The transport of ions is governed by a species conservation equation and the Nernst-Planck flux expression. The latter requires information on the electrical potential, for which an additional transport equation is required. Traditional numerical approaches, such as solving the Poisson equation or applying the electroneutrality condition, face limitations in their applicability. In this work, a new numerical model is introduced for the electrical potential that effectively functions as a numerical switch between the Poisson equation and the electroneutrality condition. This model is tested for three different scenarios: a small-scale system where charge separation is expected in a large part of the domain, a large-scale system where charge separation is significantly less important, and a multi-ion liquid junction system. This new numerical model is capable of producing accurate results for all the tested systems.

Stirred gas–solid fluidized bed reactors are commercially employed in polyolefin manufacturing, but the complex gas–solid contacting dynamics pose challenges in design, scale-up, and operation. In this study, the influence of agitation on the fluidization performance of Geldart B particles was investigated experimentally by X-ray imaging and pressure drop measurements and numerically by Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) - Immersed Boundary Method (IBM). The experimentally obtained minimum fluidization curve and time-averaged pressure drop show good qualitative agreement with the simulation results. Visual observations underscore that an increase in the angular velocity of the agitator results in reduced bubble size and improved bed homogeneity, as further evidenced by reduced pressure fluctuations. Furthermore, the simulations reveal that while the impeller enhances solids agitation, a proper design study is imperative, considering that static immersed bodies, such as the stirrer shaft, can adversely impact solids motion.