Options
A lagrangian model for the prediction of bubble breakup
Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Advisor
Referee
Marchisio, Daniele
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-07-11
Institute
First published in
Number in series
15
Citation
Berichte aus dem Institut für Mehrphasenströmungen 15: (2025)
Publisher
Cuvillier
ISBN of container
978-3-68952-350-3
978-3-68952-351-0
In many applications in the chemical or biochemical industry the mass transfer of a species from one phase into another has a huge influence on the whole process. Often, the relevant species are available as gas and, thus brought into the observed system as gaseous bubbles. The transport of mass from those bubbles into the liquid takes place at the bubbles’ surfaces. Bubbles can break up, resulting in two or more daughter bubbles, increasing the total surface area and coalesce with each other, merging two or more bubbles into one, reducing the total surface area. Further impact on the mass transfer lies in the sizes of the boundary layers surrounding the bubbles and the local concentration differences, resulting in a difference in the chemical potential, being the main driver of the transfer itself. In this work, the focus lies on the derivation, implementation, and validation of the newly proposed model to describe the breakup of gaseous bubbles. For this purpose, a trajectory-based attempt is used while each bubble is modelled individually as Kelvin-Voigt element. Further, the bubbles are assumed to behave like rotational ellipsoids in the current state of the model. The interfacial tension is mirrored by a theoretical spring, inducing a tension on each observed bubble forcing it into its equilibrium, the spherical state. The gaseous phase’s viscosity is depicted by a theoretical damper, acting against the current direction of the bubble’s further deformation or restoration. The tension which drives the deformation is retrieved from a Lagrangian analysis, quantifying the local occurring stretch implied by the surrounding liquid. The deformed bubble is then destabilised in comparison to the spherical state. For the description of the breakup the force induced by interfacial tension, lowered by the deformation, is compared to the inertial forces acting on the bubble. These inertial forces are quantified by the drag force which acts on the bubble. In the Trajectory-Based Breakup Model, the drag force is approximated by the buoyancy force. This description has a potentially severe disadvantage. There is one critical value for the state of deformation for a given bubble volume, regardless the flow conditions of the liquid. To account for this, a more precise formulation of the drag force is derived. Both model variations are tested by carrying out Lattice Boltzmann simulations. The mass transfer is modelled based on the retrieved bubbles sizes coupled with either the penetration theory or a Sherwood correlation. The results are compared to experimental data for validation.
DDC Class
600: Technology