Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis

The Edwards-Vilgis (EV) slip-link theory (1986) derives the elastic free energy of a rubber-like network model containing stable and sliding network junctions (crosslinks and slip-links) and predicts both low-strain softening and high-strain hardening. The four-parameter stress-strain relations calculated by the theory for geometrically different deformation modes up to high strains were tested experimentally using published biaxial stress-strain data on simple covalently crosslinked networks. For networks with low degrees of strain softening and low extensibilities, the experimental dependencies could be described rather well but, generally, a simultaneous satisfactory fit to uniaxial, pure shear and equibiaxial data was not obtained. Systematic experiment-theory deviations exceeding 10% were observed and some of the parameters had a tendency to assume values lying outside the reasonably expected range. The prediction of a pronounced maximum in the strain dependence of stress supported by slip-links seems to be a reason for the discrepancy. Also, modeling of the high-strain singularity in entropy is done in the EV theory using a rather simple approximation. As a result, the finite extensibility contribution to the stress of a slip-link-free network model becomes improbably high and significantly exceeds that following, at a given modulus and locking stretch, from the rigorously derived Langevin-statistics-based eight-chain-network elasticity theory of Arruda and Boyce.     

Langevin-elasticity-theory-based description of the tensile properties of double network rubbers

A previously proposed and successfully tested constitutive equation denoted by the ABGIL code (a combination of the Arruda-Boyce equation based on the Langevin elasticity theory and a constraint term based on tube theories; strain-induced increase in the finite extensibility parameter is assumed) has been found to provide a good basis for quantitative interpretation of the stress-strain data recently obtained by Mott and Roland on double networks of natural rubber, prepared by introducing additional crosslinks (second network) into a first network stretched to various extents. Experimental information on properties of the first and second networks has been used to obtain their ABGIL parameters and to calculate, under the common assumption of additivity of contributions, the stress-strain properties and residual stretch of the resulting double networks. The predictive ability of the ABGIL equation has been found to be very good. Effects of the finite extensibility of network chains appear to be significant in double networks while the possible role of orientational crystallization cannot be excluded.     

On Mooney and Mooney stress relaxation. II. A nonlinear viscoelastic description: Experimental and numerical results

It has been investigated whether the stress build‐up and the stress relaxation involved in a Mooney test, with subsequent Mooney stress relaxation, can be described by nonlinear viscoelastic theory, more particularly the Wagner constitutive model. For this purpose, the viscoelastic behavior of three nonvulcanized EPDM materials, with similar Mooney viscosity but varying elasticity, has been studied. Relaxation time spectra were obtained from dynamic mechanical experiments, from which the step‐strain stress‐relaxation modulus was calculated. Stress build‐up experiments were performed with a cone and plate system in order to obtain the so‐called damping function (a measure for the deformation sensitivity) of the materials. Using these material functions, the Mooney test was successfully described with the Wagner constitutive model. Experimental and theoretical Mooney stress‐relaxation rates are in close agreement. The predicted Mooney viscosity is up to 25% lower than the measured value. This may be due to nonideal conditions during the Mooney test, such as inhomogeneous heating and secondary flows, and to inaccuracy of the damping function. The model calculations confirm the strong experimental dependence of Mooney measurements on small variations in instrumental conditions such as geometry, rotation speed, and so forth. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 1220–1233, 1999     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part II. Application to complex mixtures

In part I of the present article [Yoo et al., 1995], new rigorous and simplified lattice-fluid equations of state (EOS) were derived and their characteristic features of the molecular thermodynamic foundation were discussed by applying to pure fluids. In this part II, both EOSs were extended to various phase equilibrium properties of mixtures. Comparison of the models with experimental mixture data ranges from density, to equilibria of vaporliquid, vapor-solid and liquid-liquid phases for nonpolar/nonpolar, nonpolar/polar, polar/polar mixtures. Both models were also applied to supercritical fluid phase equilibria and activities of solvents in polymer solutions. With two temperature dependent parameters for pure compounds and one temperature-independent binary interaction energy parameter for a binary mixtures, results obtained to date illustrated that both EOSs are quantitatively applicable to versatile phase equilibria of mixtures over a wide range of temperatures, pressures and compositions.     

