On the apparent dispersion coefficient of the equilibrium dispersion model: An asymptotic analysis

To model chromatography, researchers have developed several approaches. These cover a broad range of applications and, depending on the assumptions adopted, have different levels of accuracy. In general, the most suitable modelling approach is the simplest that can describe a process with the desired accuracy. A model that often meets this criterion is the equilibrium dispersion model (EDM). This features one mass balance equation per analyte, including an axial dispersion term, and assumes the analyte concentrations in the mobile and stationary phases to be in local equilibrium. To account for the finite mass transfer rate between the phases, the model employs an apparent dispersion coefficient. Two expressions are available for this coefficient, one being used much more frequently than the other. In this paper, we aimed to clarify which one should be favoured. A desirable feature of simple models is that they can be derived from more general ones with appropriate physical assumptions and rigorous mathematical methods. Thus, to answer our research question, we derived the EDM from the more general pore diffusion model (POR), using an asymptotic method. The expression obtained for the apparent dispersion coefficient does agree with one of the two reported in the literature – the less frequently used. To test the validity of this expression, we simulated elution profiles using the two versions of the EDM and compared the results against those from the POR model. The simulations were conducted in the range where the POR and EDM models should be essentially equivalent, their results confirming the outcome of the asymptotic analysis. This work offers a solid theoretical grounding for the EDM, clarifies which formulation of the model is correct, and provides usable applicability conditions for the model

Predicting sample injection profiles in liquid chromatography: A modelling approach based on residence time distributions

The pharmaceutical and bio-pharmaceutical industries rely on simulations of liquid chromatographic processes for method development and to reduce experimental cost. The use of incorrect injection profiles as inlet boundary condition for these simulations may, however, lead to inaccurate results. This study presents a novel modelling approach for accurate prediction of injection profiles for liquid chromatographic columns. The model uses the residence time distribution theory and accounts for the residence time of the sample through the injection loop, connecting tubes and heat exchangers that exist upstream of the actual chromatographic column, between the injection point and the column inlet. To validate the model, we compare simulation results with experimental injection profiles taken from the literature for 20 operating conditions. The average errors in the predictions of the mean and variance of the injection profiles result to be 8.98% and 8.52%, respectively. The model, which is based on fundamental equations and actual hardware details, accurately predicts the injection profile for a range of sample volumes and sample loop-filling levels without the need of calibration. The proposed modelling approach can help to improve the quality of in-silico simulation and optimization for analytical chromatography

Characterising powder flowability at high shear rates by the ball indentation method

The Ball Indentation Method has been experimentally investigated as a new technique to characterize powder flow at high shear rates. The results indicate that the hardness is independent on the strain rate in quasi-static conditions, whilst the flow resistance can be related to the strain rate in intermediate flow regime, where the rheological behaviour of the powders becomes liquid-like. Despite the results agree with the simulations reported in literature, the method has some limitations

Modellazione numerica dei meccanismi di segregazione in materiali granulari sfusi

I materiali granulari sono profondamente radicati nella lunga storia della scienza e della tecnologia. Essi vengono trattati quotidianamente da numerose industrie tra cui l’industria chimica, l’industria alimentare e l’industria farmaceutica. Tuttavia, la loro manipolazione e la loro lavorazione rimangono un importante problema in numerose applicazioni industriali. Uno dei problemi più rilevanti è quello della miscelazione di particelle aventi proprietà diverse dal momento che tendono a segregare spontaneamente. Pertanto, lo sviluppo di strumenti per prevedere la segregazione è essenziale per controllare e ridurre al minimo il fenomeno. Questo progetto di ricerca riguarda la modellazione numerica dei meccanismi di segregazione in materiali sfusi, per miscele con vari gradi e tipi di dispersione particellare e applicati a diversi contesti industriali. Nello specifico, studieremo dapprima la segregazione per dimensione in miscele binarie diluite. Successivamente tratteremo la segregazione per taglia in sistemi di particelle multicomponenti e polidispersi. In questi casi, le equazioni di segregazione sono accoppiate con la reologia del flusso solido in modo bidirezionale. Poiché l’accoppiamento bidirezionale è piuttosto complesso, esistono solo pochi altri studi a riguardo. Proporremo poi un nuovo modello matematico per descrivere la segregazione per densità in miscele binarie. A differenza dei modelli precedenti, in questo caso utilizzeremo un accoppiamento unidirezionale. Inoltre, il campo di velocità sarà determinato direttamente da soluzioni analitiche piuttosto che risolvendo l’equazione di conservazione della quantità di moto. L’inclusione delle differenze di densità avrebbe portato a campi di velocità comprimibili e quindi, a modelli più complessi. Un ulteriore capitolo descrive un nuovo modello di segregazione per taglia che include la comprimibilità del campo di velocità. Ove possibile, i modelli saranno validati con esperimenti. Negli altri casi, la procedura di validazione si realizzerà con simulazioni DEM. Tutte le teorie sono in grado di riprodurre sia qualitativamente che quantitativamente ciò che accade nella realtà. Pertanto, i modelli di segregazione proposti rappresentano un ulteriore passo avanti verso una descrizione completa e accurata della segregazione in una varietà di flussi granulari densi. Questi modelli possono inoltre aiutare gli ingegneri a sviluppare strategie di mitigazione, a progettare e dimensionare razionalmente apparecchiature e a sviluppare più efficaci sistemi di controllo di processo.Granular materials are deeply rooted in the long history of science and technology. Furthermore, several industries process granular materials routinely, including chemical, food and pharmaceutical industries. Handling and processing of these materials remain a major challenge in numerous industrial applications. The main difficulty regards the mixing of particles with different properties because of their tendency to segregate spontaneously. Thus, the development of tools for predicting segregation is essential in order to control and minimize the occurrence. This research project is concerned with the numerical modelling of segregation mechanisms in bulk materials for mixtures with varying degrees and types of particle dispersity, in many industrial settings. More specifically, we first study size-driven segregation in diluted binary mixtures. We then tackle segregation due to size differences in multi-component and polydisperse particle systems. In these cases, the segregation equations are fully coupled with the solid flow rheology. Since the coupling is challenging, only a few other studies exist in this area. We then propose a new mathematical model for density-driven segregation in binary mixtures. Unlike the previous models, in this case, we employ a one-way coupling. Furthermore, the velocity field is determined directly from analytic solutions rather than by solving the momentum equation. The inclusion of density differences would have led to compressible velocity fields and hence, to more complex models. An additional chapter describes a new model for particle-size segregation that include the compressibility of the velocity field. Wherever possible, the models are validated in a two-way comparison among experiments and theory. In the other cases, the validation procedure is accomplished with DEM simulations. All theories are capable of reproducing both qualitatively and quantitatively what happens in reality. Thus, the proposed segregation models represent a step towards a complete and accurate description of segregation in a variety of dense granular flows. Furthermore, the models can help engineers in developing mitigation strategies and in rationally designing and scaling equipment, processes, and process control

