Geppert, Anne K. Geppert

Palmetshofer P., Wurst J., Geppert A.K., Schulte K., Cossali G.E., Weigand B.

Steigerwald J., Ibach M., Geppert A.K., Weigand B.

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number Mu=texp/tθ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter β, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For Mu>10, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For Mu

Schubert S., Steigerwald J., Geppert A.K., Weigand B., Lamanna G.

Abstract This work presents a systematic experimental study of droplet impact onto a wet substrate. Four different silicone oils are used, covering a range of Reynolds number between $$116< \text{Re} <1106$$ 116 < Re < 1106 at two different initial wall film heights. The objective is to characterize the temporal and radial evolution of the velocity field within the crown crater by means of micro-PIV. Our findings show that the velocity field has the structure of an axisymmetric stagnation point flow with decaying strength a(t). The latter exhibits an exponential decay and can be explained in terms of the exponential decay of the pressure force exerted by the impacting droplet onto the wall film. In this context, the commonly accepted functional dependence $$a(t) \propto t^{-1}$$ a ( t ) ∝ t - 1 represents only the first-order Taylor approximation of the exponential decay and has therefore only a limited temporal validity. The analysis also corroborates the existence of an inertial regime concerning the velocity field for $${\text{Re}} > 270$$ Re > 270 . This is not observed at lower Re numbers due to the increased pressure losses caused by the extensional (normal) strain during the radial spreading of the lamella. To validate these findings a holistic approach is chosen, which combines numerical results, analytical solutions and experimental data from literature. In particular, by using the continuity equation, it is shown that the experimental decay of the wall film height can be reconstructed from the velocity measurements. Consilience of results from different approaches provides a robust validation of the micro-PIV data obtained in this work. Graphical abstract

Palmetshofer P., Geppert A.K., Steigerwald J., Arcos Marz T., Weigand B.

AbstractWe experimentally observe a new phenomenon, the formation of a toroidal region of lower film thickness in the center of the lamella formed during high Weber number water droplet impacts onto smooth heated walls. This region forms around the air bubble, which is entrapped during the initial impact phase at the impact center. Our study encompasses a variation of the droplet size, impact velocity, surface wettability and temperature. We show how this phenomenon can be explained considering a two-step process involving thermocapillary convection in two separate regions: The temperature gradient along the surface of the entrapped air bubble caused by heat conduction induces flow that pumps warmer liquid to the lamella-ambient interface due to the Marangoni effect. The non-uniform temperature distribution along it then causes fluid acceleration in the radial direction, depleting the fluid volume around the bubble in a self-amplifying manner. We use direct numerical simulations of a stagnant liquid film with an enclosed bubble at the wall to confirm this theory.

Geppert A.K., Stober J.L., Steigerwald J., Schulte K., Tonini S., Lamanna G.

Single droplet impacts onto thin wall-films are a common phenomenon in many applications. For sufficiently high impact velocities, the droplet impact process consists of three phases, i.e., initial contact stage, droplet deformation with radial momentum transfer inducing an upward rising lamella, and crown propagation. Here, we present the results of a combined numerical and experimental study focusing on the early dynamics of the impact process. Specifically, the effects of the initial droplet shape, wall-film thickness, and contact line motion are analyzed. Prior to impact, an oblate spheroidal droplet shape was observed. Using direct numerical simulation, we show that the droplet shape affects the impact dynamics only during the first two phases, as it is one of the key parameter influencing the correct prediction of the impact zone. The contact line propagation is described by a square-root-time dependence R¯CL=ατ for both, dry and wetted surfaces. On dry surfaces, the advancement of the contact line is determined by the rolling motion of the truncated droplet. On wetted surfaces, the value of the α-parameter is controlled by two concurrent effects, namely, rolling motion and wall-film inertia. For impact onto thin films, the rolling motion prevails. With increasing wall-film height, the droplet penetrates into the soft substrates and wall-film inertia becomes the controlling factor. These insights into the early impact dynamics on wetted surface are important for the formulation of a unified modeling approach.

Lamanna G., Geppert A., Bernard R., Weigand B.

An unsteady analytical solution is proposed to predict the spreading rate of the crown generated by an impacting droplet onto wetted walls. The modelling strategy is based on the direct integration of the boundary layer correction into the potential flow solution that leads to the well-established square-root time dependence. The original potential flow has the structure of an unsteady, stagnation point flow with decaying strength. For initial strengths of the potential flow $a_0 \geqslant 100\ {\rm s}^{-1}$, we find that a self-similar solution can also be obtained for the boundary layer in the variables $\left (r \sqrt {a(t)/(\nu t)}, z \sqrt {a(t)/(\nu t)} \right )$. The self-similarity of the solution enables a straightforward estimation of momentum losses during the spreading of the liquid layer along the wall. The proposed modelling approach yields an excellent agreement with experiments during the entire spreading phase. Moreover, it enables a smooth transition from the inertia-driven to the shear-controlled regime of crown propagation. In general, the analysis shows that momentum losses arising from viscous effects cannot be neglected during a significant portion of crown propagation, particularly for thin wall films.

