Fundamentals of steady state, non-Newtonian rimming flow

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and the liquid film is thin. Since the Deborah number is very small the flow is viscometric. The shear-thinning number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The rheological models, which show Newtonian behavior at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit Newtonian behavior near the free surface and power-law behavior near the wall of the rotating cylinder.

Viscosity of binary mixtures of cycloalkane with cycloalkane, alkane and aromatic hydrocarbon at 303.15 K

The viscosity ? for eighteen binary mixtures cyclopentane + cyclohexane and + cyclooctane; cyclohexane + cycloheptane, + cyclooctane, + methylcyclohexane, + n-hexane, + n-heptane, + n-octane, + i-octane, + benzene, + toluene, + ethylbenzene, + p-xylene, and + propylbenzene; methylcyclohexane + n-hexane, + i-octane, and + benzene; and cyclooctane + benzene have been reported at 303.15 K over the entire range of composition. The viscosity deviations ?? and excess Gibbs energy of activation ?G*E of viscous flow based on Eyring's theory have been calculated. The effects of molecular sizes and shapes of the component molecules and of interaction energy in the mixture have been discussed. The viscosity data have been correlated with the equations of Grunberg and Nissan, Hind, McLaughlin and Ubbelohde, Tamura and Kurata, Katti and Chaudhri, McAllister, Heric and Brewer, and of Auslaender.

Densities, speeds of sound, isentropic compressibilities, refractive indices and viscosities of binary mixtures of tetrahydrofuran with hydrocarbons at 303.15 K

Isentropic compressibilities, Rao's molar sound functions, molar refractions, excess isentropic compressibilities, excess molar volumes, viscosity deviations and excess Gibbs energies of activation of viscous flow for seven binary mixtures of tetrahydrofuran (THF) with cyclohexane, methylcyclohexane, n-hexane, benzene, toluene, p-xylene and propylbenzene over the entire range of composition at 303.15 K have been derived from experimental densities, speeds of sound, refractive indices and viscosities. The excess partial molar volumes of THF in different solvents have been estimated. The experimental results have been analyzed in terms of the Prigogine–Flory–Patterson theory.

Densities, speeds of sound, isentropic compressibilities, refractive indexes, and viscosities of tetrahydrofuran with haloalkane or alkyl ethanoate at T = 303.15 K

Isentropic compressibilities ?S, excess isentropic compressibilities image, excess molar volumes VE, viscosity deviations ??, and excess Gibbs energy of activation of viscous flow ?G*E for nine binary mixtures of C4H8O with CCl4, CHCl3, CHCl2CHCl2, 1-C6H13Cl, 1-C6H13Br, CH3CO2CH3, CH3CO2C2H5, CH3CO2C4H9, and CH3CO2C5H11 at 303.15 K have been derived from experimental densities ?, speeds of sound u, refractive indexes nD and viscosities ?. The limiting values of excess partial molar volumes of C4H8O at infinite dilution image in different solvents have been estimated. The results obtained for dynamic viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg–Nissan, Tamura–Kurata, Hind–McLaughlin–Ubbelohde, Katti–Chaudhri, McAllister, Heric, and Auslaender. Finally, the experimental refractive indexes were compared with the predicted results for Lorentz–Lorenz, Dale–Gladstone, Eykman, Arago–Boit, Newton, Oster, Heller, and Wiener equations.

Speeds of sound, isentropic compressibilities, viscosities, and excess molar volumes of binary mixtures of alkanoates with tetra- and trichloromethanes at 303.15 K

Speeds of sound u, isentropic compressibilities ?S, viscosities ?, excess isentropic compressibilities ?SE, excess molar volumes VE, viscosity deviations ??, and excess Gibbs energies of activation ?G*E of viscous flow have been investigated for six binary mixtures of diethyl malonate, diethyl bromomalonate, and ethyl chloroacetate with tetra- and trichloromethane at 303.15 K. The values of ?SE, VE, ??, and ?G*E are highly dependent on the type of components involved and the composition curves are unsymmetrical. The results obtained for viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg-Nissan, Tamura-Kurata, Hind-McLaughlin-Ubbelohde, Katti-Chaudhri, McAllister, Heric-Brewer and Auslaender. The experimental speeds of sound have been analyzed in terms of collision factor theory and free length theory of solutions.

