Temperature dependence of the interfacial tension of PS/PMMA, PS/PE, and PMMA/PE blends

The effect of temperature on the interfacial tension for PS/PMMA, PS/PE, and PMMA/PE was measured using the imbedded fiber retraction method. Interfacial tensions for PS/PMMA, PS/PE, and PMMA/PE were measured over temperature ranges of 160–250 °C, 140–220 °C, and 140–220 °C, respectively. The interfacial tension was found to follow a dependence of 3.6–0.013 T dyn/cm, 7.6–0.051 T dyn/cm and 11.8–0.017 T dyn/cm for PS/PMMA, PS/PE, and PMMA/PE, respectively. Comparison of the data with the mean field theory of Helfand and Sapse were made; however, a simple linear fit to the data described the temperature dependence in the experimental window as well as the predictions of the mean field theory. Received: 6 July 1999 Accepted: 23 March 2000     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Formulation of Multidimensional Scalar Conservation Laws

We show that Kruzhkov’s theory of entropy solutions to multidimensional scalar conservation laws (Kruzhkov in Mat Sb (N.S.), 81(123), 228–255, 1970) can be entirely recast in L ² and fits into the general theory of maximal monotone operators in Hilbert spaces. Our approach is based on a combination of level-set, kinetic and transport-collapse approximations, in the spirit of previous works by Brenier (in C R Acad Sci Paris Ser I Math, 292, 563–566, 1981; in J Diff Equ, 50, 375–390, 1983; in SIAM J Numer Anal, 21, 1013–1037; in Methods Appl Anal, 11, 515–532, 2004), Giga and Miyakawa (in Duke Math J, 50, 505–515, 1983), and Tsai et al. (in Math Comp, 72, 159–181, 2003).     

Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

Non-Ergodicity of the Nosé–Hoover Thermostatted Harmonic Oscillator

The Nosé–Hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical Gibbs distribution. Newton’s equations are modified by coupling an additional reservoir variable to the physical variables. The correct sampling of the phase space according to the Gibbs measure is dependent on the Nosé–Hoover dynamics being ergodic. Hoover presented numerical experiments to show that the Nosé–Hoover dynamics are non-ergodic when applied to the harmonic oscillator. In this article, we prove that the Nosé–Hoover thermostat does not give an ergodynamical system for the one- dimensional harmonic oscillator when the “mass” of the reservoir is large. Our proof of non-ergodicity uses KAM theory to demonstrate the existence of invariant tori for the Nosé–Hoover dynamical system that separate phase space into invariant regions. We present numerical experiments motivated by our analysis that seem to show that the dynamical system is not ergodic even for a moderate thermostat mass.     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000     

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

Aspect-ratio dependence of transient Taylor vortices close to threshold

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.      

Convective heat transfer characteristics of laminar pulsating pipe air flow

 Heat transfer characteristics to laminar pulsating pipe flow under different conditions of Reynolds number and pulsation frequency were experimentally investigated. The tube wall of uniform heat flux condition was considered. Reynolds number was varied from 780 to 1987 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by pulsation frequency while it is slightly affected by Reynolds number. The results showed enhancements in the relative mean Nusselt number. In the frequency range of 1–4 Hz, an enhancement up to 30% (at Reynolds number of 1366 and pulsation frequency of 1.4 Hz) was obtained. In the frequency range of 17–25 Hz, an enhancement up to 9% (at Reynolds number of 1366 and pulsation frequency of 17.5 Hz) was indicated. The rate of enhancement of the relative mean Nusselt number decreased as pulsation frequency increased or as Reynolds number increased. A reduction in relative mean Nusselt number occurred outside these ranges of pulsation frequencies. A reduction in relative mean Nusselt number up to 40% for pulsation frequency range of 4.1–17 Hz and a reduction up to 20% for pulsation frequency range of 25–29.5 Hz for Reynolds numbers range of 780–1987 were considered. This reduction is directly proportional to the pulsation frequency. Empirical dimensionless equations have been developed for the relative mean Nusselt number that related to Reynolds number (750 < Re < 2000) and the dimensionless frequency (3<Ω<18) with about 10% rms. Received on 16 May 2000 / Published online: 29 November 2001     

Charging and coagulation of water aerosols with a small admixture of highly radioactive droplets

The mechanism of electrocoagulation of water aerosols with a small admixture of highly radioactive droplets is examined. A corresponding mathematical model describing the processes of ionization, electrization and coagulation of radioactive water aerosols is developed. The time dependence of the ion concentration and the charge and concentration of the nonradioactive droplets and of the charge and radius of the radioactive droplets is numerically investigated for a number of typical aerosols. It is shown that the electrocoagulation process may lead to an increase in the radius of the droplets from 5–10 to 30–40μm in ≃10⁴ sec ≃3 h and, consequently, may play a significant part in the development of aerosols with a droplet radius of up to 20μm, when gravitational coagulation is unimportant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 90–96, March–April, 1994.     

Specific features of microparticle deformation upon impact on a rigid barrier

Based on experimental data and numerical modeling, it is shown that a lamina of melted metal of thickness of order0.01 d, in which the temperature is close to the melting point of the particle material, can be formed upon high-speed impact (v ₀≈500–1200 m/sec) of a fine metal particle (d=1–50 μm) on a rigid undeformable barrier near the contact surface. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 204–209, January–February, 2000.     

