(262w) Eulerian Volume-Averaged Model and Numerical Simulations of Reactive Solid-Liquid Mixtures

Solid-liquid mixtures, also named sols, are colloidal systems in which an aggregate of very fine solid particles is dispersed in a liquid dispersion medium. In contrast with single-phase fluids, the physical principles that govern the thermodynamics of solid-liquid mixtures are definitely more complex due to the presence of multiple deformable moving interfaces, and the possibility of mass, momentum and energy interfacial transfers. Moreover, the existence of fluctuation of variables, which appears as a natural result of turbulences and the motions of the interfaces, is also an inherent complication in solid-liquid mixtures.

In this work, an Eulerian volume-averaged model for reactive solid-liquid mixtures is proposed with basis on the Müller-Liu approach of the second law of thermodynamics, and the Eulerian spatial averaging theory. Then, one demonstrates that the precipitation of solid particles depends on non-local effects associated to the gradients of average chemical potential, average temperature and average velocity, as well as the interfacial exchanges of mass and energy.

Linearized transport equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations in the reactive solid-liquid mixture are proposed. A particularity of the thermodynamic model is that the interfacial mass transfer rate is regarded as an independent variable. The obtained results show that the inclusion of the interfacial mass transfer rate as an independent variable of the model permits to describe phase changes associated with the precipitation chemical reactions.

Furthermore, in order to check the validity of the proposed thermodynamic model, numerical simulations are performed for a fully-developed vertical flow of a calcium carbonate colloidal suspension. The velocity profiles for both phases and the concentration profile for the particles of calcium carbonate are predicted, by assuming that the interaction between the liquid phase and the solid particles is given by a drag force dependent on their relative velocity. From the numerical results, settling curves are then constructed and the sedimentation profile of calcium carbonate colloidal suspensions in fully-developed vertical flows is analyzed.