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.

Physico-chemical properties of non-newtonian shear thickening diisopropyl-ethylammonium-based protic ionic liquids and their mixtures with water and acetonitrile

New protic ionic liquids (PILs) based on the diisopropyl-ethylammonium cation have been synthesized through a simple and atom-economic neutralization reaction between the diisopropyl-ethylamine and selected carboxylic acid. Densities and rheological properties were then measured for two original diisopropyl-ethylammonium-based protic ionic liquids (heptanoate and octanoate) at 298.15 K and atmospheric pressure. The effect of the presence of water or acetonitrile on the measured values was also examined over the whole composition range at 298.15 K and atmospheric pressure. From these values, excess properties were calculated and correlated by using a Redlich-Kister-type equation. Finally, a qualitative analysis of the evolution of studied properties with the alkyl chain length of the anion and with the presence or not of water (or acetonitrile) was performed. From this analysis, it appears that selected PILs and their mixtures with water or acetonitrile have a non-Newtonian shear thickening behavior, and the addition of water or acetonitrile on these PILs increases this phenomena by the formation of aggregates in these media.

Run off Conditions on Rimming Power Law Fluids

The rimming ?ow of a power-law ?uid in the inner surface of a horizontal rotating cylinder is investigated. Exploiting the fact that the liquid layer is thin, the simplest lubrication theory is applied. The generalized run-off condition for the steady-state ?ow of the power-law liquid is derived. In the bounds implied by this condition, ?lm thickness admits a continuous solution. In the supercritical case when the mass of non-Newtonian liquid exceeds a certain value or the speed of rotation is less than an indicated limit, a discontinuous solution is possible and a hydraulic jump may occur in the steady-state regime. The location and height of the hydraulic jump for the power-law liquid is determined.

Density-viscosity product of small-volume ionic liquid samples using quartz crystal impedance analysis

Quartz crystal impedance analysis has been developed as a technique to assess whether room-temperature ionic liquids are Newtonian fluids and as a small-volume method for determining the values of their viscosity-density product, rho eta. Changes in the impedance spectrum of a 5-MHz fundamental frequency quartz crystal induced by a water-miscible room-temperature ionic liquid, 1-butyl-3-methylimidazolium. trifluoromethylsulfonate ([C(4)mim][OTf]), were measured. From coupled frequency shift and bandwidth changes as the concentration was varied from 0 to 100% ionic liquid, it was determined that this liquid provided a Newtonian response. A second water-immiscible ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C(4)mim][NTf2], with concentration varied using methanol, was tested and also found to provide a Newtonian response. In both cases, the values of the square root of the viscosity-density product deduced from the small-volume quartz crystal technique were consistent with those measured using a viscometer and density meter. The third harmonic of the crystal was found to provide the closest agreement between the two measurement methods; the pure ionic liquids had the largest difference of similar to 10%. In addition, 18 pure ionic liquids were tested, and for 11 of these, good-quality frequency shift and bandwidth data were obtained; these 12 all had a Newtonian response. The frequency shift of the third harmonic was found to vary linearly with square root of viscosity-density product of the pure ionic liquids up to a value of root(rho eta) approximate to 18 kg m(-2) s(-1/2), but with a slope 10% smaller than that predicted by the Kanazawa and Gordon equation. It is envisaged that the quartz crystal technique could be used in a high-throughput microfluidic system for characterizing ionic liquids.

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.

Determination of the Physical Properties of Room Temperature Ionic Liquids Using a Love Wave Device

In this work, we have shown that a 100 MHz Love wave device can be used to determine whether room temperature ionic liquids (RTILs) are Newtonian fluids and have developed a technique that allows the determination of the density-viscosity product, rho eta of a Newtonian RTIL. In addition, a test for a Newtonian response was established by relating the phase change to insertion loss change. Five concentrations of a water-miscible RTIL and seven pure RTILs were measured. The changes in phase and insertion loss were found to vary linearly with the square root of the density-viscosity product for values up to (rho eta)(1/2) similar to 10 kg m(-2) s(-1/2). The square root of the density-viscosity product was deduced from the changes in either phase or insertion loss using glycerol as a calibration liquid. In both cases, the deduced values of rho eta agree well with those measured using viscosity and density meters. Miniaturization of the device, beyond that achievable with the lower-frequency quartz crystal microbalance approach, to measure smaller volumes is possible. The ability to fabricate Love wave and other surface acoustic wave sensors using planar metallization technologies gives potential for future integration into lab-on-a-chip analytical systems for characterizing ionic liquids.

Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.

Specific and unspecific interactions in polar fluids in view of wideband dielectric far-infrared spectra

A simple molecular analytical theory of dielectric relaxation in strongly polar fluids is considered in terms of a semi- phenomenological approach. Theoretical spectra epsilon(v), a(v) of complex permittivity and absorption coefficient are fully determined by a form of intermolecular potential well, in which a dipole reorients. In a recent publication by VI. Gaiduk, O.F. Nielsen, and T.S. Perova [J. Molliq 95 (1002) 1-25] the wideband spectra of liquid H2O and D2O were described in terms of a composite model comprising the rectangular and the cosine squared potential wells. Much better results are achieved in this work, where the rectangular well is replaced by a well with a rounded bottom termed the hat-curved well. The spectrum of the auto-correlation function (ACF) is calculated for such a potential. The proposed theory of a composite model, comprising hat-curved and parabolic wells, is applied for liquid water. This model is capable for describing the Debye relaxation region, the second relaxation region in the submillimeter wavelength range, and the far infra-red (FIR) e(v), a(v) spectra, where an intense librational band and an additional weak band are placed, respectively, near 700 cm(-1) and 200 cm(-1). The latter band reflects the features of so-called specific (viz. directly related to H-bonds) interactions and the former band reflects the features of unspecific interactions. The physical mechanisms connected with these types of interactions are discussed in terms of two relevant types of water structure (types of molecular rotation). The proposed theory is also applied to a non-associated liquid in terms of one hat-curved potential well. (C) 2004 Elsevier B.V. All rights reserved.