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.

Steel is an important product in many engineering sectors; however, steelmaking remains one of the largest CO2 emitters. Therefore, new governmental policies drive the steelmaking industry toward a cleaner and more sustainable operation such as the gas-based direct reduction–electric arc furnace process. To become carbon neutral, utilizing more scrap is one of the feasible solutions to achieve this goal. Addressing knowledge gaps regarding scrap heterogeneity (size, shape, and composition) is essential to evaluate the effects of increased scrap ratios in basic oxygen furnace (BOF) operations. This review systematically examines heat and mass transfer correlations relevant to scrap melting in BOF steelmaking, with a focus on low Prandtl number fluids (thick thermal boundary layer) and dense particulate systems. Notably, a majority of these correlations are designed for fluids with high Prandtl numbers. Even for the ones tailored for low Prandtl, they lack the introduction of the porosity effect which alters the melting behavior in such high temperature systems. The review is divided into two parts. First, it surveys heat transfer correlations for single elements (rods, spheres, and prisms) under natural and forced convection, emphasizing their role in predicting melting rates and estimating maximum shell size. Second, it introduces three numerical modeling approaches, highlighting that the computational fluid dynamics–discrete element method (CFD–DEM) offers flexibility in modeling diverse scrap geometries and contact interactions while being computationally less demanding than particle-resolved direct numerical simulation (PR-DNS). Nevertheless, the review identifies a critical gap: no current CFD–DEM framework simultaneously captures shell formation (particle growth) and non-isotropic scrap melting (particle shrinkage), underscoring the need for improved multiphase models to enhance BOF operation.

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.