Modelling crystal growth between potash particles near contact points during drying processes. Part II: Analysis,results, and comparison with experimental data

Caking of bulk granular materials is a serious problem that affects many industries including the mineral processing industry. Caking occurs when bulk materials undergo wetting and drying cycles and it has been thought that it occurs due to the formation of new crystal bridges between individual particles. In the first paper in this series a mathematical model is developed for the crystal formation process that occurs at the contact point between two particles. In Part II, numerical simulations of the model are used to determine the effects of changes for several independent parameters in this model: initial moisture content; rate of evaporation of the salt solution from the particle surface; relative size of the contact region compared to the initial film thickness of salt solution; and supersaturation levels near the contact point. Non‐dimensional graphical curves of these simulations are used to compare the effects of each parameter for the deposition of salt crystals near the contact point. These results, when compared to data for cake strength in potash specimens which were obtained for various initial moisture contents, drying rate, and chemical composition of the particle surfaces, show good qualitative agreement even though cake strength and mass recrystallization near a contact point are different physical phenomena. The numerical results show that the mass of crystal deposition near the contact point will increase with increased initial moisture content and decreased evaporation rate. It is also found that variations in the degree of supersaturation near the contact point causes significant variations in the crystal mass deposition near the contact point.     

Calcination of phosphate in impinging streams. Part II. Phosphates with high organic matter and with pulverized coal

Calcination of a high organic matter phosphate and a phosphate containing pulverized coal up to 10 wt % was performed successfully in an impinging stream calciner. The results re-established previous conclusions that the present calciner is a useful device. A simplified model has been developed for exploring the effect of various operating parameters on the concentration of phosphate particles at the impingement plane of the streams. It also assisted us in explaining the effect of the phosphate flow rate on the efficiency of calcination. It was established that the calcination rate of phosphate is governed by the internal resistance of the particle to the heat transfer, which was consistent with previous results.     

Viscoelastic models for Mexican heavy crude oil and comparison with a mixture of heptadecane and eicosane. Part I

The viscoelastic knowledge of crude oil is limited by the complexity and variability of the raw material. Viscoelastic models of Maxwell type describe widely Mexican crude oils when an Oldroyd contravariant derivative is considered. Moreover, a Weissenberg number is defined by the product of the shear rate and the characteristic time constituted by the inverse of the rate constant of C-C bonds rotations of alkanes. This dimensionless number allows the scaling of viscosities of both crude oil, at different temperatures, and mixtures of n-eicosane/n-heptadecane. Blends of linear alkanes can simulate the viscous behavior of crude oil after adequate scaling and can be used to predict crude oil rheological properties with the advantage to be completely known and reproducible systems.     

A simplified method for analyzing mold filling dynamics. Part II: Extensions and comparisons with experiment

A dimensional analysis based on four parameters has been developed previously to predict injection pressure; clamp force, and bulk temperature for the injection molding of amorphous materials in center-gated disk-shaped cavities. In this paper geometric and semicrystalline-materials approximations are introduced and tested for extending the previous analysis to include multigated thin cavities and semicrystalline materials. The combination of these approximations and the previous analysis, known hereafter as the Radial Flow Method (RFM), greatly simplifies the analysis of mold filling. The geometric approximation, which is based on a simple model for the axial stress distribution in the cavity, is shown to give reasonable predictions when compared with experimental data and a numerical two-directional flow simulation for the filling of an off-center-gated rectangular cavity with acrylonitrilebutadiene-styrene copolymer (ABS). The semicrystallinematerials approximation, in which heat capacity and viscosity changes during crystallization are neglected, is shown to give good agreement with experimental data for the filling of a center-gated disk-shaped cavity with polypropylene. As an illustration, the Radial Flow Method is used to analyze the molding of a large, thin-wall automobile interior trim panel. The inlet melt temperature, mold-wall temperature, part thickness, injection rate, viscosity and gate locations are varied in a series of calculations to determine the relative effectiveness of these variables in lowering the injection pressure and Clamp force. The results obtained with the Radial Flow Method are in good agreement with those obtained by a finiteelement simulation of two-directional flow.     