Ren W., Foltyn P., Geppert A., Weigand B.

We study the vertical impact of a droplet onto a cubic pillar of comparable size placed on a flat surface, by means of numerical simulations and experiments. Strikingly, during the impact a large volume of air is trapped around the pillar side faces. Impingement upon different positions of the pillar top surface strongly influences the size and the position of the entrapped air. By comparing the droplet morphological changes during the impact from both computations and experiments, we show that the direct numerical simulations, based on the Volume of Fluid method, provide additional and new insight into the droplet dynamics. We elucidate, with the computational results, the three-dimensional air entrapment process as well as the evolution of the entrapped air into bubbles.

Liu Y., Geppert A., Chu X., Heine B., Weigand B.

Medical inhalers have been used for the treatment of a wide range of respiratory diseases including COVID-19. In this study, we investigate the annular liquid jet breakup with a coaxial supersonic gas jet using large eddy simulations. This contributes to a further understanding and improvement of medical inhaler designs. The liquid is sucked in by the low pressure as a result of the high velocity gas jet and breaks up due to the interaction with the gas jet. This type of spray nozzle configuration is commonly used in medical inhalers. Two different gas nozzle diameters are studied. The simulated liquid structure is compared with preliminary, qualitative experimental results. The gas jet pressure and radial velocity of the liquid are found to be coupled and the interaction between them plays an important role in formation of the liquid structure. The effect of gas nozzle diameter on flow rate, mean radius of the liquid, and mean radial velocity, as well as its oscillation behavior has been investigated. The power development of dominate frequencies of averaged radial liquid velocity along the flow direction is shown. The growth of the instabilities can be observed from these results.

Geppert A., Bernard R., Weigand B., Lamanna G.

Drop impact onto wetted surfaces is of relevance to any spray coating application since the maximum spreading diameter and the residual film thickness of the applied liquid droplets affect the efficient distribution of the coating materials. In this paper, we propose a modification to existing models for crown propagation during single drop impact onto a wall-film based on the stagnation-point flow solution of Hiemenz. This offers two main advantages: a simple estimation of the film thickness decay rate, induced by the impulse transfer from impacting droplet to resting wall-film. Besides, the self-similarity of Hiemenz’s solution allows a straightforward estimation of the momentum losses during radial liquid spreading along the wall. The incorporation of these estimations into existing inviscid models provides an excellent agreement with experiments over the entire crown elevation phase. Additionally, the effect of fluid viscosity and initial film thickness on the momentum transfer from droplet to wall-film is highlighted.

Terzis A., Kirsch M., Vaikuntanathan V., Geppert A., Lamanna G., Weigand B.

The rapid implementation of Selective-Catalytic-Reduction (SCR) technologies into light passenger and commercial vehicles, led to the omission of fundamental research creating several reliability issues that are largely related to the research field of droplet dynamics. In this study, the splashing behaviour of an AdBlue droplet impacting onto thin urea-water solution films is experimentally investigated over a range of impact parameters. In particular, the crown-type splashing threshold, the number of fingers and the characteristics of the ejected secondary droplets are evaluated for various drop impact velocities, wall-film thicknesses and urea concentrations in the liquid film. The results show that impact parameters that are able to enhance the energy dissipation in the wall-film, e.g. film thickness and viscosity, influence negatively the intensity of splashing. On the other hand, as the droplet kinetic energy increases or the wall-film thickness decreases, more energy is available to intensify the splashing outcome, and consequently, the upward ejected secondary droplet volume. The obtained trends are correlated in simple empirical expressions providing a remarkable industrial design tool, and they are also compared to the state-of-the-art literature of single- and binary-droplet/wall-film interactions aiming to draw generalised theories and paradigms that will support the connection between SCR applications and academic research.

Geppert A., Terzis A., Lamanna G., Marengo M., Weigand B.

The present paper investigates experimentally the impact dynamics of crown-type splashing for miscible two- and one-component droplet wall–film interactions over a range of Weber numbers and dimensionless film thicknesses. The splashing outcome is parametrised in terms of a set of quantifiable parameters, such as crown height, top and base diameter, wall inclination, number of fingers, and secondary droplet properties. The results show that the outcome of a splashing event is not affected by the choice of similar or dissimilar fluids, provided the dimensionless film thickness is larger than 0.1. Below this threshold, distinctive features of two-component interactions appear, such as hole formation and crown bottom breakdown. The observation of different crown shapes (e.g. V-shaped, cylindrical, and truncated-cone) confirms that vorticity production induces changes in the crown wall inclination, thus affecting the evolution of the crown height and top diameter. The evolution of the crown base diameter, instead, is mainly dependent on the relative importance of liquid inertia and viscous losses in the wall-film. The maximum number of liquid fingers decreases with increasing wall, film thickness, due to the enhanced attenuation of the effect of surface properties on the fingering process. The formation of secondary droplets is also affected by changes in the crown wall inclination. In particular, for truncated-cone shapes the occurrence of crown rim contraction induces a large scatter in the secondary droplet properties. Consequently, empirical models for the maximum number and mean diameter of the secondary droplets are derived for V-shaped crowns, as observed for the hexadecane-Hyspin interactions.

