Volume 23, Issue 3, March 2011
Index of content:

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.

 LETTERS


The symmetry of mobility laws for viscous flow along arbitrarily patterned surfaces
View Description Hide DescriptionGeneralizations of the noslip boundary condition to allow for slip at a patterned fluidsolid boundary introduce a surface mobility tensor, which relates the shear traction vector tangent to the mean surface to an apparent surface velocity vector. For steady, lowReynoldsnumber fluid motions over planar surfaces perturbed by arbitrary periodic height and Navier slip fluctuations, we prove that the resulting mobility tensor is always symmetric, which had previously been conjectured. We describe generalizations of the results to three other families of geometries, which typically have unsteady flow.

Thermal transpiration flow: A circular crosssection microtube submitted to a temperature gradient
View Description Hide DescriptionThermal transpiration is the macroscopic movement of rarefied gas molecules induced by a temperature gradient. The gas moves from the lower to the higher temperature zone. An original method is proposed here to measure the mean macroscopic movement of gas in the case of a long circular crosssection glass microtube onto which a gradient of temperature is applied. The mass flow rate and the thermomolecular pressure difference have been measured by monitoring the absolute pressure evolution in time at both ends of the capillary using highspeed response pressure gauges. Two gases, nitrogen and helium, are studied and three different temperature differences of 50, 60, and are applied to the tube. The analyzed gas rarefaction conditions vary from transitional to slip regime.

 ARTICLES


Interfacial Flows

Velocity field reconstruction in gravitydriven flow over unknown topography
View Description Hide DescriptionA numerical method for reconstructing the velocity field of a viscous liquid flowing over unknown topography is presented. For a given fluid this procedure allows one to determine the velocity field as well as the topographic structure from the freesurface shape only. First, we confirm the results with previous computations in the thinfilm limit and then generalize the numerical solution to arbitrary film thicknesses and focus on the velocity field. It is documented that even smoothly corrugated freesurface shapes require strongly undulated topographies to maintain the flow structure. Finally, we discuss details of the implementation in applications, solvability in general, and sensitivity of the solution.

Nonlinear dynamics of confined thin liquidvapor bilayer systems with phase change
View Description Hide DescriptionWe numerically investigate the nonlinear evolution of the interface of a thin liquidvapor bilayer system confined by rigid horizontal walls from both below and above. The lateral variation of the vapor pressure arising from phase change is taken into account in the present analysis. When the liquid (vapor) is heated (cooled) and gravity acts toward the liquid, the deflection of the interface monotonically grows, leading to a rupture of the vapor layer, whereas nonruptured stationary states are found when the liquid (vapor) is cooled (heated) and gravity acts toward the vapor. In the latter case, vaporflowdriven convective cells are found in the liquid phase in the stationary state. The average vapor pressure and interface temperature deviate from their equilibrium values once the interface departs from the flat equilibrium state. Thermocapillarity does not have a significant effect near the thermodynamic equilibrium, but becomes important if the system significantly deviates from it.

Viscous and NonNewtonian Flows

Role of fluid elasticity on the dynamics of rinsing flow by an impinging jet
View Description Hide DescriptionRinsing 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.

Particulate, Multiphase, and Granular Flows

Settling dynamics of asymmetric rigid fibers
View Description Hide DescriptionThe threedimensional motion of asymmetric rigid fibers settling under gravity in a quiescent fluid was experimentally measured using a pair of cameras located on a movable platform. The particle motion typically consisted of an initial transient after which the particle approached a steady rate of rotation about an axis parallel to the acceleration of gravity, with its center of mass following a helical trajectory. Numerical and analytical methods were used to predict translational and angular velocities as well as the evolution of the fiber orientation as a function of time. A comparison of calculated and measured values shows that it is possible to quantitatively predict complex motions of particles that have highly asymmetric shape. The relations between particle shape and settling trajectory have potential applications for hydrodynamic characterization of fiber shapes and fiber separation.

