Traveling wave packets are key coherent features contributing to the dynamics of several advective flows. This work introduces the Hilbert proper orthogonal decomposition (HPOD) to distill these features from flow field data, leveraging their mathematical representation as modulated traveling waves. The HPOD is a complex-valued extension of the proper orthogonal decomposition, where the Hilbert transform of the dataset is used to compute its analytic signal. Two versions of the technique are explored and compared: the conventional HPOD, computing the analytic signal in time, and a novel space-only HPOD, computing it along the advection direction. The HPOD is shown to extract wave packets with amplitude and frequency modulation in time and space. Its broadband nature offers an alternative to spectrally pure decompositions when instantaneous, local wave characteristics are important. The space-only version, leveraging space/time equivalence in traveling waves to swap temporal operations with spatial ones, is proven mathematically equivalent to its conventional counterpart. The two HPOD versions are characterized and validated on three datasets ordered by complexity: a two-dimensional (2D) direct numerical simulation of a laminar bluff-body wake with periodic vortex shedding; a large eddy simulation of a turbulent jet with intermittent, highly modulated wave packets; and a 2D particle image velocimetry experiment of a turbulent jet with measurement errors and no temporal resolution. In advecting flows, both HPOD versions deliver practically identical complex-valued advecting wave-packet structures, characterized by spatiotemporal amplification and decay, wave modulation, and intermittency phenomena in turbulent flow cases, such as in turbulent jets. The space-only variant allows the extraction of these structures from temporally under-resolved datasets, typical of snapshot particle image velocimetry.

An inverse problem (IP) approach is proposed to simultaneously determine the three-dimensional position and size of bubbles or droplets in a two phase flow from a single camera image. The method is based on interferometric particle imaging (IPI) and defocusing particle tracking velocimetry. A forward model (FM) is introduced that integrates a scattering model based on geometrical optics and the Lorentz–Mie theory, along with a wave propagation model based on the Huygens–Fresnel principle to simulate particle images. Using bounding boxes from object detection methods as initialization, the InvP approach approximates the position and diameter of each particle in the image. The performance of the presented approach is evaluated on the grounds of the data achieved by Sax et al (2025 Phys. Rev. Appl. 24 044083): As key aspects it achieves sub-pixel accuracy in position determination, exceeds the diameter accuracy of current FFT-based benchmarks on real data and furthermore achieves sub-micrometre precision in diameter resolution, even for three-dimensionally distributed particles. The InvP approach achieves a decoupling of the diameter estimation from the out-of-plane position estimation, thus avoiding error propagation from one to the other, which significantly increases the sizing accuracy. The incorporated FM accounts for aliasing effects in the interference pattern, effectively increasing the measurable volume both closer to and further from the focal plane. This improvement qualifies the approach to measure closer to the focal plane, which in turn allows to obtain images with higher signal-to-noise ratio (SNR). The InvP approach is capable of handling significantly lower SNRs compared to commonly applied algorithms and noise levels at which detection algorithms typically fail, presenting significant potential for single optical access IPI in side- and backscatter regions where low SNR usually necessitates sophisticated data processing methods. Notably, the InvP approach is largely unaffected by particle image overlaps, addressing another major challenge in single-camera particle tracking and sizing at high source densities in a given field of view.

The present work addresses the investigation of the spatio-temporal character of dielectric barrier discharge plasma actuator arrays applied to generate virtual wall oscillations. To this end, an electro-optical diagnostics approach is introduced. Optical measurements by means of intensified charge-coupled device imaging are conducted to capture the light emission of the oscillatory gas discharges, allowing observation of the discharge characteristics of the plasma actuator array for individual phase positions within both the oscillation and plasma cycle. Through simultaneous acquisition of electrical signals of the actuator limited to the captured image domain, the entire light emission is directly linked to the ignited surface discharges. On this basis, occurring discharge structures are observed throughout the plasma cycle that can be related to the applied voltage signals. A quasi-linear correlation of the integral discharge light emission and transferred charge is determined. It is shown that the present experimental assessment allows to uncover the spatio-temporal relation of opposing discharge filaments occurring for the present plasma actuator array and forcing strategy, and (as a future scope) their influence on the resulting flow manipulation upon periodically changing forcing direction can be evaluated.

ABSTRACT Fluid‐mediated patterning techniques offer a promising avenue for the cost‐effective and scalable fabrication of structured surfaces across multiple length scales. Widespread adoption of fluid‐based approaches, however, requires an in‐depth understanding of the governing mechanisms to ensure precise control over pattern formation and dynamics toward reliable and affordable design modulation. Here, we present control strategies for creating diverse surface architectures by employing condensate water droplets as dynamic microscale templates. The temporally arrested breath figure patterning technique used here provides the opportunity for macroscale pattern organization with an elevated level of structural modification. We demonstrate systematic variation over isotropic and directional anisotropic breath figure micropatterns, leveraging control over the governing thermodynamic and photochemical phase change processes. Finely‐tuned pattern formation is achieved in an order of minutes, creating breath figures of droplets ranging in size from hundreds of nanometers to tens of microns. Potential modulated surface architectures include organized macroscale spatial arrangements of breath figure pores, through‐pore perforated membranes of discrete sizes, and elastomeric replication to transform the re‐entrant cavity designs into protruding spherical caps. This adapted breath figure patterning technique thus provides a fast, scalable, and low‐cost method for fabricating tunable surface morphologies tailored for future functionality.

