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Item type:Publication, Access status: with files , Dynamical compartments in stirred tank reactors and Markov state modeling for mixing quantification: A transfer operator approach(American Chemical Society (ACS), 2026-08-31); ; ; ; Identifying coherent flow structures in chemical reactors is crucial for understanding the mixing dynamics, which is essential for optimizing reactor performance. We demonstrate the use of a transfer operator method to find coherent flow structures such as almost-invariant sets and coherent sets, which are characterized by minimal mixing with the surrounding fluid, in a lab-scaled stirred tank reactor using both simulated and experimental Lagrangian trajectory data. The proposed method further enables a detailed analysis of the mixing behavior by computing expected residence times and mixing times. Additionally, a Markov state model describes the macroscopic transport dynamics between compartments in the reactor.Publicationtype: Journal Article54 19 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Can we live Danckwerts' dream? Mixing analysis in a baffled stirred tank reactor based on 4D-particle tracking experiments(2026-07-29); ; ; ; We present an experimental investigation of mixing dynamics within a laboratory-scale 3-liter stirred tank reactor (STR) equipped with two Rushton turbines and three baffles. Using time-resolved, four-dimensional particle tracking velocimetry, we successfully capture trajectories of up to 40,000 tracer particles in the full reactor volume despite obstructions by stirrer and baffles, providing unprecedented time-resolved flow and mixing information. From these Lagrangian data, we analyze velocities, accelerations, and spatial dispersion, revealing anisotropic mixing. By utilizing novel network-based analysis methods on the experimental particle trajectories, we identify coherent fluid compartments that exhibit strong internal mixing but weak exchange with neighboring compartments. We uncover five distinct compartments acting as transport barriers, which have a high impact on substrate distribution in chemical and biochemical processes. Our approach thus realizes and extends early thought experiments from Danckwerts and Levenspiel by providing detailed insight into the behavior of single fluid parcels and Lagrangian mixing withing chemical and biochemical reactors, offering a valuable approach for evaluation and optimization of chemical and biochemical processes. The trajectory data are made freely available to serve as an experimental reference for further research.Publicationtype: Preprint26 24 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Comprehensive study of 3D liquid flow fields in additively manufactured structures for SMART reactors using large-scale vertical magnetic resonance imaging and computational fluid dynamics(Elsevier, 2026-04-24); ; ; ; Triply Periodic Minimal Surface (TPMS) structures have emerged as a new class of porous materials with variable geometries and favourable transport properties, making them promising for reactor internals in chemical engineering. However, experimental data on internal TPMS flow behaviour are still limited. To address this gap, the flow behaviour in additively manufactured TPMS structures is analysed using three-dimensional Magnetic Resonance Imaging (MRI) velocimetry in a large-bore vertical 3 T MRI system, in cylindrical columns of 38 mm diameter and Reynolds numbers between 50 and 300. Three different TPMS geometries are investigated, and consistency between Computational Fluid Dynamics (CFD) simulations and experimentally measured MRI velocity fields is established through cross-validation. The MRI system provides fully three-dimensional velocity fields with a divergence deviation below 6 %. MRI revealed distinct flow features: the Gyroid TPnS exhibited pronounced channelling, while the Schwarz-Diamond TPSf showed merge-split behaviour, achieving a 46 % increase in lateral mixing compared to the Gyroid TPnS structures. Numerical simulations reproduce the flow features and show agreement with the MRI data. The combined methodology demonstrates the suitability of MRI velocimetry for the experimental validation of CFD simulations and establishes a robust foundation for future studies of heat and mass transfer, as well as reactive flow, in structured reactor systems.Publicationtype: Journal Article68 84 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Modeling and validating of oxygen transport in wave bioreactors: optimized experimental mass transfer method and novel Lattice-Boltzmann CFD approach(Frontiers Media S.A., 2026-01-21); ; ; Wave bioreactors are commonly used in biopharmaceutical upstream processes as an intermediate stage between shake flasks and stirred tanks within the seed train. They offer a controlled environment for cell cultivation while minimizing shear stress. Accurate characterization of these systems is essential for optimizing cell culture performance, particularly as state of the art cell lines require higher volumetric mass transfer coefficients k<inf>L</inf>a. This study aims to determine the volumetric mass transfer coefficient through experiments and computational fluid dynamics (CFD) simulations. An improved experimental method for the measurements of the volumetric mass transfer is presented, with results correlated to key process parameters: rocking angle, rocking rate, and filling volume. In addition, CFD simulations were caried out using M-Star CFD by means of a Lattice-Boltzmann Method-based solver. The mass transfer was calculated using Higbie’s penetration theory, incorporating the Kolmogorov scale to define contact time. The analysis also integrates concepts from Friedl and the surface renewal model, introducing the surface normal velocity as an additional parameter in the mass transfer coefficient k<inf>L</inf> calculation. Analyzes were carried out for 10 and 50 L wave bioreactors, with one degree of freedom movement. Optimized process parameters were identified and validated in biological cultivations, resulting in increased dissolved oxygen levels in the medium. These findings contribute to improved characterization and control of wave bioreactors, enabling more accurate prediction of process parameter effects.Publicationtype: Journal Article27 14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A lagrangian model for the prediction of bubble breakupIn 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.Publicationtype: Doctoral Thesis76 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Trajectory-based breakup modelling for dense bubbly flowsA new model to predict the breakup of gaseous bubbles in a continuous liquid phase is developed. In the model each bubble is modelled as a spring–damper system, namely a Kelvin–Voigt element, while the outer force is derived by a Lagrangian analysis determining the largest stretching rate of the flow field below. The developed