A new generalized corresponding-states equation of state for the extension of the Lee-Kesler equation to fluids consisting of polar and larger nonpolar molecules

The Lee-Kesler equation of state for the thermodynamic properties of small nonpolar fluids is extended to all fluids consisting of polar and larger nonpolar molecules, based on the general corresponding-states theory for highly nonspherical fluids. The thermodynamic functions are represented by an analytical equation of state. The results for polar fluids are substantially better than those obtainable from other currently available methods, while the results for nonpolar fluids are equivalent to and mostly better than those obtained by the Lee-Kesler method. The input data required are the critical temperature, the critical volume, the acentric factor and the aspherical factor, which is related to the critical compression factor; the critical volume is therefore required in the present method. The method developed in this work shows good accuracy for 15 representative nonpolar, polar, hydrogen bonding and associating fluids and provides a simple method for industrial applications. Average deviations for the compressibility factor, the heat capacity and the speed of sound for six nonpolar and nine polar fluids from the new equation of state are 0.74%, 2.1% and 2.3%, which are about 8 times smaller than those obtained from the Lee-Kesler equation (about 5.6%, 17% and 29%, respectively).     

A Monte Carlo simulation study of the mechanical and conformational properties of networks of helical polymers. Part II. The effect of temperature

In a recent article (Carri GA, Batman R, Varshney V, Dirama TE. Polymer 2005;46:3809 [17]) we presented a model for networks of helical polymers. In this article we generalize our results to include the effect of temperature and focus on the mechanical, conformational and thermo-elastic properties of the network. We find that the non-monotonic stress-strain behavior observed at constant temperature also appears in the stress-temperature behavior at constant strain. The origin of this behavior is traced to the induction and melting of helical beads by the application of large strains or reduction in temperature. Other conformational properties of the polymer strands are also discussed. We also study the network entropy and heat capacity, and find a non-monotonic dependence on temperature and strain. Our study shows that the entropy is controlled by the helical content whenever the latter is significant. Otherwise, the entropy corresponds to the one of a network made of random coils. In addition, the study of the heat capacity shows that strain shifts the helix-coil transition temperature significantly. Other results are also discussed.     

A simple approach for improving high-temperature mechanical and insulation performance in chamotte with added zircon

Chamotte is one of the most commonly used raw materials for aluminosilicate refractories. The present work concerns the high-temperature performance of the chamotte-zircon composite. The crystalline phase, mechanical property, and thermal conductivity were evaluated. In addition, the finite element method was applied to analyze stress distribution. Zircon accelerated the melting of cristobalite in chamotte during sintering. After adding zircon, a drastic elastic modulus change at about 230°C was avoided, and the infrared shielding effect of zircon reduced the thermal conductivity when the temperature was greater than 500°C. At last, based on the results of finite element method, increasing zircon content reduced stress concentration.     

On characterizing microscopically the adhesion interphase for the adhesion between metal and rubber compound Part II. Effect of copper content for brass-plated steel cord

Three brass-plated steel cords with different copper contents from 51.4 to 75.5% were prepared and their adhesion properties to rubber compound were examined. Adhesion properties improved with the decrease in the copper content. The high adhesion of brass-plated steel cord with low copper content to the rubber was obtained after cure and after hostile aging treatments. The stability against humidity aging and the cause for the high adhesion of the brass-plated steel cord with low copper content were discussed in conjunction with the formation and growth of adhesion interphase determined by Auger electron spectroscopy depth profile. The excellent adhesion stability of brass-plated cord with low copper content can be explained by the suppression of the excessive growth of copper sulfide and the inhibition of dezincification due to the low copper content.     