A numerical simulation of external heat transfer around turbine blades

External heat transfer prediction is performed in two-dimensional turbine blade cascades using the Reynolds-averaged Navier–Stokes equations. For this purpose, six different turbulence models including the algebraic Baldwin–Lomax (AIAA paper 78-257, 1978), three low-Re k−ɛ models (Chien in AIAA J 20:33–38, 1982; Launder and Sharma in Lett Heat Mass Transf 1(2):131–138, 1974; Biswas and Fukuyama in J Turbomach 116:765–773, 1994), and two k−ω models (Wilcox in AIAA J 32(2):247–255, 1994) are taken into account. The computer code developed employs a finite volume method to solve governing equations based on an explicit time marching approach with capability to simulate subsonic, transonic and supersonic flows. The Roe method is used to decompose the inviscid fluxes and the gradient theorem to decompose viscous fluxes. The performance of different turbulence models in prediction of heat transfer is examined. To do so, the effect of Reynolds and Mach numbers along with the turbulent intensity are taken into account, and the numerical results obtained are compared with the experimental data available.     

Equations of foam hydrodynamics

A closed system of differential equations describing a foam as a viscoelastic compressible continuum is obtained on the basis of the general theory of the mechanics of deformable continua [3–5]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–95, September–October, 1988.     

On the extendability of solutions of a difference equation “to the left”

We give sufficient conditions for the extendability of solutions of a nonlinear difference equation “to the left” in a Banach space. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 3, pp. 298–302, July–September, 2007.     

Effect of salt on boiling heat transfer of ammonia-water mixture

Nucleate pool boiling heat transfer coefficients were determined experimentally for NH₃–H₂O, NH₃–H₂O–LiNO₃ and NH₃–H₂O–LiBr mixtures. Both the salts were effective in increasing the heat transfer coefficient of NH₃–H₂O mixture. A concentration of 10 mass% of the salts in water, produced the greatest enhancement in heat transfer coefficient at all the range of pressure, heat flux and ammonia concentration studied in this investigation. The experiments indicated that ammonia concentration also has the impact on the augmentation of heat transfer coefficient in NH₃–H₂O binary mixture by the addition of salts. For the solution of ammonia mass fraction 0.30, high concentration of LiBr gives the highest heat transfer coefficient, for ammonia mass fraction of 0.25, high concentration of LiNO₃ gives the maximum heat transfer coefficient, for ammonia mass fraction of 0.15, both the salts are equally effective in increasing the heat transfer coefficient.     

Linearized Burnett Equation for the Dynamic Pressure of a Relativistic Gas

The linearized Burnett equation for the dynamic pressure of a relativistic gas of hadrons is calculated from a relativistic kinetic theory. It is shown, as in a previous paper [1], that the coefficient of the term with a non-homogeneous temperature field, – the heating term – is bigger than the one with the divergence of the four-velocity, – the bulk viscosity term.     

Gas-dynamic spraying. An experimental study of the spraying process

We present results of an experimental study of the specific features of the gas-dynamic formation of coatings from metallic powders (d_p<50 μm) on substrates of various materials depending on the particle velocity (200–1200m/sec), the jet temperature (300–700K), and other parameters. Results of a prospecting study of the implementation of the methods of particle acceleration in supersonic (M=2.0–3.0) rectangular nozzles are described. The rate of bond formation in a cold particle-cold substrate contact occurring in gas-dynamic spraying is estimated within the framework of the concepts applied in analysis of gas-dynamic spraying. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 182–188, March–Apil, 1998.     

One approximate solution of the Nekrasov problem

An approximate solution ω = A[ω, μ] of the nonlinear integral Nekrasov equation is obtained by successive replacement of the kernel of the integral operator by a close one. The solution is sought not directly at the bifurcation point μ₁ = 3 of the linearized equation ω = μL[ω] but at the point μ = 1 at which operator A[ω, μ], remaining nonlinear in ω, is linear in μ. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 50–56, November–December, 2007.     

Transport properties in mixtures involving carbon dioxide at low and moderate density: test of several intermolecular potential energies and comparison with experiment

It is the purpose of this paper to extract unlike intermolecular potential energies of five carbon dioxide-based binary gas mixtures including CO₂–He, CO₂–Ne, CO₂–Ar, CO₂–Kr, and CO₂–Xe from viscosity data and compare the calculated potentials with other models potential energy reported in literature. Then, dilute transport properties consisting of viscosity, diffusion coefficient, thermal diffusion factor, and thermal conductivity of aforementioned mixtures are calculated from the calculated potential energies and compared with literature data. Rather accurate correlations for the viscosity coefficient of afore-cited mixtures embracing the temperature range 200 K < T < 3273.15 K is reproduced from the present unlike intermolecular potentials energy. Our estimated accuracies for the viscosity are to within ±2%. In addition, the calculated potential energies are used to present smooth correlations for other transport properties. The accuracies of the binary diffusion coefficients are of the order of ±3%. Finally, the unlike interaction energy and the calculated low density viscosity have been employed to calculate high density viscosities using Vesovic–Wakeham method.     

Effect of longitudinal aberration in an ion-optical system on the properties of a focused beam

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 3–13, May – June 1994.     

Asymptotic properties of solutions of systems of nonlinear functional differential equations of neutral type

We establish sufficient conditions for systems of nonlinear functional differential equations of neutral type to have solutions that are continuously differentiable and bounded for t ∈ ℝ (together with their first derivatives) and investigate the asymptotic properties of these solutions. Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 20–26, January–March, 2009.