Laminar Flows

Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number
View Description Hide DescriptionThis article describes a strategy of active flow control for lift force reduction of circular cylinder subjected to uniform flow at low Reynolds numbers. The flow control is realized by rotationally oscillating the circular cylinder about its axis with , where is the dimensionless angular speed of rotation cylinder, is the control parameter and is the feedback signal of lift coefficient. The study focuses on seeking optimum for the low Reynolds numbers of 60, 80, 100, 150, and 200. The effectiveness of the proposed flow control in suppressing lift force is examined comprehensively by a numerical model based on the finite element solution of twodimensional Navier–Stokes equations. The dependence of lift reduction on the control parameter is investigated. The threshold of , denoted by , is identified for the Reynolds numbers considered in this work. The numerical results show that the present active rotary oscillation of circular cylinder is able to reduce the amplitude of lift force significantly as long as , at least 50% for the laminar flow regime. Meanwhile, the present active flow control does not result in the undesirable increase in the drag force. The Strouhal number is observed to decrease slightly with the increase of . As for a specific Reynolds number, the larger gives rise to the larger amount of lift reduction. The lift reduction reaches the maximum at . The mechanism behind the present lift reduction method is revealed by comparing the flow patterns and pressure distributions near the active rotationally oscillating circular cylinder and the stationary circular cylinder. It is found that the critical value generally increases with Reynolds number. Two types of lift shift are observed in the numerical results for the cases with . The first is characterized by the regular fluctuation of lift coefficient but with nonzero mean value, while the second is associated with the sustaining increase of lift coefficient. The phenomenon of lift shift is found to be related closely to the evolution of vortex pattern in the near wake of circular cylinder.

Low Reynolds number flow over a square cylinder with a splitter plate
View Description Hide DescriptionFlows over a square cylinder of side length with and without a splitter plate are numerically investigated at a Reynolds number of 150. The length of the splitter plate is varied systematically from to so the sensitivity of the flow structure to the inclusion of the splitter plate can be inspected. It is found that the splitter plate introduces a strong hydrodynamic interaction to the near wake of the cylinder and the length of the plate affects significantly the flow structure. The behavior of the flow can be grouped into three regimes. For short plate lengths , the free shear layers are convected further downstream before rolling up when the plate length is increased. For intermediate plate lengths , a secondary vortex is clearly visible around the trailing edge of the splitter plate and the shear layers begin to roll up closer to the trailing edge. For long plate lengths , a regime is observed in which the free shear layers reattach to the splitter plate. The study also proposes the minimum wake halfwidth as the length scale for a possible universal Strouhal number, which is found to be valid for .

Instability and Transition

Quasitwodimensional convection in a threedimensional laterally heated box in a strong magnetic field normal to main circulation
View Description Hide DescriptionConvection in a laterally heated threedimensional box affected by a strong magnetic field is considered in the quasitwodimensional (Q2D) formulation. It is assumed that the magnetic field is strong and is normal to the main convective circulation. The stability of the resulting Q2D flow is studied for two values of the Hartmann number scaled by half of the width ratio, 100 and 1000, and for either thermally insulating or perfectly conducting horizontal boundaries. The aspect lengthtoheight ratio of the box is varied continuously between 4 and 10. It is shown that the magnetic field damps the bulk flow and creates thermal and Shercliff boundary layers at the boundaries, which become the main source of instabilities. In spite of the general tendency of the flow stabilization by the magnetic field, the flow instability takes place in different ways depending on the boundary conditions and the aspect ratio. Similarities with other magnetic field directions and flows with larger Prandtl numbers are discussed.

Liquid mixture convection during phase separation in a temperature gradient
View Description Hide DescriptionWe simulate the phase separation of a lowviscosity binary mixture, assuming that the fluid system is confined between two walls that are cooled down to different temperatures below the critical point of the mixture, corresponding to quenches within the unstable range of its phase diagram. Spinodal decomposition patterns for offcritical mixtures are studied numerically in two dimensions in the creeping flow limit and for a large Lewis number, together with their dependence on the fluidity coefficient. Our numerical results reproduce the largescale unidirectional migration of phaseseparating droplets that was observed experimentally by Califano et al. [“Largescale, unidirectional convection during phase separation of a densitymatched liquid mixture,” Phys. Fluids17, 094109 (2005)], who measured typical speeds that are quite larger than the Marangoni velocity. To understand this finding, we then studied the temperaturegradientinduced motion of an isolated droplet of the minority phase embedded in a continuous phase, showing that when the drop is near local equilibrium, its speed is of the same order as the Marangoni velocity, i.e., it is proportional to the unperturbed temperature gradient and the fluidity coefficient. However, far from local equilibrium, i.e., for very large unperturbed temperature gradients, the drop first accelerates to a speed that is larger than the Marangoni velocity, then, later, it decelerates, exhibiting an increasedecrease behavior, as described by Yin et al. [“Thermocapillary migration of nondeformable drops,” Phys. Fluids20, 082101 (2008)]. Such behavior is due to the large nonequilibrium, Kortewegdriven convection, which at first accelerates the droplets to relatively large velocities, and then tends to induce an approximately uniform inside temperature distribution so that the drop experiences an effective temperature gradient that is much smaller than the unperturbed one and, consequently, decelerates.
