Phase Behavior of Aqueous Na-K-Mg-Ca-CI-NO3 Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na{sup +}, K{sup +}, Mg{sup 2+}, Ca{sup 2+}, Cl{sup -}, and NO{sub 3}{sup -} ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 C. The measurements have been performed using Oak Ridge National Laboratory's (ORNL) previously designed gravimetric isopiestic apparatus, which makes it possible to detect solid phase precipitation. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid-liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor-liquid and solid-liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems

Model of coupled pulsation and translation of a gas bubble and rigid particle

A model of the interaction of a spherical gas bubble and a rigid spherical particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model accounts for pulsation and translation of the bubble as well as translation of the particle in an infinite, incompressible liquid. The model derived here is accurate to order R5∕d5, where R is a characteristic radius and d is the separation distance between the bubble and particle. This order is the minimum accuracy required to account for the interaction of the bubble and particle. Dependence on the size and density of the particle is demonstrated through numerical integration of the dynamical equations for both the free and forced response of the system. Numerical results are presented for models accurate to orders higher than R5∕d5 to demonstrate the consequences of truncating the equations at order R5∕d5