Geppert A., Chatzianagnostou D., Meister C., Gomaa H., Lamanna G., Weigand B.

Li Z., Wang G., Zheng E., Wang L., Wang T., Xu J.

Flores Jazmín O., Rodriguez J., Martinez Villafañe J.F., Morales Davila R., Guarneros J., Nájera-Bastida A.

The study analyzes the splash dynamics of liquid steel jets impacting solid surfaces, using a physical model with scaled-down water experiments. Two turbulence inhibitor designs are compared, focusing on droplet formation and distribution. The interaction of the jet with the inhibitors influences droplet generation and dispersion, impacting the safety and quality of the continuous casting process. Key parameters such as the Weber number and surface tension are identified as factors affecting the stability of liquid films. Finally, similarities between splash dynamics in water and steel are highlighted.

Cieniek L., Kopia A., Kowalski K., Moskalewicz T.

This study investigates the structural and catalytic properties of pure and Sr-doped LaCoO3 and LaFeO3 thin films for potential use as resistive gas sensors. Thin films were deposited via pulsed laser deposition (PLD) and characterized using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), atomic force microscopy (AFM), nanoindentation, and scratch tests. XRD analysis confirmed the formation of the desired perovskite phases without secondary phases. XPS revealed the presence of La3+, Co3+/Co4+, Fe3+/Fe4+, and Sr2+ oxidation states. SEM and AFM imaging showed compact, nanostructured surfaces with varying morphologies (shape and size of surface irregularities) depending on the composition. Sr doping led to surface refinement and increased nanohardness and adhesion. Transmission electron microscopy (TEM) analysis confirmed the columnar growth of nanocrystalline films. Sr-doped LaCoO3 demonstrated enhanced sensitivity and stability in the presence of NO2 gas compared to pure LaCoO3, as evidenced by electrical resistivity measurements within 230 ÷ 440 °C. At the same time, it was found that Sr doping stabilizes the catalytic activity of LaFeO3 (in the range of 300 ÷ 350 °C), although its behavior in the presence of NO2 differs from that of LaCo(Sr)O3—especially in terms of response and recovery times. These findings highlight the potential of Sr-doped LaCoO3 and LaFeO3 thin films for NO2 sensing applications.

Palmetshofer P., Wurst J., Geppert A.K., Schulte K., Cossali G.E., Weigand B.

Singh M., Basu S., Samanta D.

Droplet impact on liquid films is a ubiquitous phenomenon in nature and many industrial applications. The present study highlights the impact dynamics of viscoelastic droplets on thin films of water and the same viscoelastic fluid as the droplet. In this experimental study, we have highlighted the variations in the impact dynamics that arise due to the non-Newtonian effects. The ejection of secondary droplets from the crown rim normally observed in the case of Newtonian droplet impacts on water films is suppressed, in the case of non-Newtonian droplet impacts on water films. Due to the fluid elasticity, the Rayleigh–Plateau instability-induced ejection of secondary droplets from the crown rim is inhibited. Long-lasting slender liquid filaments resembling beads-on-a-string structures are observed in the case of viscoelastic droplet impact on water films. However, when the drop and film are of the same viscoelastic fluid, such filaments are not observed during the crown formation stage. Subsequently, we have characterized the geometrical features of the crown and the regime maps of various outcomes of the droplet impact dynamics. It is observed that the elasticity of the liquid suppresses the crown growth and secondary droplet formation. The dependence of the impact dynamics on Weber number (We), polymer concentration in terms of elasticity number (El), Bond number (Bo), and film thickness (h*) are also highlighted in the form of regime maps. It is observed that secondary droplet ejection does not take place on an increase in Bond number and film thickness for both water and viscoelastic films.

Ding H., Chai X., Song X., Yang Y., Wen C.

Droplet impacting on the film has been an important research topic, which is relevant to many important industries and is of high utilization value. The droplet impacting process shows excellent mass and heat transfer capability, whereas the liquid film is often in a flowing state, the morphological deformation and energy conversion of successive droplets impacting a moving liquid film were investigated. A three-dimensional volume of fluid model coupled with level-set function was established to investigate the single and successive droplet impact on the moving film. The asymmetry dynamic and energy dissipation and in the morphological evolution of the simultaneous single and successive droplet impacting processes under different droplet Weber numbers Wed and film Reynolds numbers Ref were thoroughly investigated. With smaller Wed and larger Ref, the liquid sheet downstream of the crown is more suppressed and the asymmetry of the crown is more significant. When Ref is constant, the dimensionless radius of the crown is related to the Wed0.2 and also to the power of dimensionless time, with the exponents differing between the upstream and downstream. The relationship of energy dissipation with dimensionless number was discussed, in which the kinetic energy Ek reduction accounts for a major part of the dissipation even though the surface energy Es increases due to the formation of the crown. Additionally, the upstream liquid sheets merging of the inner and outer crowns due to successive droplets continuous impacting on the moving film were also observed. With larger Ref and lower impingement frequency, the merging of the upstream liquid sheets is earlier.

