ABSTRACT Among the various nanoparticle synthesis techniques to address the growing demand for nanoparticles, pulsed laser fragmentation in liquids (PLFL) stands out as a simple, versatile, and sustainable method for obtaining nanoparticles (NPs) with unprecedented purity. Despite the potential to tailor the size, composition, structure, and defects of NPs via laser irradiation of a free‐flowing colloid jet, upscaling PLFL is oftentimes realized by employing costly high‐power laser sources. Herein, two improved flat‐film setups are introduced and compared with the conventional PLFL setup for the synthesis of ZnO NPs, which represent a promising model material for manifold applications. Indeed, a twofold reduction of average NP size down to less than 7 nm at 60% productivity increase and constant energy input can be achieved. Moreover, the microparticle conversion efficiency increases up to 65%, while crucial upscaling criteria, such as colloid heating, are optimized to prevent NP ripening and colloid evaporation. Numerical simulations reveal that a flat liquid surface reduces nonlinear interactions and provides more consistent irradiation conditions. The results emphasize the potential of synergistic optimization of the laser and liquid parameters for upscaled PLFL as a competitive technique for obtaining ligand‐free, green, and ultra‐small NPs.

The inline measurement of process parameters describing the separation process of disk stack separators is expensive and complex. An alternative method for assessing the current process parameters employing more accessible data is required. In this work, the separation efficiency during the operation is estimated using vibration measurements by determining characteristic vibration patterns due to the increasing load of the separation bowl. The disk stack separator used is an industry-scale laboratory model of a disk stack separator, equipped with three accelerometers for vibration measurements. The influence of different bowl geometries and particle systems on the vibration patterns and the separation efficiency has been investigated. The gathered data and knowledge about the inlet conditions (volume flow and solid concentration) are used to create a soft-sensor for the separation efficiency. A deviation of approx. 2% between direct measurements of the separation efficiency and the results of the soft-sensor is reached.

Efficient removal of solid particles and liquid droplets is essential in many industrial processes. The primary objective is to achieve high separation efficiency while minimizing the associated pressure drop. This trade-off presents a central challenge in filter media design, where the objective is to optimize filtration performance without compromising energy efficiency or operational stability. Over recent decades, both experimental techniques and numerical modeling have advanced substantially. Nevertheless, the micro-scale nature of filtration still restricts our understanding. Experiments often suffer from limited reproducibility and require costly prototype media. Conventional numerical approaches, such as the finite-volume method, can resolve the relevant transport mechanisms, but the small spatial and temporal scales involved require extremely fine meshes and time steps. These constraints make classical computational fluid dynamics (CFD) simulations expensive and sometimes impractical. In this work, a modeling approach for simulating the filtration process is presented, which integrates physics-informed neural network (PINN) with smoothed particle hydrodynamics (SPH). The PINN approximates the three-dimensional velocity and pressure fields inside the fibrous medium directly from the Navier–Stokes equations, without relying on any training data. The resulting flow field is passed to the SPH solver, which tracks the droplet trajectories and their interactions with the fibers. Because both PINN and SPH are mesh-free, the workflow eliminates complex grid generation and the need to solve the Navier–Stokes equations in small spatial and temporal increments. A bidirectional data exchange links the two solvers. As the deposited droplets grow large enough to influence the flow field, their geometrical information is transferred back to the PINN, which recomputes the flow field through Transfer Learning. Comparison between the flow field predicted by the PINN models and those calculated using CFD solver for four representative filter structures demonstrates a very good agreement between the PINN and CFD.

Sessile drops play an important role in nature and the operation of many technical and biological systems as for instance fuel cells, cleaning processes, lab-on-a-chip devices and single-cell analysis. Nonetheless, their dynamic behavior in a shear flow is still not fully understood (e. g. detachment mechanism). Challenges exist regarding the precise simulation of two-phase flows as well as difficulties in conducting flow measurements with sufficient temporal resolution of more than 1 kHz. In this article, we present the first three-dimensional flow measurements in strongly oscillating drops stemming from a shear flow by using a monocular 3D localization microscope based on a Double-Helix Point Spread Function combined with Particle Tracking Velocimetry. The high temporal resolution and the large measurement volume - in terms of microscopy - make it possible to measure the time- and phase-averaged flow in small drops with Bond numbers (Bo) smaller than 1. Water drops were placed in an air flow channel and measurements were conducted for Reynolds numbers (Red) from about 750 to 1700. Our measurements show that the results of previous investigations for drops with Bo>1 concerning vortex pattern and flow reversal inside the drop apply for smaller drops as well. In addition, we are able to reveal the three-dimensional flow structure and multiple vortex-pattern in time and space. We discover a periodic 3D vortical flow pattern that corresponds to the first and second eigenfrequency of the drop. Moreover, we demonstrate the potential of adaptive optics to correct measurement errors stemming from time-varying light refraction when conducting measurements through the fluctuating drop surface, in particular for opaque substrates. The results may help in understanding the coupling of inner and outer flow for sessile drops in shear flow which allows for an analysis of the onset motion of these drops, i.e. drop removal. Removal of sessile drops plays a crucial role in many applications, which includes among other things the water management of fuel cells where small drops with Bo<1 predominantly occur.

