The spreading of a liquid, subjected to centrifugal forces or an air jet, leads to a lowering of the liquid height at the center. If the system is partially wetting, experiments show a break up of the liquid and the appearance of a dry patch at the center. In this article, the spreading of a liquid droplet or a liquid film, featuring a dry patch at the center, is investigated. Via a generalized Tanner’s law, we allow for a contact-angle hysteresis in partially wetting systems. By means of the lubrication approximation, an analytical quasi-steady solution can be derived in the limit of small capillary numbers. We find a power-law regime for the spreading, in which at least one of the contact lines follows a power law in time, almost independent of both static contact angles. The influence of the static contact angles remains restricted to the beginning of the spreading and to transition periods. Four different types of spreading can be identified, namely spreading (i) with a very thin central liquid layer, (ii) as annular ring with central dry patch, (iii) into a static equilibrium, and (iv) with closing of the central dry patch. In a flow map, these types of spreading are mapped as function of both static contact angles. Moreover, the dependency from gravitational and centrifugal forces is investigated and included in the flow map. For a perfectly wetting system, a disjoining-pressure correction in combination with Tanner’s law prohibits negative liquid heights at the center. Hereby, the magnitudes of the Hamaker constants have a negligible influence and arbitrary-small values can be used, since the dynamics of the contact line remains controlled by Tanner’s law.

Coalescence filtration is used in a variety of process industries to remove liquid mists from gas flows. Non-woven materials are widely used due to their high separation efficiency and low cost. The operating conditions of these filters are dependent on the internal structure of the filter material. Inhomogeneities, arising from the manufacturing process, not only affect the flow of air through the filter but also determine which areas are preferentially wetted, and in turn modify the airflow through the blocked regions. This study uses three-dimensional (3D) micro-computer-tomography imaging to analyze, in a non- destructive manner, the internal structure of a commercial coalescence filter, made of oleophilic glass fibres in dry and wetted state. Using image processing software, a post-processing routine is developed to identify filter parameters based on coarse spatially-resolved images. Afterwards, the dry-filter images are compared with wetted-filter images to establish that inhomogeneous local solidity is responsible for inhomogeneous wetting in an oleophilic filter. (C) 2021 Elsevier Ltd. All rights reserved.

The validity of Darcy’s law at very low Reynolds numbers is discussed controversially in literature, as some authors propose a pre–Darcy flow regime below some critical Reynolds number. The scope of this work is to investigate this problem experimentally. Therefore, a packing of glass spheres is perfused by different glycerin–water solutions. A linear behaviour between the flow velocity and the pressure drop through the packed spheres is found in the complete investigated range of Reynolds number $${Re}_{d'}$$ Re d ′ , based on the mean-pore diameter $$d'$$ d ′ and mean-pore velocity $$v'$$ v ′ with $$10^{-9} \le {Re}_{d'} \le 10^{-1}$$ 10 - 9 ≤ Re d ′ ≤ 10 - 1 . This contradicts the results of different authors like Fand et al. (1987) or Kececioglu and Jiang (1994), postulating a pre–Darcy regime for $${Re}_{d'} \le 2.8 \cdot 10^{-6}$$ Re d ′ ≤ 2.8 · 10 - 6 or $${Re}_{d'} \le 0.13$$ Re d ′ ≤ 0.13 , respectively. Graphical abstract

