Thermodynamics of mixtures containing alkoxyethanols. Part xxiii. Speed of sound predictions and ultrasonic studies of hydroxyether + organic solvent mixtures

The ability of different models to predict speeds of sound, u, of binary mixtures formed by alkoxyethanol and octane, oxaalkane or propylamine has been examined. The models applied are: the free length theory (LFT), the collision factor theory (CFT), and equations such as those proposed by Nomoto, Junjie or Van Dael. Collision factor theory, Nomoto's and Junjie's equations provide similar deviations between experimental and calculated u, which is represented quite accurately by these three models. Poorer predictions are obtained when applying the Junjie's equation to propylamine systems, probably due to the existence of strong interactions between unlike molecules in such mixtures. In contrast, slightly better u predictions from CFT are obtained for the systems 2-methoxyethanol + polyether, or hydroxyether + propylamine. The good u predictions obtained using Nomoto's equation remark the validity of Rao's assumption on additivity of molar sound velocity contributions from atoms, atom groups and chemical bonds of the constituent molecules. Discrepancies between experimental and calculated u are larger when using FLT than those obtained from CFT, Nomoto's or Junjie's equations. This has been ascribed to association and size or shape effects. The linear dependence on the molar fractions of the component liquids of the Rao's and Wada's constants suggests that there is no complex formation in the investigated mixtures, and that the interactions present in such systems are of dipolar type.     

On numerical solution of stochastic partial differential equations of elliptic type

We study lattice approximations of stochastic PDEs of elliptic type, driven by a white noise on a bounded domain in ? ^d , for d = 1, 2, 3. We obtain estimates for the rate of convergence of the approximations.