A numerical approach to investigate the correlation between particle deposition and vibration of disk stack separators is presented. Experimental observations have indicated that the deposition of solid particles within the rotating bowl significantly influences the vibration of the machine. To explore this phenomenon, a numerical model is developed, capable of representing both the particle deposition process and the corresponding dynamic response of the separation bowl of the disk stack separator. The simulation results represent the change in vibration amplitude and thus provide a deeper insight into the underlying physical interactions. A direct comparison between simulation and experiment shows an average deviation of less than 3% in the calculation of the displacement amplitude. Further numerical parameter variations show that, for example, a change in solid density from 1010 kg/m3 to 1320 kg/m3 causes a quadrupling of the change in vibration amplitude. This study contributes to the optimization of disk stack separator operation by enabling predictive assessments of internal deposition states through external vibration analysis.

This study examines the interaction between single oil droplets and an oleophobic fiber subjected to sinusoidal mechanical excitation, with particular emphasis on the vibrational effects on the resulting droplet motion patterns. The research combines experiments providing high-speed images and CFD simulations, employing a dynamic overset grid technique, to explore various droplet motion patterns, such as pumping, swinging, vertical oscillation, rotation, and collapsing. A key finding is that fiber oscillation induces a lasting transformation, whereby clamshell-shaped droplets—typically seen on oleophobic fibers—permanently adopt a barrel shape, characteristic of oleophilic fibers, even after the excitation ceases. Despite differences in wettability, oil droplets exhibit similar motion patterns on both fiber types after their transition and prior to detachment. The results highlight the importance of droplet dynamics for optimizing coalescence and drainage in industrial settings.

Droplets and their movement on solid walls can be observed in many technical applications. The droplets can be moved by external forces, e.g. aerodynamic or vibrational forces. If the velocity of the gas flow is higher than a critical one, the gliding motion of the droplet starts. Before the gliding motion, i.e. the droplet is still pinned, an oscillation of the contour can be observed. In this work, the interaction of the droplet oscillation and the surrounding gas flow is studied experimentally and numerically for two droplets with different diameters and in a channel flow which are positioned at various distances in flow direction. It can be shown, that the frequency of the gas flow separation corresponds to the Eigenfrequencies (EFs) of the droplets. For larger distances between droplets, only the second EF of the droplet in the backflow can be detected in the frequency spectra of the gas flow. If the distance is smaller than two droplet diameters, the first and second EF can be measured.

Long liquid retention times in industrial gaps, due to capillary effects, significantly affect product lifetime by facilitating corrosion on solid surfaces. Concentration-driven evaporation plays a major role in mitigating this corrosion. Accurate evaporation rate predictions are crucial for improved product design. However, simulating capillary-driven flows with evaporation in complex geometries is challenging, requiring consideration of surface tension, wetting, and phase-change effects. Traditional approaches, such as the Volume-of-Fluid method, are prone to curvature calculation errors and have long simulation times due to strict time step limitations. This study introduces a novel semi-transient simulation approach for fast evaporation rate prediction in arbitrarily shaped cavities. The approach involves a unidirectional coupling circuit, simulating the fluid surface in Surface Evolver and combining it with a vapor-in-gas diffusion simulation in OpenFOAM. The approach assumes that the evaporation rate is calculated solely based on the conditions at a given liquid filling level, without considering the evaporation history. This allows for highly parallelized simulations, achieving simulation runtimes in the order of 10 min to cover up to 150 h of physical time. Numerical investigations are conducted for water evaporation in air at a temperature of 23 degrees C and a relative humidity of 17 %, for round and polygonal-shaped capillaries with inner diameters ranging from 1 mm to 13 mm. The results are validated using experimental data and show strong agreement. Simulations are also performed for complex industrial relevant gaps, demonstrating the applicability of the approach to a wide range of crevice geometries.

