, where Q is a function (static or time-dependent) of the phase variables and <…> is an average over an equilibrium grand canonical ensemble. As an example of the use of these expressions we then consider the case whereis a time-dependent density-density correlation function. Thermodynamic derivatives of the time-dependent Van Hove correlation functions are considered in detail, and examples of how the resulting expressions can be used to interpret neutron-scattering data are given. The expressions developed lead to more stringent ways of testing theories of fluids, and provide a method for studying triplet correlation functions which have been nearly inaccessible in the past. We expect the general relationships to prove equally useful when applied to other experimental methods for studying time-correlation functions (e.g. absorption or scattering of electromagnetic radiation, relaxation phenomena). DA - 1978/2// PY - 1978/2// DO - 10.1080/00268977800100241 VL - 35 IS - 2 SP - 315-328 J2 - Molecular Physics LA - en OP - SN - 0026-8976 1362-3028 UR - http://dx.doi.org/10.1080/00268977800100241 DB - Crossref ER - TY - JOUR TI - Thermodynamics of polyatomic fluid mixtures—II AU - Twu, C.H. AU - Gubbins, K.E. T2 - Chemical Engineering Science AB - The theory described in the previous paper is used to study pure and mixed fluids composed of polar, (HCl, HBr), quadrupolar (CO2, C2H2, C2H4, C2H6) and octopolar (CH4, CF4) molecules. The theory accurately predicts vapour-liquid equilibria for the ten binary and one ternary system studied. Comparisons with experiment are also made for excess volumes, and critical and azeotropic loci, where these are available. DA - 1978/// PY - 1978/// DO - 10.1016/0009-2509(78)85177-x VL - 33 IS - 7 SP - 879-887 J2 - Chemical Engineering Science LA - en OP - SN - 0009-2509 UR - http://dx.doi.org/10.1016/0009-2509(78)85177-x DB - Crossref ER - TY - JOUR TI - Thermodynamics of polyatomic fluid mixtures—I theory AU - Gubbins, K.E. AU - Twu, C.H. T2 - Chemical Engineering Science AB - Solution theories currently in use by chemical engineers (regular solutions, conformal solution theory, etc.) are based on an oversimplified view of the intermolecular forces, so that they are strictly valid only for such simple fluids as argon. We present here a solution theory (based on thermodynamic perturbation theory) which allows strong directional inter-molecular forces to be taken into account when calculating thermodynamic properties. This theory is in excellent agreement with computer simulation results for strongly polar or quadrupolar fluids. It is applied to the prediction of phase equilibrium surfaces, critical loci, three-phase lines, and azeotropic loci for mixtures containing constituents with (a) polar, (b) quadrupolar, and (c) anisotropic shape (charge overlap) intermolecular forces. The relation between these intermolecular forces and the type of phase behaviour is explored for binary mixtures. The anisotropic shape forces have little effect on the phase diagram; however, a wide variety of phase behaviour is found for the other cases. Mixtures with polar or quadrupolar constituents are shown to give rise to five of the six classes of binary phase diagrams found in nature. DA - 1978/// PY - 1978/// DO - 10.1016/0009-2509(78)85176-8 VL - 33 IS - 7 SP - 863-878 J2 - Chemical Engineering Science LA - en OP - SN - 0009-2509 UR - http://dx.doi.org/10.1016/0009-2509(78)85176-8 DB - Crossref ER - TY - JOUR TI - Low Péclet number behavior of the transfer rate in packed beds AU - Fedkiw, Peter AU - Newman, John T2 - Chemical Engineering Science AB - Abstract The asymptotic behavior of the mass-transfer coefficient in a packed bed reactor at low Peclet numbers is dependent upon how the coefficient is defined. A singular perturbation approach coupled with heuristic arguments is used to demonstrate that the film mass-transfer coefficient in deep beds approaches a constant value as the Peclet number decreases. The film coefficient is utilized in the one-dimensional model of a bed as a sink term in the governing equation. The volumetric, or effective, mass-transfer coefficient which relates the overall reactant conversion to a logarithmic mean concentration driving force, decreases linearly with the Peclet number as the Peclet number approaches zero. The distinction between the two coefficients is important in the low Peclet number region. Analogous results apply to beat transfer. Reported experimental data support these predicted trends. It has been, demonstrated that the low Peclet number behavior of the Sherwood number in a packed bed reactor is dependent upon its defining equation. A rigorous singular perturbation approach coupled with heuristic arguments indicates that for a deep bed the effective mass-transfer coefficient (defined by eqn 1) is directly proportional to the Peclet number. The film coefficient (defined by eqn 3) approaches a constant in the same limit. These conclusions are independent of the detailed geometric void structure in the bed. DA - 1978/// PY - 1978/// DO - 10.1016/0009-2509(78)85008-8 VL - 33 IS - 8 SP - 1043-1048 J2 - Chemical Engineering Science LA - en OP - SN - 0009-2509 UR - http://dx.doi.org/10.1016/0009-2509(78)85008-8 DB - Crossref ER - TY - JOUR TI - Numerical calculations for the asymptotic, diffusion dominated mass-transfer coefficient in packed bed reactors AU - Fedkiw, Peter AU - Newman, John T2 - Chemical Engineering Science AB - For deep beds, the effective Sherwood number approaches a proportional relationship to the Peclet number as the Peclet number tends to zero. A sinusoidal periodically constricted tube model for the voids in the bed has been used to predict the constant of proportionality. This constant depends upon the dimensionless ratios of three lengths: the average tube radius, the oscillation amplitude, and wavelength. DA - 1978/// PY - 1978/// DO - 10.1016/0009-2509(78)85212-9 VL - 33 IS - 11 SP - 1563-1566 J2 - Chemical Engineering Science LA - en OP - SN - 0009-2509 UR - http://dx.doi.org/10.1016/0009-2509(78)85212-9 DB - Crossref ER -