whitenoise stochastic thermostat. It is found in both cases that the Maxwellian approximation for the temperature ratio does not deviate much from the Sonine prediction. On the other hand, nonMaxwellian properties measured by the cumulants cannot be ignored, especially in the homogeneous cooling state for medium and small roughness. In that state, moreover, the cumulant directly related to the translational velocity differs in the quasismooth limit from that of pure smooth spheres . This singular behavior is directly related to the unsteady character of the homogeneous cooling state and thus it is absent in the stochastic thermostat case.

Performance analysis of the continuous trace gas preconcentrator
View Description Hide DescriptionIn gas molecule detection systems, certain trace gas components can go undetected. This is due to ultralow yet dangerous concentrations combined with limitations of the detection methods. To remedy this problem, a preconcentrator can be included in a system to increase the trace gas concentrations, before the gas samples enter the detection unit. The widely used adsorption/desorption preconcentrators enable detection by interrupting the sampled gas flow for significant periods, in order to accumulate detectable periodic concentrations of trace gas molecules. The recently patented continuous trace gas preconcentrator (CTGP) provides a unique approach for enhancing the trace gas concentration, without stopping the flow. In this study, a performance model is developed for the CTGP, by application of the Poiseuille flow coefficients for long tubes. Based on the Cercignani–Lampis scattering kernel, Sharipov calculated the Poiseuille flow coefficients for various geometries and numerous operating Knudsen numbers. The concentrations of sampled molecules were analyzed in this study using Sharipov’s flow coefficients. The results presented here reinforce the potential benefits of the CTGP.

Lownoise Monte Carlo simulation of the variable hard sphere gas
View Description Hide DescriptionWe present an efficient particle simulation method for the Boltzmann transport equation based on the lowvariance deviational simulation Monte Carlo approach to the variablehardsphere gas. The proposed method exhibits drastically reduced statistical uncertainty for lowsignal problems compared to standard particle methods such as the direct simulation Monte Carlo method. We show that by enforcing mass conservation, accurate simulations can be performed in the transition regime requiring as few as ten particles per cell, enabling efficient simulation of multidimensional problems at arbitrarily small deviation from equilibrium.

Shock wave structure for generalized Burnett equations
View Description Hide DescriptionStationary shock wavesolutions for the generalized Burnett equations (GBE) [A. V. Bobylev, “Generalized Burnett hydrodynamics,” J. Stat. Phys.132, 569 (2008)] are studied. Based on the results of Bisi et al. [“Qualitative analysis of the generalized Burnett equations and applications to halfspace problems,” Kinet. Relat. Models1, 295 (2008)], we choose a unique (optimal) form of GBE and solve numerically the shock wave problem for various Mach numbers. The results are compared with the numerical solutions of Navier–Stokes equations and with the Mott–Smith approximation for the Boltzmann equation (all calculations are done for Maxwell molecules) since it is believed that the Mott–Smith approximation yields better results for strong shocks. The comparison shows that GBE yield certain improvement of the Navier–Stokes results for moderate Mach numbers.

Rarefied gas dynamics on a planetary scale
View Description Hide DescriptionLarge scale rarefied gas dynamic effects are found in the tenuous atmospheres of several planets and satellites in our Solar System. These phenomena range from thickened shock structures in supersonic flows, to strong thermal nonequilibrium in a stratified atmosphere, to thermal and velocity slip at the body surface. Sublimated atmospheric components in particular are dominated by the detailed nature of the gassurface interaction. Some direct simulation Monte Carlo (DSMC) results for global scale flows on the Jovian moon Io are presented to illustrate key phenomena in both the sublimated and the volcanic plume components of the atmosphere. The simulations stretch the limits of applicability of DSMC; computational approaches beyond those limits are described.

Boundary conditions at the vaporliquid interface
View Description Hide DescriptionThe paper aims at presenting a review of kinetic theory applications to evaporationcondensation problems. The main results for monatomic and polyatomic gases and mixtures are described. The role of boundary conditions at the vaporliquid interface is discussed and a description of molecular dynamics studies aimed at formulating vaporliquid interaction models is given.