A comparative electrochemical study of diffusion in room temperature ionic liquid solvents versus acetonitrile

Measurements on the diffusion coefficient of the neutral molecule N,N,N',N'-tetramethyl-para-phenylenediamine and the radical cation and dication generated by its one- and two-electron oxidation, respectively, are reported over the range 298-348 K in both acetonitrile and four room temperature ionic liquids (RTILs). Data were collected using single and double potential step chronamperometry at a gold disk electrode of micrometer dimension, and analysed via fitting to the appropriate analytical expression or, where necessary, to simulation. The variation of diffusion coefficient with temperature was found to occur in an Arrhenius-type manner for all combinations of solute and solvent. For a given ionic liquid, the diffusional activation energies of each species were not only closely equivalent to each other, but also to the RTIL's activation energy of viscous flow. In acetonitrile supported with 0.1 M tetrabutylammonium perchlorate, the ratio in diffusion coefficients of the radial cation and dication tot he neutral molecule were calculated as 0.89 +/- 0.05 and 0.51 +/- 0.03, respectively. In contrast, amongst the ionic liquids the same ratios were determined to be on average 0.53 +/- 0.04 and 0.33 +/- 0.03. The consequences of this dissimilarity are considered in terms of the modelling of voltammetric data gathered within ionic liquid solvents.

Framework for Establishing Limits of Tabular Aerodynamic Models for Flight Dynamics Analysis

This paper describes the use of the Euler equations for the generation and testing of tabular aerodynamic models for flight dynamics analysis. Maneuvers for the AGARD Standard Dynamics Model sharp leading-edge wind-tunnel geometry are considered as a test case. Wind-tunnel data is first used to validate the prediction of static and dynamic coefficients at both low and high angles, featuring complex vortical flow, with good agreement obtained at low to moderate angles of attack. Then the generation of aerodynamic tables is described based on a data fusion approach. Time-optimal maneuvers are generated based on these tables, including level flight trim, pull-ups at constant and varying incidence, and level and 90 degrees turns. The maneuver definition includes the aircraft states and also the control deflections to achieve the motion. The main point of the paper is then to assess the validity of the aerodynamic tables which were used to define the maneuvers. This is done by replaying them, including the control surface motions, through the time accurate computational fluid dynamics code. The resulting forces and moments are compared with the tabular values to assess the presence of inadequately modeled dynamic or unsteady effects. The agreement between the tables and the replay is demonstrated for slow maneuvers. Increasing rate maneuvers show discrepancies which are ascribed to vortical flow hysteresis at the higher rate motions. The framework is suitable for application to more complex viscous flow models, and is powerful for the assessment of the validity of aerodynamics models of the type currently used for studies of flight dynamics.

Volumetric Properties, Viscosities, and Isobaric Heat Capacities of Imidazolium Octanoate Protic Ionic Liquid in Molecular Solvents

Densities (F), viscosities (?), and isobaric heat molar capacities (Cp) of binary mixtures containing imidazolium octanoate, [Im][C7CO2], a protic ionic liquid (PIL), with four molecular solvents, water, acetonitrile, ethanol, and 1-octanol, are determined as a function of temperature from (298.15 to 323.15) K and within the whole composition range at atmospheric pressure. Excess molar volumes, VE, excess molar heat capacities, Cp E, and the deviation from additivity rules of viscosities, ??, of imidazolium octanoate solutions were then deduced from the experimental results, as well as apparent molar volumes, Vfi, and partial molar volumes, V j m,i. Results are discussed according to the nature of the interaction between the PIL and the molecules and the effect of temperature. The excess Gibbs energies of activation of viscous flow (?G*E) for these systems were then calculated at 298.15 K. The excess isobaric heat capacities, Cp E, of binary ([Im][C7CO2] + solvent) systems, depend also of the nature of the molecular solvent in mixture. The excess properties were then correlated, at each temperature, as a function of composition by a Redlich-Kister-type equation. Finally results have been discussed in terms of molecular interactions and molecular structures in these binary mixtures, and thermodynamic properties of investigated binary mixtures were then compared to literature values together to investigate the impact of the nature of the solvent on these reported properties.