Palmetshofer P., Weigand B.

While droplet impacts on micrometric cuboids or cylinders have been studied frequently, the effects of other structure shapes remain less understood. Here, we study water and isopropanol droplet impacts onto microstructured surfaces with surface features shaped as pyramids, ramps, and staggered cubes while varying the inherent surface wettability between superhydrophilicity and hydrophobicity. The surface structures feature characteristic sizes between 20 and 100 μm while the impact Weber numbers of the impacting droplets range between 90 and 1200. We show how the surface structures can affect the droplet impact morphologies asymmetrically. Crown splashing is increased in directions on ramps on the diagonals where fluid can flow “up the ramps,” while pyramids and staggered cubes show more classical behavior. Additionally, the wetting shapes are reported using a total internal reflection view. While the maximum spreading diameters for cases in which a receding motion is observed are still well predicted by existing correlations, the structures can affect the shape of the spread region significantly. Furthermore, the structures can lead to heterogeneous dewetting on pyramids and ramps. Finally, air entrapment characteristics during the droplet impacts are compared and it is found that for ramps, air is mostly entrapped behind the tops of the ramps, while in pyramids gaps in air entrapments are seen in regions where splashing is observed.

Wang J., Cao Y., Guo R., Zhao N., Zhu C., Wu Y.

The flow and heat transfer of the oblique impact of a droplet on a stationary liquid film with various dimensionless thicknesses (01.0–0.5) are investigated experimentally and numerically. A superhydrophobic guideway is used to create the oblique impact of a droplet, which causes subsequent asymmetric crown structure and splashing. The thermal level set method is employed to capture the deformation and heat transfer of warm droplets' oblique impact on a cold liquid film. A parameter study of the effect of Weber number, oblique angle, and liquid film thickness on geometrical characteristics and wall heat flux is carried out. The results show that in the downstream direction, during the crown rising period, the radius is independent of the normal Weber number but increases for a larger tangential Weber number and a thinner liquid film. The maximum downstream crown height increases with an increase in the Weber number and exhibits a non-monotonic trend with the liquid film thickness. The heat transfer rate between the liquid film and surface decreases with larger oblique angles and thicker liquid films while having a poor dependence on the Weber number. In addition, the critical oblique angles for prompting splashing at different liquid film thicknesses are presented. Finally, modified thermodynamics models and splashing thresholds for the liquid film are developed to further enhance the understanding of aircraft icing.

Dutta S.K., Mandal D.K.

An emulsion drop's impact on inclined meshes is studied. The drop is observed to penetrate and spread along the mesh. The penetration reduces with a rise in inclination for a height and becomes limited at the highest angle for all heights. Capillary resistance outshines inertia, making the drop penetrate less and flow along the mesh. The maximum spread rises. The spread is compared with three existing models applicable to flat surfaces. One compares well for lower inclinations, whereas the other for higher ones. The study brings out the penetration limitation for an emulsion drop's impact on inclined meshes.

Hamid M.O., Kunwar A.

Abstract This study presents an Eulerian-Lagrangian framework for the numerical analysis of spray dynamics, with a focus on droplet movement, spray-wall interactions, and the effects of varying injection parameters associated with port fuel injection (PFI) system. A grid-independent criterion is introduced to optimize mesh analysis for accurate predictions of fuel penetration length. The size distribution of secondary droplets is described using a probability density function, and statistical optimization is subsequently implemented to estimate their mean size. This probabilistic approach enhances the Lagrangian wall film (LWF) model, leading to accurate predictions of the Sauter mean diameter (SMD) at a given radial width ( $$R_\text{{w}}$$ R w ), with results closely matching experimental data. For $$8.0 ~\text {mm} \le R_\text{{w}} \le 24.0 ~\text {mm}$$ 8.0 mm ≤ R w ≤ 24.0 mm , the maximum SMD of 21.67 $$\mu$$ μ m corresponds to $$R_\text{{w}} = 14.0, \text {mm}$$ R w = 14.0 , mm , while the smallest SMD of 12.68 $$\mu$$ μ m is computed for a radial position of $$R_\text{{w}} = 24.0 ~\text {mm}$$ R w = 24.0 mm . The numerical investigation quantifies the role of spray-wall interactions in determining the trajectory of fuel distribution, particularly in the formation of wall films and the relative spatio-temporal diesel concentration (F/A) %. The study explores aspects such as droplet size variations, heat transfer during evaporation, and film behavior under different injection pressures, providing insights into the multiphysical characteristics of spray-wall systems. Near the impingement site ( $$2.0 ~\text {mm} \le R_\text{{w}} \le 4.0 ~\text {mm}$$ 2.0 mm ≤ R w ≤ 4.0 mm ), the plume height ( $$H_\text{{w}}$$ H w ) slightly decreases with an increase in injection pressure. While the CFD methodology in this current work has been primarily developed for automotive engineering sector (PFI engines), it also has potential applications in areas such as additive manufacturing, hydropower engineering, climate science, and environmental engineering.

Yang G., Xu R., Tian Y., Guo S., Wu J., Chu X.

