Electrically-Driven Natural Convection in Colloidal Suspensions

Abstract

A basic physical model of electrodecantation has been developed and tested. Experimental data of Belongia (1999) were used to compare with computational results obtained from the model. The model was developed to calculate the transient velocity field, electric potential and particle distribution for the parameter space encountered in stable colloidal dispersions. The model included the effects of a spatially nonuniform electric field that existed in the experiments of Belongia (1999) because of the type and position of the electrodes used. As a result, the model required numerical methods for its solution. The problem was found to depend largely on three dimensionless groups: Re, a Reynolds number, Pe an electric Péclet number and ¤ a large dimensionless parameter denoting the Grashof number divided by the Reynolds number. Because A^(1/3) >> 1, nonuniform computational meshes were needed to resolve the exceedingly thin natural convection boundary layers that occur. Additionally, because Pe >> 1, a flux-limiting (FCT) numerical method was used to solve the particle transport equation. Results from the basic physical model show excellent agreement with the scaling of the experimental data but exhibit about 80% relative error when compared with experimental data on the decantation time. Consequently, a physicochemical model of electrodecantation was developed to include electrical conductivity variations that develop as ions transport during electrodecantation. Results show markedly better agreement (about 10% relative error) with experimental data concerning the decantation rate. Additionally, the physicochemical model is able to predict the pH and electrical conductivity stratification that was measured experimentally by Belongia (1999). A problem concerning the electrohydrodynamic deformation of miscible fluids, with differing electromechanical properties (electrical conductivity and dielectric constant), was also investigated. Numerical results predicting the sense and extent of deformation for various values of the two fluids’ electrical conductivity ratio compare well (less than 10% relative error) with measurements by Rhodes, et al. (1989). The role of dielectric constant differences in electrohydrodynamic deformations was also investigated. It was determined that an O(1) difference in the fluids’ dielectric constants is necessary to produce electrohydrodynamic deformations on the time scales reported by Rhodes, et al. (1989) and Trau, et al. (1995).