A modelling approach to explore the optimum bubble size for micro-nanobubble aeration

Bubble aeration has been widely applied in water/wastewater treatment, however its low gas utilization rate results in high energy consumption. Application of micro-nanobubbles (MNB) has emerged as a process with the potential to significantly increase gas utilisation due to their high relative surface area and high gas-liquid mass transfer efficiency. In this study, we demonstrate through calibrated models that MNB of an optimum bubble size can shrink and burst at or below the water surface enabling (1) all encapsulated gas to thoroughly dissolve in water, and (2) the bursting of nanobubbles to potentially generate free radicals. Through the understanding of MNB dimensional characteristics and bubble behaviour in water, a dynamic model that integrated force balance (i.e. buoyancy force, gravity, drag force, Basset force and virtual mass force), and mass transfer was developed to describe the rising velocity and radius variation of MNB along its upward trajectory. Unlike for conventional millimetre-sized bubbles, intensive gas dissolution of MNBs led to radius reduction for small bubbles, while a large initial radius triggers bubble swelling. The initial water depth was also crucial, where greater depth could drive the potential for bubble shrinkage so that they were more liable to contract. For example, the optimum bubble size of air (42-194 μm) and oxygen (127-470 μm) MNB that could achieve complete gas transfer (100% gas utilisation) for a range of specific water depths (0.5-10 m) were calculated. The modelling results for microbubbles (10-530 μm) were well validated by the experimental data (R²>0.85). However, the validation of the modelling results for nanobubble (<1 μm) aeration requires further study due to a lack of available empirical data. In this study, the proposed model and analysis provided new insights into understanding bubble dynamics in water and offered fundamental guidance for practitioners looking to upgrade bubble aeration system.

Small-Scale Phenomena in Reactive Bubbly Flows: Experiments, Numerical Modeling, and Applications

Improving the yield and selectivity of chemical reactions is one of the challenging tasks in paving the way for a more sustainable and climate-friendly economy. For the industrially highly relevant gas-liquid reactions, this can be achieved by tailoring the timescales of mixing to the requirements of the reaction. Although this has long been known for idealized reactors and time- and space-averaged processes, considerable progress has been made recently on the influence of local mixing processes. This progress has become possible through joint research between chemists, mathematicians, and engineers. We present the reaction systems with adjustable kinetics that have been developed, which are easy to handle and analyze. We show examples of how the selectivity of competitive-consecutive reactions can be controlled via local bubble wake structures. This is demonstrated for Taylor bubbles and bubbly flows under technical conditions. Highly resolvednumerical simulations confirm the importance of the bubble wake structure for the performance of a particular chemical reaction and indicate tremendous potential for future process improvements.

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.