Mixing rules hard sphere

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

The method can be extended to include nonpherical, nonpolar species (such as the lower molecular weight alkanes) by introduction of a third parameter in the equation of state, namely the Prigogine factor for chain-type molecules (9). This modified hard-sphere equation of state accurately describes VE(T, x) for liquefied natural gas mixtures at low pressures. Ternary and higher mixture VE values are accurately predicted using only binary mixing rule deviation parameters. 

Theory and computer simulation provides information in addition to the virial equation of state that can be used to develop mixing and combining rules. The equation of state for the pure hard-sphere fluid can be represented by the equation of state of Carnahan-Starling ... 

In all the equations that include the double power-series expansion (or variations thereof), such as the family of perturbed-hard-chain equations, the parameters are related to molecular rather than critical properties, and the mixing and combining rules are quadratic in composition for the attractive term and based on hard-sphere theory for the repulsive term. 

The next step in the procedure of evaluation of the mixture properties is the evaluation of the pseudo-radial distribution functions for all i — j interactions in the mixture as well as the mean free-path parameter atj for the unlike interaction. It is consistent with the remainder of the procedure to estimate them from mixing rules based upon a rigid-sphere model. Among the many possible mixing rules for the radial distribution function one that has proved successful is based upon the Percus-Yevick equation for the radial distribution function of hard-sphere mixtures (Kestin Wakeham 1980 Vesovic ... 

The mixing rules for the repulsive potential result from the assumption that there is a close relationship between molecular "size and the repulsive potential. A useful measure of molecular size is the distance parameter a described above. If a hard-sphere model for molecular interaction is assumed, it can be shown that for molecules i and j ... 

The Group Contribution Equation of State (GC-EoS) has two eonlributions to the residual Helmholtz energy of the system a repulsive hard sphere Camahan-Starling type term and an attractive term, which combines the group contribution approach wifli the local-composition mixing rules. A complete explanation of the model is given by Skjold-Jorgensen. ... 

We use mixing rules to extend equations of state to mixtures. The mixing rules allow us to extrapolate these equations to mixtures, from mosdy pure component data. Mixing rules for van der Waals-type parameters a and b were developed based on a two-body attractive interaction and a hard sphere repulsion, respectively. The binary interaction parameter allows us to better describe the cross coefficient, ai however, data from the mixture are needed. Mixing rules for the viral coefficients arise from a theoretical basis. Mixing rules for the second virial coefficient, B, are based on two-body interactions for the third virial coefficient, C, on three-body interactions and so on. Finally, Kay s rules were presented, from which we can find the psuedocritical properties of the mixture from the pure component properties. These values allow us to apply the generalized compressibility charts to mixtures. 

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