Fluid flows are present in various fields of science and engineering, so their mathematical description and modeling is of high practical importance. However, utilizing classical numerical methods to model fluid flows is often time consuming and a new simulation is needed for each modification of the domain, boundary conditions, or fluid properties. As a result, these methods have limited utility when it comes to conducting extensive parameter studies or optimizing fluid systems. By utilizing recently proposed physics-informed neural networks (PINNs), these limitations can be addressed. PINNs approximate the solution of a single or system of partial differential equations (PDEs) by artificial neural networks (ANNs). The residuals of the PDEs are used as the loss function of the ANN, while the boundary condition is imposed in a supervised manner. Hence, PDEs are solved by performing a nonconvex optimization during the training of the ANN instead of solving a system of equations. Although this relatively new method cannot yet compete with classical numerical methods in terms of accuracy for complex problems, this approach shows promising potential as it is mesh-free and suitable for parametric solution of PDE problems. This is achieved without relying on simulation data or measurement information. This study focuses on the impact of parametric boundary conditions, specifically a variable inlet velocity profile, on the flow calculations. For the first time, a physics-based penalty term to avoid the suboptimal solution along with an efficient way of imposing parametric boundary conditions within PINNs is presented.

Numerical methods to solve partial differential equations (PDEs) have become indispensable in the field of fluid mechanics. Despite the intensive development of numerical methods such as the finite volume method and the finite element method over the past decades, these methods still have certain limitations, especially when dealing with numerical modeling of complex three-dimensional fluid flows. Moreover, a new simulation is needed for each modification of the domain, boundary conditions and material properties, which make the use of these methods inefficient for parameter studies in the design process or optimization. A new approach to solve PDEs has been recently introduced in the field of scientific machine learning. Physics-informed neural networks (PINNs) utilize the residuals of one or more PDEs as the loss function of an artificial neural network (ANN), while the boundary conditions are imposed in a supervised manner. Instead of solving a system of equations, with the PINN approach a nonconvex optimization is performed to approximate the specific solution of the PDEs by an ANN. Although this relatively new method cannot yet compete with classical numerical methods in terms of accuracy especially for complex geometries, this approach shows promising potentials, as it is mesh-free and suitable for parametric solution of PDE problems. As an exemplary application, we examine a three-dimensional pipe flow problem featuring a variable inlet boundary condition and a twisted baffle that mimics a static mixer. The flow fields predicted by the PINNmodel are compared and validated with CFD simulations.

In this study, for the first time, the droplet–fiber interaction on a mechanically excited fiber is examined in the direction of the fiber axis. Highly spatially and temporally resolved simulations and experimental investigations provide information on the relative position of the center of the projected area of the droplet and the center of the fiber, the relative angular position, and the deformation of the droplet using a skeleton line. To attain this, a state-of-the-art camera technology was employed in the experiments, while the volume of fluid method was utilized for the modeling of the multi-phase flow. Additionally, an overset method for the movement of the fiber was applied in the computational fluid dynamics simulations. Characteristic motion patterns, whether occurring in isolation, in sequence, or superimposed, are identified, representing a prerequisite for the detachment of the droplet from the fiber. Despite the simplified assumption of a two-dimensional simulation, the motion patterns observed in the simulation are in good agreement with the experimental data. The obtained results contribute to a fundamental understanding of the mechanisms responsible for the detachment of a droplet in the context of the droplet–fiber interaction within the excited coalescence filters.

Filtration processes are a complex combination of deposition and rearrangement of particles and agglomerates of particles on fibres. The small scales of particles and fibres lead to a lot of difficulties in the experimental analysis of filtration processes. On the other hand, numerical methods are mostly bases on a Lagrangian modelling, i. e. treating the particles as a point of mass neglecting its shape. This requires the use of analytical or empirical correlations for drag and adhesion forces which are often only available for spherical particles. Especially in configurations of particle-particle and particle-wall interactions these correlations may lead to deviations. If non-spherical particles should be considered, the Lagrangian method cannot be applied. In this work, the geometry of the particle is volumetrically resolved and is taken into account in the computational grid for the flow calculation. This is achieved by using an Immersed Boundary Method implemented in the open source CFD code . The method is characterized by a determination of the particle forces through an integration of the viscous and pressure forces acting on the surface as well as the adhesion forces over the particle surface between different parts (particles, walls). Besides the detailed presentation of the model and its implementation in , different application areas of the model are presented.