Apell N., Tropea C., Roisman I.V., Hussong J.

Yang Z., Jin Z., Yang Z.

In the present study, we experimentally investigated the oblique impinging process of an ice particle on a water film. A parameter study of the impact velocity, impact angle, and water film thickness was carefully carried out. The results showed that three impact categories occurred, namely uprising liquid sheet, crown with a notch, and complete crown. The uprising liquid sheet only occurred in the case when the dimensionless water film thickness was 0.1, which appeared to be independent of the impact velocity and the impact angle. The crown with a notch only occurred in the case when the impact velocity was 23.0 m/s. The left tilt angles of uprising liquid sheet, crown with a notch, and complete crown all increased first and then decreased with the dimensionless time. Among the three experimental parameters investigated in the present study, the dimensionless water film thickness had the most significant effect on the evolutions of the left tilt angles. The dimensionless spreading lengths in x- and y-direction all increased with the increase in dimensionless water film thickness. In addition, the correlations of dimensionless spreading lengths in x- and y-direction were proposed. In addition, the lifetime of complete crown generally increased with the increase in the impact velocity and the dimensionless water film thickness. Within the scope of the present study, the dimensionless maximum height of uprising liquid sheet generally ranged from 3.0 to 3.5. When the impact angle was 30.0°, the dimensionless maximum height of the crown with a notch increased with the increasing dimensionless water film thickness. The present work not only provides a new insight into the study of the ice crystal icing but also offers effective support for the development of efficient anti/de-icing methods.

Zhang X., Liu Y., Wang W., Yang G., Chu X.

We investigated the effects of bubble count, flow direction, and Eötvös number on deformable bubbles in turbulent channel flow. For a given shear Reynolds number Re = 180 and fixed bubble volume fractions (1.263% and 2.525%), we conducted a series of direct numerical simulations using a coupled level-set and volume-of-fluid solver to evaluate their impact on bubble volume fraction distribution, velocity fields, and turbulence characteristics. Each aspect was studied based on the microscopic equations of two-phase flow, and the accuracy of the modeling terms used in current Reynolds-averaged Navier–Stokes equation (RANS) models was assessed. The influence on the anisotropic state was analyzed using the Lumley triangle, and the anisotropy of Reynolds stresses was captured through the exact balance equations. The results indicate that in upward flow, bubbles tend to accumulate near the wall, with smaller Eötvös numbers leading to closer proximity to the wall and greater attenuation of the liquid-phase velocity. This distribution enhances energy dissipation and turbulence isotropy. In downward flow, bubbles cluster in the channel center, generating additional pseudo-turbulence and attenuating energy in the buffer layer. Moreover, the interfacial transfer of turbulent energy, as currently modeled in RANS, is found to be inadequate for upward flows.

Steigerwald J., Ibach M., Geppert A.K., Weigand B.

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number Mu=texp/tθ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter β, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For Mu>10, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For Mu

Steigerwald J., Ibach M., Geppert A.K., Weigand B.

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number Mu=texp/tθ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter β, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For Mu>10, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For Mu

Xia L., Yang Z., Chen F., Liu T., Tian Y., Zhang D.

The solid fraction of the substrate is expected to influence the bouncing behavior of an impinging droplet, thereby affecting spreading and contact time. Hence, it should be possible to alter the velocity and pressure distribution of impacting droplet, and also affect the impact velocity for droplet penetration right upon impact. We systematically investigate the impact dynamics of water droplets on pillared hydrophobic surfaces with different solid fractions using phase-field simulations. The velocity and pressure distributions of impacting droplets on pillared hydrophobic surfaces with varied Weber numbers and solid fractions are studied. In addition, the influences of the solid fraction on the bouncing behaviors of the impinging droplet, such as the maximum wetting spreading, the maximum impacting depth, and the contact time, are also investigated to further understand the impact event. We show that a three-peak pressure profile appears on the top of the pillared hydrophobic surface during droplet impact by varying the solid fraction of the surface. The first peak is generated by the impact of the droplet itself, while the second peak arises from the droplet recoil impact associated with the dynamic properties of the jet. Moreover, we identify a hitherto unknown third pressure peak related to the hydrodynamic singularity that emerges due to the convergence of the fluid during the droplet rebound. This solid fraction-dependent impacting behavior reveals the intricate interplay between droplet dynamics and the underlying surface characteristics, providing valuable insights into the design and optimization of micro/nano structured hydrophobic surfaces for various applications.

Potyka J., Schulte K., Planchette C.

