When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker–Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

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The evolution of individual crystals of ellipsoidal shape in supercooled one-component and binary melts as well as in supersaturated solutions is studied theoretically. The crystal volume growth rate is derived using the prolate ellipsoidal coordinates. We show that this rate is a function of the current crystal volume and supercooling/supersaturation of the ambient liquid. Also, we demonstrate that the particle growth rate increases with increasing the volume of ellipsoidal crystals and supercooling.

Development of energy-efficient and high-performance bioreactors requires progress in methods for assessing the key parameters of the biosynthesis process. With a wide variety of approaches and methods for determining the phase contact area in gas–liquid flows, the question of obtaining its accurate quantitative estimation remains open. Particularly challenging are the issues of getting information about the mass transfer coefficients instantly, as well as the development of predictive capabilities for the implementation of effective flow control in continuous fermentation both on the laboratory and industrial scales. Motivated by the opportunity to explore the possibility of applying classical and non-classical computer vision methods to the results of high-precision video records of bubble flows obtained during the experiment in the bioreactor vessel, we obtained a number of results presented in the paper. Characteristics of the bioreactor’s bubble flow were estimated first by classical computer vision (CCV) methods including an elliptic regression approach for single bubble boundaries selection and clustering, image transformation through a set of filters and developing an algorithm for separation of the overlapping bubbles. The application of the developed method for the entire video filming makes it possible to obtain parameter distributions and set dropout thresholds in order to obtain better estimates due to averaging. The developed CCV methodology was also tested and verified on a collected and labeled manual dataset. An onwards deep neural network (NN) approach was also applied, for instance the segmentation task, and has demonstrated certain advantages in terms of high segmentation resolution, while the classical one tends to be more speedy. Thus, in the current manuscript both advantages and disadvantages of the classical computer vision method (CCV) and neural network approach (NN) are discussed based on evaluation of bubbles’ number and their area defined. An approach to mass transfer coefficient estimation methodology in virtue of obtained results is also represented.