Modern particle detectors crucially depend on efficient cooling systems. Two-phase carbon dioxide (CO$_2$) is a suitable solution as a cooling agent. This publication presents the observations and results of investigations of horizontal and vertical flow of two-phase CO$_2$ at a temperature of $T=-15\,^\circ$C and a pressure of approximately $23\,$bar. Heat fluxes between $98.5\,$kW/m$^2$ and $200\,$kW/m$^2$ were applied to the CO$_2$, covering the range expected to occur in the future ATLAS Pixel detector being built for the high-luminosity phase of the Large Hadron Collider. Flow speeds ranged from $11.8\,$m/s to $28.1\,$m/s. Dedicated sensors were used to measure the temperature and pressure before and after heating the CO$_2$. Two-phase flow patterns occuring in the pipe after heating the CO$_2$ were recorded with a high-speed camera. Stratified, wavy and slug flow are found to be the predominant patterns for horizontal flow, while upward vertical flow is mainly found to be slug or churn. Based on the recorded images the void fraction of the CO$_2$ after heating is determined and compared for the different setups. The results are summarised in a flow-pattern map. A clear distinction between vertical and horizontal flow is found, with horizontal flow exhibiting a significantly higher void fraction than vertical flow. Based on the pressure measurements, the pressure drop after heating the CO$_2$ is measured and the corresponding Euler number is computed. While the pressure drop increases with the heat flux for horizontal flow due to frictional losses, the pressure drop reduces with the heat flux in case of upward vertical flow, since static pressure is important in this case.

The motion and particularly the detachment mechanism of sessile drops in an air-shear-flow is highly relevant for many technical applications. For instance, water drops in fuel cells can block the oxygen transport and thus lower the overall efficiency. Hence, a deeper understanding of the drop detachment mechanism could facilitate efficiency optimisations. Nonetheless, until now only simplified models exist for predicting the critical velocity that do not take into account the mutual interaction of the air and the liquid via the non-rigid interface. One reason for this is the lack of knowledge of the flow inside the oscillating drop. In this contribution, we present the first three-dimensional flow measurements in oscillating sessile drops in shear flow. Time-averaged flow measurements were conducted for different Reynolds numbers. Furthermore, the phase-averaged flow field was measured. The measurements were conducted with a novel 3D-PTV method, which offers scanless three-dimensional flow measurements with a single optical access for a measurement volume that covers about 90 % of the drop volume. Moreover, we present a novel technique for conducting flow measurements through fluctuating gas-liquid interfaces based on adaptive optics. We demonstrate that this technique enables the correction of a systematic error corresponding to the magnitude of the first drop eigenfrequency, which seems to play an important role in the detachment mechanism of drops. The results give new insights about the fluid mechanics of sessile drops and thus may help in the optimisation of drop removal in e. g. fuel cells.

The movement of a sessile droplet can be initiated by different mechanisms. In addition to an incident flow, a vibration or differences in the surface properties can initiate the movement of a droplet. In many cases, the mechanisms occur in combination and their interaction is not well understood. We report on the investigation of superposition of an incident flow and a two-dimensional vibration excitation acting simultaneously. The focus is on the analysis of the critical air flow velocity required for the detachment of a droplet. More precisely, it is investigated how a simultaneous two-dimensional vibration affects the critical incident flow velocity. In particular, the influence of a phase shift of both excitation sources with respect to each other is investigated. For this purpose a rectangular Plexiglas flow channel equipped with two electromagnetic shaker is used. One oscillation source acts vertical to flow direction, while the second shaker operates simultaneously in horizontal direction. Two scenarios are considered for the orientation of the horizontal vibration excitation. Case 1: the horizontal vibration excitation is in the direction of the incident flow. Case 2: the horizontal vibration is transverse to the incident flow. The excitation frequency and acceleration are varied within the series of experiments. Water droplets of different volumes (7.8 – 23.4 μl) are studied. The substrate is polymethylmethacrylate (PMMA), which has a hydrophilic character, at static contact angles of about 74°for a water droplet. The data obtained reveal that the critical velocity for detachment of a sessile droplet can be significantly reduced by superimposing an oscillatory excitation only for certain frequencies. A significant decrease in the critical velocity is observed for an excitation in the range of the first and second eigenfrequencies. The phase offset of the two vibration sources will also affect the critical droplet detachment velocity if the horizontal excitation source is parallel to the incident flow. However, if the excitation is in the horizontal plane perpendicular to the incident flow, a phase shift between the two vibration sources has no effect.