Clean air or gas is critical e.g. in many industrial or health applications. Various filtration processes are employed to ensure that liquid droplets and/or solid particles, i.e. so-called aerosols, are removed efficiently and at low costs from the respective gas streams. Fibrous filters are often used in this context, because of their low cost, their high capture efficiency, and their low pressure drop. Hence, the performance of fibrous filter materials is judged based on their pressure drop and capture efficiency. A generalized model to describe and predict these two parameters would be helpful in developing optimal filter material. In the current work, numerical investigations using the commercial CFD tool ANSYS CFX are engaged to predict the pressure drop caused by multiple randomly-oriented fibres in a 3D domain. The fibres are randomly generated until the desired filter solidity is met. Hereby, the generation algorithm ensures that no fibres intersect. The implementation is based on a fictitious-domain approach, which has the great advantage to perfectly decouple the mesh from the fibre generation, as fibres are implemented as volumes of infinitely-high flow resistance in the fixed mesh. Hence, there is no need for a case-specific and body-fitted mesh. The effect of the domain size is particularly investigated and we find that a domain size of more than 45 times the fibre diameter in all three directions, proves to give domain-size-independent results for the pressure drop. The boundary conditions are also carefully analyzed, and we find that particularly the symmetry planes parallel to the mean flow direction are not appropriate as the representative domain is cut out of the filter layer. Here, the introduction of a pseudo-plane proves to minimize non-physical flow fields. Moreover, using scanning microscopy, a sample fibrous filter is analysed to characterize the (random) fibre orientation. It is found, that within the filter plane an evenly-distributed fibre orientation angle alpha can be observed, while out of the filter plane the orientation angle beta appears rather limited. This limitation is also implemented into the model. Finally, several simulations are performed for various operating conditions to infer an empirical correlation to predict the pressure drop. This correlation is validated using experimental data. (C) 2021 Elsevier Ltd. All rights reserved.

We investigate how the walls of cylindrical capillaries affect the velocity of rising gas bubbles of various diameters. Of course, as the capillary diameter increases, the velocity of the rising bubble will approach the case of free rising. Such systematic experiments on the bubble rise in capillaries, in which the ratio of bubble diameter and capillary diameter is varied from one towards smaller values, can hardly be found in literature. Experiments within the system water/air have been conducted in stagnant water and will be discussed in this paper.

Modern spray-coating processes are based on high-volume, low-pressure, airless atomization or high-speed rotary bell atomization, often assisted by electrostatic charging to increase the transfer efficiency. The process from the liquid film flow beneath the bell, through ligament formation and consecutive disintegration to droplet deposition, has been constantly explored during the evolution of automotive spray coating. This work proposes a set of dimensionless groups that fully describe the process from film flow to ligament disintegration, including shear and elongational flow effects during atomization of particle laden, shear thinning, viscoelastic fluids.

Coalescence filtration is a mechanical filtration process, which is used for the removal of liquid droplets from a gas stream. A numerical model is proposed using an Euler-Euler multi-phase formulation to model the macroscale filtration process. The model is implemented for a 2D case using the commercial CFD software ANSYS (c) CFX. The capture of the dispersed phase is modelled using the penetration approach for single fiber capture efficiency which is extrapolated to multiple fibers, resulting in an exponentially-decaying interpolation scheme. To model the flow of gas through the dry filter, an empirical pressure-drop correlation is developed based on fiber-scale flow simulations for varied flow parameters. For the fiber-scale simulations, three-dimensional fibers are generated with random position, thickness and orientation using algorithms developed in house, ensuring that all fibers remain in the filter bed and that the fibers do not intersect. The correlation is extended to a wet filter by adapting the correlation parameters, with the assumption that the oil completely wets the fibers and results in a homogeneous increase in net packing density. The local velocity of the fiber-wetting oil is estimated analytically using the local oil saturation and gas velocity using a thin-film approach, taking into account the effect of the mean fiber orientation (determined using three-dimensional micro-CT scans) on the absorbed oil residence time in the filter bed. An analytical model is used to approximate the thickness of the oil film formed at the back of the filter surface and the pressure drop caused by the gas flow through it. Both steady-state and transient simulations are run and validated against measurement data provided by the Institute for Energy and Environmental Technology (IUTA), Germany. The steady-state pressure drop and oil-saturation predictions from the simulations follow the same trend as the experimental data albeit showing a stronger influence on air flow velocity. The transient simulations show the expected three-stage process with an initial gradual increase of the pressure drop, followed by a drastic increase, and finally, an approach to an equilibrium state.

The aerosol filtration technique deserves extensive attention, due to its wide applications found in health, environment, and industry. The simulation of aerosol filtration over fibrous filters involves the numerical investigation of the motion and capture of particles (aerosols) under different fluid operating conditions.

The influence of the wall effect on the liquid flow through a porous bed of spheres in a planar casing is investigated. The porosity in the wall-effect region is determined experimentally. Further experiments lead to a suitable model for the permeability in the wall-effect region. Functions are determined correcting the volumetric flow rate and the permeability depending on the wall effect.