Equally sized droplets made of the same liquid are known to either bounce, coalesce, or separate under collision. Comparable outcomes are observed for immiscible liquids with bouncing, encapsulation instead of coalescence, and separation with two or more daughter droplets. While the transitions between these regimes have been described, the liquid distribution arising from separation remains poorly studied, especially in the case of head-on collisions, for which it cannot be predicted. This distribution can be of three types: either two encapsulated droplets form (single reflex separation), or a single encapsulated droplet plus a droplet made solely of the encapsulating liquid emerge, the latter being found either on the impact side (reflexive separation) or opposite to it (crossing separation). In this paper, a large number of experimental and simulation data covering collisions with partial and total wetting conditions and Weber and Reynolds numbers in the ranges of 2–720 and 66–1100, respectively, is analyzed. The conditions leading to the three liquid distributions are identified and described based on the decomposition of the collision in two phases: (i) radial extension of the compound droplet into a lamella and (ii) its relaxation into an elongated cylindrical droplet. In accordance with these two phases, two dimensionless parameters, Λ=ρi/ρoWei−1/2 and N=νo/νi σo/σio, are derived, which are built on the collision parameters and liquid properties of the encapsulated inner droplet (i) and the outer droplet (o) only. The combination of these two parameters predicts the type of liquid distribution in very good agreement with both experimental and numerical results.

Rezaie M.R., Norouzi M., Kayhani M.H., Taghavi S.M., Kim M., Kim K.C.

AbstractThis study investigates the effect of fluid elasticity on axisymmetric droplets colliding with pre-existing liquid films, using both numerical and experimental approaches. The numerical simulations involve solving the incompressible flow momentum equations with viscoelastic constitutive laws using the finite volume method and the volume of fluid (VOF) technique to track the liquid’s free surface. Here, the Oldroyd-B model is used as the constitutive equation for the viscoelastic phase. Experiments are also performed for dilute viscoelastic solutions with 0.005% and 0.01% (w/w) polyacrylamide in 80:20 glycerin/water solutions, in order to ensure the validity of the numerical solution and to investigate the elasticity effect. The formation and temporal evolution of the crown parameters are quantified by considering the flow parameters, including the fluid’s elasticity. The results indicate that the axisymmetric numerical solutions reasonably agree with the experimental observations. Generally, the fluid’s elasticity can enlarge the crown dimension at different thicknesses of the fluid film. Moreover, at intermediate values of the Weissenberg number, the extensional force in the crown wall can control the crown propagation. Furthermore, the results reveal that the effects of the Weber number and the viscosity ratio on this problem are more significant at higher values of the Weissenberg number.

Gultekin A., Erkan N., Colak U., Suzuki S.

The investigation of the underlying physical processes involved in the impact of droplets has various practical applications in engineering and science. In this research, the spreading velocities within droplet impingement on a sapphire glass were investigated for a wide range of Weber numbers using particle image velocimetry (PIV), which involves tracking the movement of polymeric fluorescent particles (6 µm) within the droplet. The experiments were carried out at room temperature, and the droplets had impact velocities ranging from 0.41 to 2.37 m/s, which corresponded to Weber numbers of 5–183. The results showed that the radial velocity was generally linear over a wide range of spreading radius but the velocity at the exterior radial positions became nonlinear over time due to the influence of capillary and viscous forces. This nonlinearity was more pronounced for lower Weber numbers because the viscosity effects in the droplet were more significant compared to the inertia forces. As the Weber number decreases, the spreading and receding of the droplets are completed faster, leading to different trends in the radial velocity profiles.

Schlottke A., Ibach M., Steigerwald J., Weigand B.

Water ingestion in gas turbines is used in industrial applications to improve the thermal efficiency by cooling the air before and throughout compression. However, this also leads to interactions between the liquid droplets and the compressor parts, which cause a faster degradation of the structure. The current work addresses the numerical investigation of the atomization process at the trailing edge of a compressor blade as there have only been experimental investigations in literature considering the ambient conditions in a gas turbine compressor. Direct numerical simulations (DNS) are carried out using the multiphase flow solver Free Surface 3D (FS3D). Therefore, a numerical setup has been developed to model the trailing edge as a thin plate corresponding to experiments performed at ITLR [22]. Four different cases have been performed to take the experimentally observed atomization processes into account. Additionally, the dependence of the simulation results on the grid resolution and with it the limits to reproduce the experimental findings has been investigated in a grid study. The results show that the developed numerical setup works well and the different atomization processes are reproduced qualitatively, with best results for very high grid resolutions. Furthermore, an investigation of the available compilers on the new Hawk supercomputer platform reveals that a performance gain up to 36% for the amount of completed calculation cycles per hour is possible compared to the standard compiler setup used as standard practice over the previous years. Optimization options as well as improvement during link time lead to a significant speed-up while simulation results remain unaffected.

Foltyn P., Ribeiro D., Silva A., Lamanna G., Weigand B.

The influence of surface roughness, especially regularly patterned micro-structures on the physical outcomes of droplet impacts, is far from fully understood. In order to get a deeper insight into the physics of the impact phenomena, a systematic experimental study of the morphology on regularly patterned micro-structured surfaces has been carried out. The used structures with different dimensions were grooves and pillars with a square cross section. With the help of plasma activation and plasma polymerization processes, the surface wettability was modified independently from the surface structure and material. Two different test fluids were used, namely, distilled water and isopropanol, impacting with various impact energies onto the patterned surface samples. For a better characterization of the impact process, high-speed images from three different perspectives have been acquired synchronously. Due to the transparent surface material, the bottom perspective using a total internal reflection configuration was able to visualize air entrapment inside the surface structure. To the authors' knowledge, such images are not available in the literature, yet. The outcomes have been qualitatively investigated, summarized, and compared. A dependency of the outcomes on the impact energy, the surface wettability, and the structure dimensions could be clearly shown. In general, increasing impact energy will promote the tendency of splashing. However, roughness features cannot only trigger splashing, but can also inhibit it, for example, crown splashing. Moreover, reproducible arrangements of air entrapment inside the structure could be found, which was addressed by the authors as “cookie” and “button” due to their appearance.

