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Carbon dioxide sequestration via carbonation of steel slags is a promising way of combining two waste products to create value. Understanding the dissolution kinetics of steel slags, which are alkaline and rich in calcium, in acidic media is essential to configure such a process. In this study, we seek to analyse the dissolution mechanism from experimental studies and develop a mathematical model considering the heterogeneous characteristics of slag. We found that the reduction in calcium extraction efficiency with an increase in particle size, which is normally associated with surface passivation or non-uniformity of samples, can be explained by considering the morphological features associated with the distribution of MgO–FeO (RO) phase in the calcium silicate matrix. We present a population balance model and show that the reduction in calcium extraction efficiency in coarse particle fractions is due to increased sporulation of the RO phase. The findings in the study suggest that the leaching of metal ions from slag is controlled by proton-promoted surface dissolution reaction, where the dependence of acid concentration follows the Langmuir–Hinshelwood adsorption isotherm. The model shows good agreement with a large set of parametric studies and demonstrates the importance of considering morphological features, as we progress towards development of a priori dissolution models for multi-mineral oxides and silicates.

Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear). This means that the upscaling (via volume averaging and homogenisation) to a macroscopic (Darcy-scale) description requires closures assumptions. We discuss this problem and derive an effective macroscopic term for the shear-induced events, such as breakage caused by shear forces on the transported particles. We focus on breakage events as prototype for linear shear-induced events and derive upscaled breakage frequencies in periodic geometries, starting from nonlinear power-law dependence on the local fluid shear rate. Results are presented for a two-dimensional channel flow and a three dimensional regular arrangement of spheres, for arbitrarily fast (mixing-limited) events. Implications for linearised shear-induced collisions are also discussed. This work lays the foundations of a new general framework for multiscale modelling of particulate flows.

In this study, we propose the study of an innovative precipitation prototype designed by ResourSEAs, guided by a CFD-PBM (Computational Fluid Dynamics and Population Balance Model) approach, aiming to understand the influence of reactant concentration and nozzle orientation on precipitation processes. The first part of the study examines the effect of reactant concentration on supersaturation and the zeroth-order moment (m0) within a controlled flow and turbulence fields. Three different concentrations of Mg2+ (0.1, 0.3, and 0.6 M) and OH− (0.005, 0.01, and 0.02 M) were tested, resulting in varying supersaturation profiles and m0 fields. Our results show that, under equal turbulence conditions, increasing the concentration of reactants beyond a certain point actually slows down mixing, which in turn hinders the generation of supersaturation. As a result, supersaturation profiles become nearly identical to those of lower concentrations, despite having consumed more reactants. The second part of this study focuses on the effect of nozzle orientation and positioning along the prototype axis on reactant mixing and particle formation. The simulations reveal that nozzle orientation has a significant impact on the formation of primary particles, especially when positioned in low-velocity regions, leading to slower mixing and greater particle growth. Conversely, high-velocity regions promote faster mixing and more intense aggregation. These findings highlight the interplay between concentration, nozzle orientation, and flow conditions in determining precipitation efficiency, offering insights for optimizing reactor design in industrial applications.

Fluidized-bed spray granulation (FBSG) enables manufacturing particles with desired characteristics, including particle size distribution (PSD), density, or dust content. This study investigated the effect of selected factors on the granules obtained in a continuous FBSG of chelated fertilizers for foliar applications. The effect of surfactant addition to the solution sprayed into the bed and perturbations of operating parameters on PSD and granules morphology was studied. The experiments were supplemented with calculations based on a population balance equation (PBE). It was shown that granules manufactured with the tenside addition are more regular in shape, and thus less prone to mechanical wear. It was demonstrated that increasing rotational mill speed does contribute to a slight increase in the amount of dust, but in the long term, it does not disturb the regular agglomeration process. The computational results confirm that, despite the complexity of the process, its description with PBE is feasible.

This work presents modelling for the aggregation process of metal nanoparticles following a theory proposed in literature. In this theory, metal atoms aggregate into particles of bigger size due to Van der Waal’s forces of attraction. Then, owing to the electrostatic forces of repulsion, the particles eventually stop aggregating and become stabilized. Based on this mechanistic description, we developed a model for the aggregation process. Because this process often occurs along with other processes, such as growth, we employed as case study the synthesis of gold nanoparticles by the citrate synthesis method for conditions where the aggregation process is decoupled from the growth process. Using this model, we calculated the seed particle sizes and compared them with the values previously reported in literature. Furthermore, we calculated the final particle sizes and compared them with experimental data. The results show excellent agreement.

