From single drop coalescence to droplet swarms – Scale-up considering the influence of collision velocity and drop size on coalescence probability

Abstract

Coalescence modelling in liquid/liquid dispersions is a challenging task and field of investigations up to now, which becomes apparent when comparing the various existent models with their different and partly even contradictive implementation of influencing factors. In this work, systematic investigations of single drop coalescence were used to compare and validate different coalescence efficiency models regarding the important influencing parameters relative collision velocity and drop size. The impact of these parameters could be analysed independently from each other for the first time and used to identify the best modelling approach. Moreover, the numerical parameter of the coalescence efficiency model could be obtained based on single drop experiments. Using this determined parameter the simulation of drop size distributions within a lab scale stirred vessel was possible. The presented method offers the possibility of independent parameter estimation for population balance equation simulations based on single drop experiments. The application of this systematic approach allows the separate validation of submodels and reliable parameter determination by small scale investigations. On this basis a sound scaleup is possible using population balance equation simulations. Postprint: Kamp, J.;, From single drop coalescence to droplet swarms -Scale-up considering the influence of collision velocity and drop size on coalescence probability, Chemical Engineering Science, 156, 162-177, https://doi.org/10.1016/j.ces.2016.08.028 2 the drop breakage (Maaß and Kraume, 2012), this work focusses on drop coalescence and its modelling in PBE. Drop CoalescenceCoalescence describes the confluence of two disperse droplets or a drop with the corresponding continuous phase. Before coalescence between two droplets occurs, the interfaces approach each other and a thin film of surrounding continuous phase has to drain between the interfaces. At a certain critical distance the continuous phase film ruptures and the drops confluence. However, a collision of droplets does not end in coalescence necessarily, but may also results in a repulsion or agglomeration of the droplets. The probability of coalescence after droplet collision is described by the coalescence efficiency in PBE. The coalescence efficiency is influenced by numerous factors especially surface active components in already small amounts (Kamp et al., 2016b). Due to the involved complex interactions in distances of several orders of magnitude, numerous modelling approaches can be found in literature (Liao and Lucas, 2010) which implement influencing factors differently and in parts even contradictorily (Kamp et al., 2016b;Kopriwa et al., 2012). Postprint: Kamp, J.;, From single drop coalescence to droplet swarms -Scale-up considering the influence of collision velocity and drop size on coalescence probability, Chemical Engineering Science, 156, 162-177, https://doi.org/10.1016Science, 156, 162-177, https://doi.org/10. /j.ces.2016.08.028 3 Population Balance Equation (PBE...

Coalescence Modeling for Design of Technical Equipment

“…A variety of models to describe coalescence have been proposed, for which recent extensive overviews are available , , , . Here, only those aspects relevant for this work are summarized.…”

“…has to be extended for an additional effect observed experimentally. Kamp as well as Lehr and Mewes evaluated the coalescence probability between individual drops and bubbles, respectively. The authors found that for high relative velocity the coalescence probability is close to zero.…”

“…To investigate, which model is better suited to describe coalescence, Kamp performed collision experiments between one fixed drop and a moving drop and found that for high relative velocity, the coalescence probability is close to zero . This cannot be described with the energy model, which is thus not applicable for liquid dispersions.…”

“…The coalescence frequency is thus frequently described as the product of collision frequency and coalescence probability , : …”

Prediction of gas density effects on bubbly flow hydrodynamics: New insights through an approach combining population balance models and computational fluid dynamics

“…The development of combined CFD/PBE models has provided unprecedented insight into the fundamentals of bubbly flows . Population balance models give a realistic representation of the behavior of the bubbles and phase interfaces, while CFD provides local information regarding flow and liquid phase turbulence . The population balance models do contain a number of correlations based on experimental observations, such as semiempirically derived models for bubble coalescence and break‐up.…”