Zhou X., Wang H., Zhang Q., Tian Y., Deng Q., Zhu X., Ding Y., Chen R., Liao Q.

Functional surfaces with controllable droplet spreading and breakup dynamics have received widespread attention in self-cleaning, spraying cooling, 3D printing, etc. The arrangement of a microstructure is of great value for the design of functional surfaces. Here, we numerically investigated the droplet impact dynamics on the sparse hydrophobic pillar surface with OpenFOAM. We investigated the effect of Weber number, impact locations, and pillar spacing. Outcomes are most strongly influenced by impact locations, pillar pitch, Weber number, and eight spreading patterns were registered, including circle, square, cross-shaped, Chinese knot, octopus, ellipse, dumbbell, and hexagram. Furthermore, a set of theoretical models were developed for the spreading pattern transition to predict the critical Weber number for different droplet spreading patterns. The breakup dynamics of droplets strongly depend on the spreading patterns and the impact location, which can emit secondary droplets in specific directions. The cross pattern significantly reduces the threshold for secondary droplet generation. The results obtained some essential characteristics for droplet impinging sparse hydrophobic pillar surface, which could provide valuable insights into functional surface design, fluidic-based systems and applications.

Stumpf B., Hussong J., Roisman I.V.

The impact of a drop onto a liquid film is relevant for many natural phenomena and industrial applications such as spray painting, inkjet printing, agricultural sprays, or spray cooling. In particular, the height of liquid remaining on the substrate after impact is of special interest for painting and coating but also for applications involving heat transfer from the wall. While much progress has been made in explaining the hydrodynamics of drop impact onto a liquid film of the same liquid, the physics of drop impact onto a wall film with different material properties is still not well understood. In this study, drop impact onto a very thin liquid film of another liquid is investigated. The thickness of the film remaining on a substrate after drop impact is measured using a chromatic-confocal line sensor. It is interesting that the residual film thickness does not depend on the initial thickness of the wall film, but strongly depends on its viscosity. A theoretical model for the flow in the drop and wall film is developed which accounts for the development of viscous boundary layers in both liquids. The theoretical predictions agree well with the experimental data.

Zhang X., Du A., Luo Y., Lv C., Zhang Y.S., Yan S., Wu Y., Qiu J., He Y., Wang L., Li Q.

Controlling morphology of liquids on solid surfaces plays an important role in both fundamental research and practical applications. We found that, the shape of the liquid after contact between a droplet and a surface could be tuned by designing the hydrophilic micropillar arrays forming this surface. Such a wetting behavior is a result of imbibition in the micropillars, leading to specific final spreading distance and pattern of the droplet. During the spreading, the morphology of the droplet is controlled by both the arrangement and shape of the micropillars. The experimental results indicated that the surface energy barriers caused by the micropillar edges was a key factor accounting for the anisotropic spreading of the liquid. Moreover, the shape of the meniscus at the front location of the spreading liquid was rebuilt based on computational simulation, which agreed well with the experimental data. Interesting, the time-dependence of the displacement of the liquid transport at the edges was found to be different from that of a wicking film. Theoretical models were accordingly proposed to reveal the shape formation of liquids on such micropillar-structured surfaces.

Jamali S., McKinley G.H.

The concept of a Deborah number is widely used in the study of viscoelastic materials to represent the ratio of a material relaxation time to the time scale of observation and to demarcate transitions between predominantly viscous or elastic material responses. However, this construct does not help quantify the importance of long transients and nonmonotonic stress jumps that are often observed in more complex time-varying systems. Many of these nonintuitive effects are lumped collectively under the term thixotropy; however, no proper nouns are associated with the key phenomena observed in such materials. Thixotropy arises from the ability of a complex structured fluid to remember its prior deformation history, so it is natural to name the dimensionless group representing such behavior with respect to the ability to remember. In Greek mythology, Mnemosyne was the mother of the nine Muses and the goddess of memory. We, thus, propose the definition of a Mnemosyne number as the dimensionless product of the thixotropic time scale and the imposed rate of deformation. The Mnemosyne number is, thus, a measure of the flow strength compared to the thixotropic time scale. Since long transient responses are endemic to thixotropic materials, one also needs to consider the duration of flow. The relevant dimensionless measure of this duration can be represented in terms of a mutation number, which compares the time scale of experiment/observation to the thixotropic time scale. Collating the mutation number and the Mnemosyne number, we can construct a general two-dimensional map that helps understand thixotropic behavior. We quantify these ideas using several of the simplest canonical thixotropic models available in the literature.

Stumpf B., Ruesch J.H., Roisman I.V., Tropea C., Hussong J.