Volumetric properties, viscosity and refractive index of the protic ionic liquid, pyrrolidinium octanoate, in molecular solvents

Densities ([rho]) and viscosities ([eta]) of binary mixtures containing the Protic Ionic Liquid (PIL), pyrrolidinium octanoate with five molecular solvents: water, methanol, ethanol, n-butanol, and acetonitrile are determined at the atmospheric pressure as a function of the temperature and within the whole composition range. The refractive index of all mixtures (nD) is measured at 298.15†K. The excess molar volumes VE and deviation from additivity rules of viscosities [eta]E and refractive index [Delta][phi]n, of pyrrolidinium octanoate solutions were then deduced from the experimental results as well as apparent molar volumes V[phi]i, partial molar volumes and thermal expansion coefficients [alpha]p. The excess molar volumes VE are negative over the entire mole fraction range for mixture with water, acetonitrile, and methanol indicating strong hydrogen-bonding interaction for the entire mole fraction. In the case of longest carbon chain alcohols (such as ethanol and n-butanol)†+†pyrrolidinium octanoate solutions, the VE variation as a function of the composition describes an S shape. The deviation from additivity rules of viscosities is negative over the entire composition range for the acetonitrile, methanol, ethanol, and butanol, and becomes less negative with increasing temperature. Whereas, [eta]E of the {[Pyrr][C7CO2]†+†water} binary mixtures is positive in the whole mole fraction range and decreases with increasing temperature. the excess Gibbs free energies of activation of viscous flow ([Delta]G*E) for these systems were calculated. The deviation from additivity rules of refractive index [Delta][phi]n are positive over the whole composition range and approach a maximum of 0.25 in PIL mole fraction for all systems. The magnitude of deviation for [Delta][phi]n describes the following order: water†>†methanol†>†acetonitrile†>†ethanol. Results have been discussed in terms of molecular interactions and molecular structures in these binary mixtures.

On visco-elastic modelling of polyethylene terephthalate behaviour during multiaxial elongations slightly over the glass transition temperature

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature Tg, the stress-strain curve presents a strain softening effect vs strain rate but a strain hardening effect vs strain under conditions of large deformations. The main goal of this work is to propose a viscoelastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained trough a comparison with the experimental uniaxial and biaxial tests. The in?uence of the temperature on the viscous part is also modelled and an evaluation of the adiabatic self heating of the specimen is compared to experimental results.

Density, conductivity, viscosity, and excess properties of (pyrrolidinium nitrate-based Protic Ionic Liquid + propylene carbonate) binary mixture

Density, ?, viscosity, ?, and conductivity, s, measurements of binary mixtures containing the pyrrolidinium nitrate Protic Ionic Liquid (PIL) and propylene carbonate (PC), are determined at the atmospheric pressure as a function of the temperature from (283.15 to 353.15) K and within the whole composition range. The temperature dependence of both the viscosity and conductivity of each mixture exhibits a non-Arrhenius behaviour, but is correctly fitted by using the Vogel–Tamman–Fulcher (VTF) equation. In each case, the best-fit parameters, such as the pseudo activation energy, View the MathML source and ideal glass transition temperature, T0 are then extracted. The excess molar volumes VE, and viscosity deviations from the ideality, ??, of each investigated mixture were then deduced from the experimental results, as well as, their apparent molar volumes, V?, thermal expansion coefficients ap, and excess Gibbs free energies (?G*E) of activation of viscous flow. The VE, apE, ?? values are negative over the whole composition range for each studied temperature therein. According to the Walden rule, the ionicity of each mixture was then evaluated as a function of the temperature from (283.15 to 353.15) K and of the composition. Results have been then discussed in terms of molecular interactions and molecular structures in this binary mixture.