Coalescing filtration is a mechanical process, which is employed to remove dispersed aerosol particles from a gas stream. This kind of filtration is a depth filtration process and it is widely used in process industries to remove particulate matter from exhaust gases, or in compressed air applications to filter oil particles introduced during compression. Fibrous filters are often used due to low cost, high capture efficiency and low pressure-drop, where droplets are first captured on fibres, then coalesce, and eventually drain out. The performance of a filter medium is judged based on its capture efficiency and its pressure drop characteristics. Estimating these parameters without setting up experimental investigations of each filter medium would be beneficial for choosing and developing optimal filters. In the present study, numerical simulations using ANSYS CFX((C))( )are used to predict the pressure drop caused due to the air flow through the randomly oriented fibrous filter medium. A fictitious domain approach is used to simulate solid fibres without the need to create a case-specific mesh for each different fibre alignment. The method is compared to a benchmark simulation and a mesh analysis is carried out to find a balance between mesh refinement and computational effort required. This method is extended to model 3D fibres with random orientations. Multiple simulations, each with a different randomized fibre alignment, is carried out, varying both Reynolds number and solidity, and the results are compared with theoretical and 2D simulation results. It is seen that both available theoretical models and 2D simulation results overestimate the pressure drop caused by a real fibrous filter which is attributed to the inherent random orientation of the fibres. (C) 2019 Elsevier Masson SAS. All rights reserved.

High-speed rotary bell atomization is the key coating technology in the automotive industry. We investigated the atomization behavior of shear-thinning fluids emphasizing the contributions of elongational flow resistance and the presence of anisotropic particles. Mixtures of two commercial acrylic thickener solutions allowed for a variation of elongational relaxation time lambda(e) by almost two orders of magnitude. Suspending different fractions of highly anisotropic, flake-shaped particles in such thickener solutions resulted in a fourfold increase of lambda(e). In both series of model fluids, shear viscosity remained essentially unchanged. Light-scattering techniques were used to determine the droplet size. The length of the ligaments formed at the bell edge during an important intermediate step preceding droplet formation was obtained from high-speed videos in combination with a customized image analysis code. For the pure thickener solutions, an increase in the elongational relaxation time resulted in an increase in the ligament length but did not affect the droplet size, since drops were not only formed from primary ligaments but were also formed after further fragmentation downstream. Suspended glass flakes accelerated ligament disintegration despite the increasing lambda(e) but, again, did not affect droplet size. The flake-shaped particles appear to act as predetermined breaking points disturbing the flow inside the ligaments. This phenomenon was verified using an industrial automotive basecoat including different amounts of aluminum flakes. These new insights regarding the high-speed atomization of complex fluids may support the targeted formulation of coating fluids.

The present work concentrates on numerical investigations of the hydrodynamics, the oxygen mass‐transfer, and the biochemical reactions in a pilot‐plant‐scale aeration tank, engaging the Euler‐Euler method and the Activated Sludge Model No. 1. The oxygen concentration, the ammonium concentration, and the nitrate concentration are discussed using results from the experimental investigations at the pilot‐plant‐scale aeration tank in the waste‐water‐treatment plant Ebersbach carried out by the HZDR.

The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a fluid flows uniformly through such a porous medium. For thin porous media, deviations are known near the regions of confinement. This so‐called wall effect is extensively investigated in literature for circular confinements. In this work, the wall effect and the flow through porous media in a rectangular domain is studied. This has great importance during the initial filling process of lithium‐ion batteries with the liquid electrolyte. Such batteries consist of collector foils, on which the porous electrodes are attached. Their thickness is only 5 – 10 times a particle diameter dP and may be modeled as a monodisperse bed of spheres. The filling flow is extremely slow and may be in the pre‐Darcy flow region, wherefore the validity of Darcy‘s law is experimentally checked. Then, the local porosity function depending on the distance to the wall is experimentally determined. For very thin porous media, the wall effect of each wall may overlap each other, which is taken into account by using an overlapping model from the literature. The widely used model of Carman‐Kozeny [1] relates the permeability with the porosity. Its validity in the near‐wall region is checked by comparing experimentally‐obtained mean pore diameters to those related to the model of Carman‐Kozeny. The flow through a porous media is computed and compared to experimental results from literature for circular confinement and preliminary optically‐matched PIV measurements.