Droplets within droplets occur in numerous situations in which two immiscible liquids interact, for instance, binary drop collisions or when a drop of one liquid impacts onto a film of a different liquid, ejecting secondary droplets containing both liquids. In the present study, an imaging technique for determining the volume fraction of each liquid component in such two-component droplets is introduced, in which multiple images of the same droplet at different times are used. The processing of these images is supported by a machine learning algorithm, which is taught using synthetically generated images and validated on droplets with known mixture fractions placed in an acoustic levitator. The application of the technique is demonstrated by measuring the volume fraction in splashed secondary droplets following the impact of a drop of one liquid onto a film of a different liquid.

Sahu G., Khandekar S., Muralidhar K.

• Thermal management of single nozzle spray for a high-power LED module is explored. • Maximum experimental heat transfer coefficient ∼12 kW/m 2 K is obtained for Re of 12000. • LED substrate temperature is maintained well below safe limits for Re = 8000 and above. • Spatial and temporal thermal fields over the LED module is computationally estimated. • The experimental results are complemented with 3D numerical heat transfer simulations. The cooling demand for a nominal 300 W power LEDs is around 200 W/cm 2 at the chip-scale, and the junction temperature must be maintained below 120 °C for reliable operation. Special thermal management packaging is required to maintain LEDs below this reliability temperature limit. The present study investigates the thermal characteristics of single-nozzle spray cooling over a high-power LED module. The detailed thermal characterization within the LED assembly is explored using both, experimental and numerical approaches. The LED substrate temperature is experimentally obtained for various input power supplies, water flow rate, inlet water temperature, nozzle height, and offset from the LED center. Heat transfer coefficient at two radial locations ( R = 0 mm and 12.5 mm) is estimated to evaluate the heat removal capacity of the spray for these operating conditions. Numerical study is performed to visualize temperature and heat flux distribution within the LED module, and to investigate the appearance of thermally critical locations. Junction temperature is the critical parameter for thermal characterization of the LED module, and is numerically investigated for various operating conditions. The junction temperature is maintained below 95 °C at the nominal electrical input power for a Re ≥ 8,000 using the proposed spray cooling design. The present study establishes the efficacy of spray cooling for high-power LED modules, even when the supply power exceeds 112% of the nominal power range.

Eisenbarth C., Haase W., Blandini L., Sobek W.

Extreme heat and heavy rainfall events with severe inundations have a significant impact on urban architecture, resulting in considerable personal injuries and material damage. Nowadays, the proportion of façade surface areas in urban areas with tall buildings is substantially larger than the proportion of horizontal roof areas or ground surface areas. A high leverage effect on climate resilience and sustainability of buildings and cities can therefore be attributed to the building envelopes. Whereas the majority of existing façades are designed to provide only minor qualities at a district or urban level, research at the Institute for Lightweight Structures and Conceptual Design (ILEK) at the University of Stuttgart focuses on development of a new type of hydroactive lightweight façades incorporating climate change mitigation and adaptation strategies. A textile- and film-based façade element called HydroSKIN is capable of providing a retention surface on the envelope of the building. With a minimal amount of embedded mass, energy, and CO2 emissions, the façade add-on element is suitable for both new and existing buildings. HydroSKIN combines rainwater harvesting (RWH) and run-off water reduction by retaining the precipitation water that strikes the façade with a time-delayed evaporative cooling (EC) of the building and its environment.

Song Y., Wang Q., Ying Y., You Z., Wang S., Chun J., Ma X., Wen R.

Dynamic interactions of the droplet impact on a solid surface are essential to many emerging applications, such as electronics cooling, ink-jet printing, water harvesting/collection, anti-frosting/icing, and microfluidic and biomedical device applications. Despite extensive studies on the kinematic features of the droplet impact on a surface over the last two decades, the spreading characteristics of the droplet impact on a solid hydrophilic surface with ultra-low contact angle hysteresis are unclear. This paper clarifies the specific role of the contact angle and contact angle hysteresis at each stage of the droplet impact and spreading process. The spreading characteristics of the droplet impact on an ultra-slippery hydrophilic solid surface are systematically compared with those on plain hydrophilic, hydroxylated hydrophilic, and plain hydrophobic surfaces. The results reveal that the maximum spreading factor (βmax) of impacting droplets is mainly dependent on the contact angle and We. βmax increases with the increase in We and the decrease in the contact angle. Low contact angle hysteresis can decrease the time required to reach the maximum spreading diameter and the time interval during which the maximum spreading diameter is maintained when the contact angles are similar. Moreover, the effect of the surface inclination angle on the spreading and slipping dynamics of impacting droplets is investigated. With the increase in the inclination angle and We, the gliding distance of the impacting droplet becomes longer. Ultra-low contact angle hysteresis enables an impacting droplet to slip continuously on the ultra-slippery hydrophilic surface without being pinned to the surface. The findings of this work not only show the important role of the surface wettability in droplet spreading characteristics but also present a pathway to controlling the dynamic interactions of impacting droplets with ultra-slippery hydrophilic surfaces.