The research project SynErgie aims to adapt large scale industrial processes to a volatile supply of renewable energy which is expected for the future. The aluminum electrolysis process is one of the biggest consumers of electric energy in Germany. The aim is to vary its nominal process power by ± 25%. This numerical study focuses on the magnetohydrodynamic (MHD) behavior of the electrolysis cells of Trimet Aluminum SE in Essen. To capture the MHD driven flow and electrodynamics inside the electrolysis cells a computational fluid dynamics (CFD) model is developed in the OpenFOAM® framework. This accounts for the influence of neighboring electrolysis cells, the magnetization of ferromagnetic materials, a static ledge profile and the dynamic changes of anode shape caused by the carbon consumption. The simulation predictions show the heave of the aluminum cryolite interface for different line currents. To analyze the behavior of flexible process operation, shifts of the line currents are studied in detail. After shifting the line current, the interface heave changes directly whereas the shape of the anode bottom reacts with a delay in time. This leads to a locally uneven anode cathode distance (ACD) followed by a disturbed current distribution inside the electrolysis cell after shifting the line current. The anodic current distribution is quantified by the model, which can help process operators to identify whether increased anode currents are caused by the line current shift or potential abnormalities like spikes. Graphical Abstract

The pressure loss and heat transfer characteristics of single-phase water flows and non-boiling air-water flows through a slender 180 degrees return bend with a rectangular cross-section are investigated. Such slender ducts appear in various applications. In comparison to abrupt return bends the unsymmetrical flow field affects a bigger surface. Therefore, there is an interest to quantify the impact of such curvature effects. For the pressure loss consideration, the curvature ratios are 19.9, 40, and 58.1, whereas for heat transfer, the focus is on the latter, the hydraulic diameter and aspect ratio are 3.9 mm and 1.067, respectively. The numerical results are compared to published experimental ones. From the numerical modeling results, where three different approaches of turbulence modeling were tested, it is confirmed that above a curvature ratio of 90 it seems reasonable to neglect curvature effects on pressure drop. The validated conjugate heat transfer models are utilized to develop local and global relationships for the Nusselt number ratios between the convex and concave surface. The two-phase flow modeling is realized via a homogenous flow model approximation. The results show that the modeling provides reasonable results and that the impact of curvature on such flows can be relevant.

Corrosion tests are standardised test procedures where specimen is subjected to different climates in test chambers with defined test cycles. The cycles are a complex scenario of spraying, drying and condensation phases. Aqueous sprays with different salts lead to liquid films and corrosion processes on the specimen. As there are various kinds of salts present which will deposit based on the local concentration of the ions, the stoichiometry and the solubility, the conventional modelling with a given number of species is extremely difficult. Therefore, the modelling approach for handling species was changed to the modelling of the transport of ions in the film including condensation and evaporation. The verification is reported on a simple U-shaped specimen whereas a more complex specimen was used for the validation with experimental results on the basis of a standardised test cycle in corrosion testing.

The impact of droplets on non-fixed spherical particles placed on a plane polymethyl methacrylate (PMMA) substrate is investigated. This interaction is a highly abstracted level of a high-pressure spray cleaning process. Water droplets in a diameter range between 0.68 and 1.66 mm and spherical particles (PMMA) with a diameter of 1.55 mm are used. The droplet velocity range of 1.05 ≤ v_d≤ 2.0 m/s results in a Weber number range of 13 ≤ We ≤ 94 . The particle-droplet-substrate interactions are investigated for different Weber numbers, droplet-to-particle diameter ratios and eccentricities. Different droplet impact scenarios are identified: A—Lift-off during initial recoil; B—Lift-off during a later recoil; C—No Lift-off, deposition of the droplet and D—No Lift-off, wetting of the substrate. The behavior of the particle-droplet-substrate interaction is determined depending on Weber number and particle-to-droplet diameter. Additionally, the analysis of the eccentricity in relation to the lift-off behavior shows that the lift-off height and duration increases with the centrality. The investigation of temporal change of the half-spread and contact angle results in a criterion for the point in time at which the lift-off takes place. Finally, a simplified analytical model is provided quantifying the probability of the lift-off of the particle-droplet system after the interaction. Experimental and analytical results are used to create a map of occurring impact regimes in terms of the particle-droplet configuration.