Prediction of emulsion drop size distributions with population balance equation models of multiple drop breakage

A multiscale modelling approach for Haematococcus pluvialis cultivation under different environmental conditions

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We develop a novel multiscale model for microalgal photoautotrophic growth.

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The model is segregated-structured type based on Population Balance Equations.

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We combine the model with cultivation experiments of Haematococcus pluvialis.

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We successfully predict cell number, average volume and density distribution dynamics.

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Model can accurately describe the nutrient depletion phase including cell lysis.

Haematococcus pluvialis can produce significant amounts of industrially important compounds belonging to lipids and starch classes, including various specific pigments such as β-carotene, lutein and astaxanthin, as well as lipids, carbohydrates and proteins. Their production can vary depending on environmental stress conditions like nutrient starvation. However, stress conditions lead also to undesired phenomena such as cell lysis, which is likely to be related to products loss. The microorganism develops towards smaller single cell volumes during the growth process, and eventually, more likely towards lysis when fission (i.e. cell division) slows down. The lysis process takes place simultaneously with nutrient depletion, so both growth and lysis are linked to the change of environmental conditions. In this work, we develop a novel multiscale segregated-structured model based on Population Balance Equations (PBEs) to describe the photoautotrophic growth of H.pluvialis, in particular cell growth, and lysis, making possible the description of the relationship between cell volume/transition, cell loss, and metabolic product availability. Cell volume is the internal coordinate of the population balance model, and its link with intrinsic concentrations is also presented. The model parameters are fitted against experimental data, extensive sensitivity analysis is performed and the model predictive capabilities are tested in terms of cell density distributions, as well as 0th and 1st order moments.

Prediction of droplet sizes for oil-in-water emulsion systems assisted by ultrasound cavitation: Transient scaling law based on dynamic breakup potential

The dynamics of droplet breakup during emulsification is a complicated process due to the interplay between multiple physico-chemical and hydrodynamic factors, especially in an energy-intensive ultrasound-assisted emulsification process. In this work, by mapping the physical processing parameters of ultrasound emulsification into a reduced domain that is governed by the power density and the initial average droplet diameter, a dimensionless parameter that resembles the dynamic breakup potential (η) was established via dimensional analysis. In addition to shedding important insights into the emulsification process, η further facilitates the establishment of a transient scaling relationship that is a function of the characteristic value (a) of the emulsion system. Experimental case study on a cellulose nanocrystals (CNC)-based olein-in-water emulsion system prepared via ultrasound cavitation confirmed the validity of the scaling relationship and sub-universal self-similarity was observed. Using the proposed model, good predictions of the transient of droplet size evolution were attained where the value of η, i.e. the proportionality constant, can be conveniently computed using data from a single time point. Application on other emulsion systems further suggested that the value of a possibly indicates the relative minimum size limit of a particular fluids-emulsifier system. Our approach is general, which encourages widespread adoption for emulsification related studies.

Droplets size evolution of dispersion in a stirred tank

Dispersion of two immiscible liquids is commonly used in chemical industry as wall as in metallurgical industry e. g. extraction process. The governing property is droplet size distribution. The droplet sizes are given by the physical properties of both liquids and flow properties inside a stirred tank. The first investigation stage is focused on in-situ droplet size measurement using image analysis and optimizing of the evaluation method to achieve maximal result reproducibility. The obtained experimental results are compared with multiphase flow simulation based on Euler-Euler approach combined with PBM (Population Balance Modelling). The population balance model was, in that specific case, simplified with assumption of pure breakage of droplets.