QMOM-based population balance model involving a fractal dimension for the flocculation of latex particles

Modeling scalability of impurity precipitation in downstream biomanufacturing

Precipitation during the viral inactivation, neutralization and depth filtration step of a monoclonal antibody (mAb) purification process can provide quantifiable and potentially significant impurity reduction. However, robust commercial implementation of this unit operation is limited due to the lack of a representative scale-down model to characterize the removal of impurities. The objective of this work is to compare isoelectric impurity precipitation behavior for a monoclonal antibody product across scales, from benchtop to pilot manufacturing. Scaling parameters such as agitation and vessel geometry were investigated, with the precipitate amount and particle size distribution (PSD) characterized via turbidity and flow imaging microscopy. Qualitative analysis of the data shows that maintaining a consistent energy dissipation rate (EDR) could be used for approximate scaling of vessel geometry and agitator speeds in the absence of more detailed simulation. For a more rigorous approach, however, agitation was simulated via computational fluid dynamics (CFD) and these results were applied alongside a population balance model to simulate the trajectory of the size distribution of precipitate. CFD results were analyzed within a framework of a two-compartment mixing model comprising regions of high- and low-energy agitation, with material exchange between the two. Rate terms accounting for particle formation, growth and breakage within each region were defined, accounting for dependence on turbulence. This bifurcated model was successful in capturing the variability in particle sizes over time across scales. Such an approach enhances the mechanistic understanding of impurity precipitation and provides additional tools for model-assisted prediction for process scaling.

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment

In this study, an extended model for describing the temporal evolution of a characteristic floc size of cohesive sediment particles when the flocculation system is subject to a piecewise varied turbulent shear rate was derived by the probability methods based on the Shannon entropy theory following Zhu (2018). This model only contained three important parameters: initial and steady-state values of floc size, and a parameter characterizing the maximum capacity for floc size increase (or decay), and it can be adopted to capture well a monotonic pattern in which floc size increases (or decays) with flocculation time. Comparison with 13 literature experimental data sets regarding floc size variation to a varied shear rate showed the validity of the entropic model with a high correlation coefficient and few errors. Furthermore, for the case of tapered shear flocculation, it was found that there was a power decay of the capacity parameter with the shear rate, which is similar to the dependence of the steady-state floc size on the shear rate. The entropic model was further parameterized by introducing these two empirical relations into it, and the finally obtained model was found to be more sensitive to two empirical coefficients that have been incorporated into the capacity parameter than those in the steady-state floc size. The proposed entropic model could have the potential, as an addition to existing flocculation models, to be coupled into present mature hydrodynamic models to model the cohesive sediment transport in estuarine and coastal regions.