Shear-induced phase changes in mixtures

A thermodynamic theory to account for the behavior of liquid mixtures exposed to a shear is developed. One consequence of the theory is that shear-induced phase changes are predicted. The theory is based on a thermodynamics that includes specifically the shear rate in the formalism and is applied to mixtures by a straightforward modification of the corresponding states, conformalsolution approach. The approach is general but is used here for a mixture of Lennard-Jones particles with a Lennard-Jones equation of state as a reference fluid. The results are discussed in the context of the Scott and Van Konynenberg phase classification. It is shown that the influence of a shear does affect substantially the type of the phase behavior. Results from the model mixture are equated loosely with those from real polymeric liquids.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

A test of the mean density approximation for Lennard-Jones mixtures with large size ratios

The mean density approximation for mixture radial distribution functions plays a central role in modern corresponding-states theories. This approximation is reasonably accurate for systems that do not differ widely in size and energy ratios and which are nearly equimolar. As the size ratio increases, however, or if one approaches an infinite dilution of one of the components, the approximation becomes progressively worse, especially for the small molecule pair. In an attempt to better understand and improve this approximation, isothermal molecular dynamics simulations have been performed on a series of Lennard-Jones mixtures. Thermodynamic properties, including the mixture radial distribution functions, have been obtained at seven compositions ranging from 5 to 95 mol%. In all cases the size ratio was fixed at two and three energy ratios were investigated, ₂₂/₁₁=0.5, 1.0, and 1.5. The results of the simulations are compared with the mean density approximation and a modification to integrals evaluated with the mean density approximation is proposed.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Application of an extended Lee-Kesler corresponding-states technique to prediction of vapor-liquid equilibria in multicomponent mixtures containing polar components

Mixing rules for an extended Lee-Kesler (ELK) corresponding-states method for prediction of thermodynamic properties are presented. The mixing rules, which do not contain adjustable parameters, permit calculation of vapor-liquid equilibria in mixtures containing one or more polar components. While a single heat-of-mixing datum may be included for strongly associating components, generally only pure component properties are used in the calculations. A comparison of calculated bubble-point pressures and equilibrium vaporization ratios to experimental values is made for 26 ternary mixtures (791 points) and 5 quaternary mixtures (175 points). Bubble-point pressures are predicted quite well with ELK (9.1 % AAD for ternaries and 7.9% for quaternaries). Composition predictions are difficult to compare in multicomponent systems, but ELK predictions appear to be acceptable on both a system-by-system and an overall AAD basis.Paper presented at the Tenth Symposium on Thermophysical properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

A new nonrandom lattice fluid model and its simplification by two-liquid theory for phase equilibria of complex mixtures

A new riogorous equation of state (EOS) and its simplified version have been proposed by the present authors based on the full Guggenheim combinatorics ] of the nonrandom lattice hole theory. The simplified EOS. with the introduction of the concept of local composition, becomes similar to the density-dependent UNIQUAC model. However, im the present approach we have a volumetric EOS instead of the excess Gibbs function. Both EOSs were tested for their applicability in correlating the phase equilibria behavior of pure components and complex mixtures. Comparison of both models with experiment includes such systems as nonpolar nonpolar, nonpolar polar, and polar polar hydrocarbons, supercritical systems, and polymer solutions. With two parameters for each pure component and one binary interaction energy parameter, results obtained to date demonstrate that both formulations are quantitatively applicable to complex systems oer a wide range of temperatures, pressures, and concentrations.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado. U.S.A.     

Virial coefficients of methane-ethane mixtures in the temperature range from 0 to 60°C determined with an automated expansion apparatus

An automated expansion apparatus has been set up which can be used for PVT measurements on gases from Il to 60 C at pressures from 2 to 7 NIPa. It consists of two chambers connected by an expansion valve. The ratio of the two volumes is 1:54. The measurements along one isotherm. which take 20 h, can be per formed routinely and without operator attendance. The uncertainty of the com pressibility factor is estimated to be 10^–3. The compressibility factors of binary mixtures of the main components of most natural gases, methane and ethane, were determined on high-grade gas, the mole fractions of ethane being 0.05, 0.15. and 0.25. Seven isotherms were measured of each of the mixtures. Data from the literature for the virial coefficients of the pure substances were used to establish a virial equation of state which approximates the measured com pressibility factors with a standard deviation of 0.4 x 10 '. This is substantially smaller than the uncertainty. The interaction virial coefficients were calculated from this equation of state. The results obtained are in good agreement with other available data.Paper presented al the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado. U.S.A.     

Mie scattering computation of spherical particles with very large size parameters using an improved program with variable speed and accuracy

The electromagnetic radiation scattering patterns were computed using an improved C program to study variations in the patterns with changes in the size distribution, size parameters and refractive index of small particles in a volume element. The particle size distributions considered were gamma, normal and lognormal. The program is stable for computation of the theoretical values of the non-zero elements of the scattering matrix, efficiency factors, single scattering albedo, radiation pressure and asymmetry parameter for particles ranging from very small to very large size parameters. One of the significant features of the program is that it incorporates two methods for the determination of the optimal number of terms required for the computation of Mie series with the added benefit of having the option of either going for computational speed or accuracy. After a comparison of the C program with other reported benchmark results, it has been found that the program is very accurate and reliable for electromagnetic scattering computations.     

An analytical procedure for dynamic response determination of a viscoelastic beam with moderately large deflection using first-order shear deformation theory

In this article, the dynamic response of a viscoelastic beam with moderately large deflection subjected to transverse and axial loads is studied using the first-order shear deformation theory. The von-Karman strain displacement relations and Hooke's law are used for formulation. The solution of the equations, which are a system of nonlinear partial differential equations, are obtained analytically using the perturbation technique in conjunction with the eigenfunction expansion method. The results are compared with the finite elements method. Also, a sensitivity analysis is performed, and the effects of geometrical and material properties are investigated on the response.     

Application of the moment scheme of the finite element method to the solution of problems with initial stresses in the incremental elasticity theory

We discuss application of the finite element method to the solution of problems with initial stresses within the elasticity theory. Based on the incremental theory of deformable solids, the relationships of the finite element method are derived to calculate the stiffness matrix coefficients for a prestressed spatial element of the serendip family with quadratic approximation of displacements. The calculation of the stressed state of an eccentrically compressed beam and a round plate under conditions of longitudinal-transverse bending is carried out. Comparison of the numerical results with analytical solutions is presented. The variation in the compression and shear strains of a cylindrical damper is studied depending on the degree of deformation and the sequence of load application. __________ Translated from Problemy Prochnosti, No. 3, pp. 131–143, May–June, 2006.