Characterising powder flowability at high shear rates by the ball indentation method

Unreliable powder flow is a major problem during processing of powders. The shear cell is the most widely used method for powders subjected to moderate or high stresses, and under quasi-static conditions, with established methods for designing large bins and hoppers based on the measurement. However, this method is not suitable for measuring the flowability of dynamic systems, such as powder mixing. Here, the ball indentation method is investigated as a technique for evaluating powders in the intermediate and dynamic regime of flow. The method, which simply consists of dropping a ball onto a cylindrical bed of powder previously consolidated, directly measures hardness, which is related to the unconfined yield stress of the powder by the constrain factor (Hassanpour and Ghadiri, 2007). The impact of the ball on the bed is recorded with a high-speed camera to determine velocity and penetration depth. The shear rate is varied by using a range of indenter materials and sizes, and a range of drop heights. The hardness against the strain rate is considered for several materials. It was found that the indenter size does not influence the hardness results, which are consistent with the flowability evaluation achieved with the rheometer. Furthermore the hardness, which is independent of the strain rate in quasi-static conditions, becomes shear rate dependent in intermediate regime of flow. Further work is needed to evaluate hardness in the rapid granular flow regime

Shear-driven density segregation: an experimental study

Granular materials can segregate spontaneously due to differences in particle properties when subjected to vibrations, shear strain or because of the equipment geometries. Although the difference in particle size is the most critical factor that drives segregation, the effects of large density difference may also be detrimental for a lot of industries. In this work, we experimentally investigate density-driven segregation in bi-disperse mixtures of particles having the same size but different density when subjected to non-uniform shear rates. We found that the features of the segregation process are related to the density ratio as well as to the dimensionless loaded mass. The experimental outcomes are then compared with the solution of a simple density-driven segregation model. The model can successfully capture the main features of segregation driven by density for a range of density ratios

Shear-driven density segregation: an experimental study

Granular materials can segregate spontaneously due to differences in particle properties when subjected to vibrations, shear strain or because of the equipment geometries. Although the difference in particle size is the most critical factor that drives segregation, the effects of large density difference may also be detrimental for a lot of industries. In this work, we experimentally investigate density-driven segregation in bi-disperse mixtures of particles having the same size but different density when subjected to non-uniform shear rates. We found that the features of the segregation process are related to the density ratio as well as to the dimensionless loaded mass. The experimental outcomes are then compared with the solution of a simple density-driven segregation model. The model can successfully capture the main features of segregation driven by density for a range of density ratios

Practical learning activities to increase the interest of university applicants in STEM careers in the era of Industry 4.0

Inspiring young students, especially young girls, about STEM disciplines is crucial to address the current shortage of engineers. Since the engineering skills that are required by graduates are evolving in line with technological progress, there is now an even stronger need for graduates with strong Process Systems Engineering skills. In this work, we describe an effective way to promote the chemical engineering curriculum, with particular emphasis on computational tools, to a group of Year 12 high school students during a one-week course in our department. The course was designed to engage students in active learning through interactive sessions and practical hands-on activities. Through the course, the students gained a better understanding of the importance of STEM subjects and, in particular, of the challenges and opportunities that engineers encounter in the era of Industry 4.0 with ever-increasing use of digitalization in process design and operation