An extension of the group contribution method for estimating thermodynamic and transport properties. Part IV. Noble gas mixtures with polyatomic gases

Earlier work on the group contribution method applied to Kihara potentials is extended to noble-polyatomic gas mixtures for the calculation of second virial cross coefficients, mixture viscosities and binary diffusion coefficients of dilute gas state using a single set of gas group parameters. Previously estimated parameter values for pure gas groups by our work [Oh, 2005; Oh and Sim, 2002; Oh and Park, 2005] were used. Assuming that noble-polyatomic gas mixtures examined are chemically dissimilar, a group binary interaction coefficient, k _{ij, gc} , was assigned to each interaction between noble-polyatomic gas groups, and 25 group binary interaction parameter values (k _{He-H2, gc} , k _{He-N2, gc} , k _{He-CO, gc} , k _{He-CO2, gc} , k _{He-O2, gc} , k _{He-NO, gc} , k _{He-N2O, gc} ; k _{Ne-H2, gc} , k _{Ne-N2, gc} , k _{Ne-CO, gc} , k _{Ne-CO2, gc} , k _{Ne-O2, gc} ; k _{Ar-H2, gc} , k _{Ar-N2, gc} ; k _{Ar-CO, gc} , k _{Ar-CO2, gc} , k _{Kr-O2, gc} ; k _{Kr-H2, gc} , k _{Kr-N2, gc} , k _{Kr-CO, gc} , k _{Ar-CO2, gc} ; k _{Xe-H2, gc} , k _{Xe-N2, gc} , k _{Xe-CO, gc} , k _{Xe-CO2, gc} ) were determined by fitting second virial cross coefficients data. Application of the model shows that second virial cross coefficient data are represented with good results comparable to values predicted by means of the corresponding states correlation. Reliability of the model for mixture viscosity predictions is proved by comparison with the Lucas method. And prediction results of binary diffusion coefficients are in excellent agreement with literature data and compared well with values obtained by means of the Fuller method. Improvements of the group contribution model are observed when group binary interaction coefficients are adopted for mixture property predictions.     

A nonconventional method for drying of Pseudomonas aeruginosa and its comparison with conventional methods

In this study, preparation of dried cultures of Pseudomonas aeruginosa using nonconventional drying method, namely, low-temperature low-humidity (LTLH) drying was investigated. The effect of carrier materials (whey protein, corn starch, and trehalose) was examined one at a time and also in combinations (to explore the synergistic effect). The results were compared with those obtained using spray drying and freeze drying in terms of cell survival and dry cell powder yield. The powder samples were analyzed also for morphology, flowability, particle size, and moisture content. In LTLH drying, good cell survival was observed along with high powder yield when compared with that in spray drying. Corn starch showed the highest cell survival (91%) and powder yield (94%, w/w) among the carrier materials employed besides resulting in good cell survival (65%) even after a storage period of 6 months.     

Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

A new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD-based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD-based design model for one-shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.     

A practical equation of state for non‐spherical and asymmetric systems for application at high pressures. Part 2: Extension to mixtures

In part I of this series the pure component PHCT‐DNSK equation of state (EOS) was presented. In this paper the EOS is extended to describe mixtures, particularly asymmetric mixtures containing one or more low molecular weight spherical compound together with one or more high molecular weight chain‐like compound. The EOS utilises theoretically correct mixing rules and is generally able to predict the correct trends quantitatively for binary mixtures, and in most cases outperform other EOSs. With the use of a small, temperature independent, interaction parameter the EOS is able to predict the phase behaviour of the investigated systems qualitatively. The EOS is able to predict the phase behaviour of a multi‐component system containing one or more light components and a range of heavy hydrocarbons with improved accuracy compared to other EOSs at reduced computational times. © 2011 Canadian Society for Chemical Engineering