Computational Fluid Dynamics (CFD) have been frequently applied to model the growth conditions in photobioreactors, which are affected in a complex way by multiple, interacting physical processes. We review common photobioreactor types and discuss the processes occurring therein as well as how these processes have been considered in previous CFD models. The analysis reveals that CFD models of photobioreactors do often not consider state-of-the-art modeling approaches. As a comprehensive photobioreactor model consists of several sub-models, we review the most relevant models for the simulation of fluid flows, light propagation, heat and mass transfer and growth kinetics as well as state-of-the-art models for turbulence and interphase forces, revealing their strength and deficiencies. In addition, we review the population balance equation, breakage and coalescence models and discretization methods since the predicted bubble size distribution critically depends on them. This comprehensive overview of the available models provides a unique toolbox for generating CFD models of photobioreactors. Directions future research should take are also discussed, mainly consisting of an extensive experimental validation of the single models for specific photobioreactor geometries, as well as more complete and sophisticated integrated models by virtue of the constant increase of the computational capacity.

Recently, the pharmaceutical industry has undergone changes in the production of solid oral dosages from traditional inefficient and expensive batch production to continuous manufacturing. The latest advancements include increased use of continuous twin-screw wet granulation and application of advanced modeling tools such as Population Balance Models (PBMs). However, improved understanding of the physical process within the granulator and improvement of current population balance models are necessary for the continuous production process to be successful in practice. In this study, an existing compartmental one-dimensional PBM of a twin-screw granulation process was improved by altering the original aggregation kernel in the wetting zone as a result of an identifiability analysis. In addition, a strategy was successfully applied to reduce the number of model parameters to be calibrated in both the wetting zone and kneading zones. It was found that the new aggregation kernel in the wetting zone is capable of reproducing the particle size distribution that is experimentally observed at different process conditions as well as different types of formulations, varying in hydrophilicity and API concentration. Finally, it was observed that model parameters could be linked not only to the material properties but also to the liquid to solid ratio, paving the way to create a generic PBM to predict the particle size distribution of a new formulation.

Predicting pump performance and ensuring operational reliability under two-phase conditions is a major goal of three-dimensional (3D) computational fluid dynamics (CFD) analysis of liquid/gas radial centrifugal pump flows. Hence, 3D CFD methods are increasingly applied to such flows in academia and industry. The CFD analysis of liquid/gas pump flows demands careful selection of sub-models from several fields in CFD, such as two-phase and turbulence modeling, as well as high-quality meshing of complex geometries. This paper presents an overview of current CFD simulation strategies, and recent progress in two-phase modeling is outlined. Particular focus is given to different approaches for dispersed bubbly flow and coherent gas accumulations. For dispersed bubbly flow regions, Euler–Euler Two-Fluid models are discussed, including population balance and bubble interaction models. For coherent gas pocket flow, essentially interface-capturing Volume-of-Fluid methods are applied. A hybrid model is suggested, i.e., a combination of an Euler–Euler Two-Fluid model with interface-capturing properties, predicting bubbly flow regimes as well as regimes with coherent gas pockets. The importance of considering scale-resolving turbulence models for highly-unsteady two-phase flow regions is emphasized.

Particle size distribution of nanoparticles plays an important role in modelling many scientific and engineering problems. In this article, we proposed a Finite Volume Method (FVM) to model TiO 2 nanoparticles formation using population balance equations (PBEs) by incorporating the simultaneous agglomeration and disintegration processes. The superposition of the PBEs for agglomeration and disintegration with different kernels leads to a system of partial-integro differential equations, which are numerically solved by using FVM. The precipitation of TiO 2 nanoparticles in the batch reactor is studied experimentally as well as by numerical simulations based on Austin and Diemer disintegration kernels and Shear agglomeration kernel. Finally, the capability of the precipitation model is evaluated and the experimental results on particle sizes are compared with the numerical results.

A hybrid two-phase flow solver is proposed, based on an Euler–Euler two-fluid model with continuous blending of a Volume-of-Fluid method when phase interfaces of coherent gas pockets are to be resolved. In a preceding study on a two-dimensional bladed research pump with reduced rotational speed, the transition from bubbly flow to coherent steady gas pockets observed in optical experiments with liquid/gas flow could be well captured by the hybrid solver. In the present study, the experiments and solver validation are extended to an industrial-scale centrifugal pump with twisted three-dimensional blades and elevated design rotational speed. The solver is combined with a population balance model, and a scale-adaptive turbulence model is employed. Compared to the two-dimensional bladed pump, the transition from agglomerated bubbles flow to attached gas pockets is shifted to larger gas loading, which is well captured by the simulation. The pump head drop with increasing gas load is also reproduced, showing the hybrid solver’s validity for realistic pump operation conditions.