model is based on physical principles and no further arbitrary parameters have to be adjusted. Each bubble is observed on its way through the bubbly flow individually, taking into account its history along its respective path. With the implemented model numerical simulations in a wide range of scales are conducted, ranging from the laboratory scale of a vessel of 3L to the large industrial scale of 15m3. The simplicity of the model allows for a good cost to benefit ratio. In the present work, the achieved results are compared to experimental data obtained from optical measurements in a replica of a 200L aerated stirred tank reactor for various stirrer frequencies.Publicationtype: Journal Article38 64 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Direct numerical simulation of bubble collision, bounce and coalescence in bubble-induced turbulence(2024-02-05); ; ; A direct numerical simulation study has been carried out to better understand the dynamics of deformable bubbles in bubble-induced turbulence. A mathematical model for bubble collision, bounce and coalescence is developed based on the Volume-of-Fluid (VoF) method. A surface-tension-holding film thickness δc is introduced to determine whether the bubbles will coalesce or bounce after collision. Bubbly flows with the gas volume fractions αg=5.6% (low), 11.2% (medium) and 22.1% (high) are considered in the study. The DNS results show that the dissipation of turbulent kinetic energy in the cases under consideration takes place when the wavenumber κ is smaller than twice the wavenumber for the bubble diameter 2κd. The bubble-induced turbulence is anisotropic at the length scales close to the bubble diameter due to the elongated turbulent structures in the bubble-rising direction. The bubbles collide intensively with each other when they are in a cluster surrounded by the liquid with low pressure. Parallel clustering of bubbles is found when the gas volume fraction has a low or medium value. Three-dimensional clustering is found when the bubbles are densely populated. Two different mechanisms of bubble collision have been identified from the DNS results, termed parallel collision and vertical collision. Parallel collision is often observed when bubbles are sparsely populated. In a parallel collision, the relative velocity of the bubbles slows down as two bubbles approach each other due to the jet flow between them, while the relative velocity increases sharply after the bounce. In a vertical collision, by contrast, the relative velocity of bubbles accelerates as two bubbles approach each other, while it slows down during the collision. Vertical collisions occur when the bubbles are more densely populated. The numerical results also show the significant effects of δc on bubble coalescence.Publicationtype: Journal Article18 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Introduction of novel characteristic time quantities to describe chemical reactors(Elsevier, 2023-11-15); ; ; ; The Mean Residence Time is a quantity which is used very often to characterise chemical reactors. This quantity can be calculated using the Residence Time Distribution of a specific, continuous reactor and assuming closed-closed boundary conditions. Many reactors in the industry though, are discontinuous ones and the direct application of these methods is in general not possible. This work presents a new distribution, the Local Residence Time Distribution, which observes each position in a specific reactor. Furthermore, two new, local quantities, the Mean Distribution Time and the Mean Dead Time, are introduced, which can be applied as characteristic times to evaluate the internal behaviour of chemical reactors used for discontinuous processes such as fermentations.Publicationtype: Journal ArticleScopus© Citations 1 29 95 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Effects of bubble-induced turbulence on interfacial species transport: A direct numerical simulation study(Elsevier, 2023-09-05); ; ; A direct numerical simulation (DNS) study is carried out to understand the effects of bubble-induced turbulence on the interfacial species transport. A volume-of-fluid (VOF) method is used in the DNS to simulate the multiphase flow in a box containing one or two deformable bubbles. The bubbly flows with Schmidt numbers 1≤Sc≤64, Reynolds numbers 100≤ReB≤750, Eötvös number Eo=1.21 and gas volume fractions 2.8%≤αg≤22.1% have been investigated. The DNS results indicate that the one-dimensional energy spectra evolve as the power −3 of the wavenumber at large scales. At a high Schmidt number, an inertial subrange characterized by the -5/3 slope can be found in the power spectra of species concentration. The power spectra of species concentration for different Schmidt numbers become close to each other when the wavenumber is scaled with Sc0.5. The bubble-induced turbulence enhances the oscillation of the transient Sherwood number, however, it has marginal effects on the time-averaged value. By contrast, the time-averaged Sherwood number for a fixed Peclet number increases with an increase of αg, indicating that convection plays a more important role in species transport when the bubbles are more densely populated. A possible reason is that, the neighboring bubbles enhance the spatial fluctuations of the velocity, which favor the interfacial species transfer. The energy spectrum confirms that an increase of αg leads to stronger spatial fluctuations of the vertical velocity component at low wavenumbers.Publicationtype: Journal Article38 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Computational study of three-dimensional Lagrangian transport and mixing in a stirred tank reactor(Elsevier, 2023-01-13); ; ; ; The detection of compartments and dead zones as well as the estimation of the mixing efficiency in stirred tanks are of vital interest for a variety of biochemical and chemical processes. Here, numerically derived time-dependent 3D fluid velocity fields of a stirred tank reactor are computed using the Lattice Boltzmann Method. Mixing in the stirred tank reactor is analysed by means of Lagrangian Coherent Structures which allow to unravel the mixing states of complex flows. This Lagrangian analysis is achieved by computing Finite Time Lyapunov Exponents and applying recent trajectory-based network methods on the three-dimensional flow. The results reveal a zone of low interaction in the upper region of the stirred tank reactor and five additional transient compartments. The trajectory-based network analysis detects low cross-mixing of fluid parcels between different compartments but a very high mixing of fluid parcels inside of each compartment. This high interaction is also found in an analysis of the Finite Time Lyapunov Mixing Intensity. Time-averaging of the fluid velocity field prior to the Lagrangian analysis is considered to extract the most influential Lagrangian Coherent Structures.Publicationtype: Journal ArticleScopus© Citations 5 79 353