High-speed rotary bell atomization is the preeminent coating technique in the automotive industry. It is widely accepted that a narrow droplet size distribution and constant spray are necessary in order to guarantee uniform film thickness and high-quality appearance. This may be deteriorated by paint flow pulsations. So far, however, no studies exist regarding such fluctuations quantitatively for this type of atomizers. We fill this gap using image analysis of high-speed recordings close to the bell edge. We could show that the fundamental pulsation frequency increases linearly with rotational speed. A ratio of pulsation frequency and true rotational speed of about 3 was found, indicating that pulsations were initiated mainly by the three struts of the distributor disc. The coefficient of variation, i.e., the amplitude of fluctuation increased with decreasing liquid volume rate and rotational speed. Beyond that, we could show that the formation of droplets larger than 100 μm, which are assumed to cause paint defects, is promoted by the degree of fluctuation. These findings may stimulate development of bell cups showing less paint flow pulsations.

AbstractCoalescing filtration is a mechanical process which is employed to remove dispersed aerosol particles from a gas stream. This kind of filtration is a depth‐filtration process and is widely used in process industries to remove particulate matter from exhaust gases or in compressed‐air applications to filter oil particles introduced during the compression process. Fibrous filters are often used due to low costs, high capture efficiency and low pressure drop. The droplets are first captured on the fibers, then coalesce, and eventually drain out. The performance of a filter medium is judged based on its capture efficiency and pressure‐drop characteristics. Estimating these parameters without setting up experimental investigations of each filter medium would be beneficial for choosing optimal filters. In the present study, numerical simulations are used to predict the behavior of a fully‐wetting fibrous filter using an Euler‐Euler formulation in ANSYS CFX. Different theoretical models to predict single fibre capture efficiencies are compared and a novel extrapolation scheme to predict the net capture of oil particles is presented. Pressure‐drop studies are carried out to find the pressure drop of a viscous fluid flowing through an array of fibers. A steady‐state multiphase simulation with the influence of gravity is set up, and the physical relevance of the results is examined.

By means of micro-process engineering, the specific process-performance performance compared to conventional apparatuses can be increased. A model for the numerical simulation of the mass transport in a liquid-liquid plug flow in a micro-capillary reactor is presented. Following the idea of the interface-tracking method, separate computational domains for both phases are arranged around an imported steady-state interface topology. Experimental investigations are carried out using a standard extraction system. Around one third of the extraction takes place during the generation of the plug.

The hydrodynamics of rising air bubbles in water filled bubble columns are examined using a transient numerical model following the Euler‐Euler method. In this particular case the bubble‐size distribution is assumed to be mono‐disperse and the influence of this assumption on the specific mass‐transfer area is discussed. Additionally, the influence of the bubble size is discussed with regard to the mass‐transfer area, the air volume‐fraction, and the axial air velocity profile. To validate the numerical model, experimental results from tomographic measurements at the Helmholtz‐Zentrum Dresden‐Rossendorf (HZDR) are used. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

AbstractLithium‐ion batteries are composed of several single cells, each consisting of conductive, impermeable electrodes made of aluminum and copper. Both are coated with a thin, porous layer on both sides (collectors) and a thin, non‐conductive and permeable layer is separating them. As the layers are stacked, the liquid enters the battery at all front edges, while the gas is trapped inside. To estimate the filling process of these batteries with the viscous suspensions containing the electrolyte, a model for the flow of a well‐wetting liquid displacing a gas in a single cell is established. This can be modeled as a stack of three porous layers with heterogeneous characteristics (cf. figure 2). The porous structure of the electrode coatings is approximated as a packed bed of spheres. Considering the small ratio of layer thickness to particle diameter, the influence of the wall effect onto the relevant forces has to be taken into account. These models according to the hydrodynamics of this multi‐phase flow are implemented into the commercial CFD‐software Ansys CFX. Derived from the numerical results, a 1D description is developed to specify the whole filling process. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)