We present a robust combination of methods for a Volume-of-Fluid (VoF) framework to investigate the influence of wettability on droplet impact onto grooved surfaces, with a particular focus on under-studied hydrophilic cases. The numerical method employs a three-phase PLIC interface reconstruction and utilizes the method of Sussman (2001) to model the contact line. This approach is shown to be compatible with both the balanced Continuum Surface Force (b-CSF) and Continuum Surface Stress (CSS) surface tension models. A mesh-dependent dynamic contact angle model based on Cox's theory is implemented, demonstrating improved grid convergence over standard no-slip conditions. The framework is validated extensively against analytical solutions for sessile drops and static menisci, as well as new experimental data for droplet impacts on both smooth and grooved surfaces. The simulations successfully reproduce the experimental spreading dynamics, though we also highlight significant discrepancies between commonly used dynamic contact angle models and experimental measurements, especially during the receding phase. Finally, a parameter study varying the contact angle from 10 degrees to 150 degrees reveals that spreading transversal to the grooves is almost independent of wettability. Conversely, spreading parallel to the grooves is strongly affected by wettability, behaving similarly to spreading on a smooth substrate. In accordance with theory, it is found that at contact angles of 45 degrees and below, corner flow governs the spreading inside the grooves.

Aerosol jet printing offers advantages over common inkjet methods for printed electronics, such as finer structures, layer homogeneity, and 3-D substrate printing capabilities. Our institute is developing a patented Aerosol-on-Demand (AoD) jet-printing process. Understanding the aerosol spray's droplet velocity fields is crucial for this development. We report on the use of the particle image velocimetry method to measure the droplet velocities and to demonstrate the on-demand capability of the AoD printing principle. The nature of the spray with very high velocity gradients on the one hand, and sparse droplet density in some regions on the other hand poses great challenges for PIV resulting in vector replacement rates of approximately 45%. Despite this, the measurements successfully quantified the maximum droplet velocities in excess of 3 m s-1 and demonstrated the on-demand capability, confirming a spray cessation time of approximately 50 ms.

Multicomponent droplet evaporation generates inherently three-dimensional, solutal-Marangoni flows that challenge single-camera velocimetry. We present STAR-APTV (Segmentation and Tracking Anything-based Robust Astigmatic Particle Tracking Velocimetry), a zero-shot, deep-learning-assisted, astigmatic particle tracking framework for time-resolved 3D-3C flow reconstruction with minimal optical hardware. We leverage zero-shot segmentation using SAM to detect particles in microscopic images without any task-specific labels or training. To characterize each detected particle under optical aberration, we combine shape-aware refinement using elliptic Fourier descriptors with intensity-based features within the refined mask region. We then estimate depth using an uncertainty-aware deep learning model, in which the estimated 3D trajectories are stabilized with a multi-object tracking algorithm and Kalman filter. Against a representative baseline (DefocusTracker), STAR-APTV detects up to six times more particles at high seeding density, while maintaining temporally coherent tracks, and preserving positional accuracy of particles in the presence of noise. Through synthetic validation, the proposed algorithm exhibited AEE = 0.077 px/frame and AAE = 1.45 degrees in a known analytical flow field reconstruction. Experimental validation in two droplet regimes confirms robustness in complex, refractive samples and cross-setup transfer without any task-specific training. Among these flows, in the more challenging flow with relatively dense particle seeding, the detection rate was increased by nearly 70%, with increased retention rates and extended trajectories by almost three times compared to the conventional method. These results altogether demonstrate high-fidelity, single-camera, volumetric velocimetry in refractive, densely seeded environments, extending defocusing/astigmatic PTV toward complex droplet flows.

Lagrangian defocusing particle tracking velocimetry (defocusing PTV, DPTV) measurements are performed in a thin volume above a plasma actuator array that is applied to mimic the effect of wall oscillations by inducing alternating, wall-parallel forcing in opposite directions into the air above the actuator surface for flow control purposes. The aim of the experiments is to capture the plasma-induced flow topology in otherwise quiescent air throughout the oscillation cycle within the measurement volume of 14 mm × 1 mm × 14 mm, immediately adjacent to the wall-mounted actuator. For this purpose, particle image velocimetry equipment for time-resolved measurements with one camera is used in a DPTV setup, where the out-of-plane particle coordinate is obtained through the diameter of a defocused particle image. Three-dimensional, three-component velocity and acceleration data is extracted by introducing a continuous particle tracking approach and an extended ex situ calibration procedure based on the detection of solid particles directly applied to a wall boundary, for which no prior knowledge of the flow topology or velocity data in the direct vicinity of the wall is required. A novel method for estimating measurement uncertainty in this context is introduced, and the influencing factors are discussed from an application perspective. Through the analysis of Lagrangian particle tracks, both individual flow events and statistical effects within the oscillation cycle can be evaluated. The extraction of phase-resolved flow fields with adaptable spatial resolution shows the forcing effect to be regular across different discharge zones on the plasma actuator array, indicating well-balanced voltage settings and precise manufacturing. Furthermore, the relation between the forcing-induced velocity and acceleration fields is quantitatively assessed, revealing the spatio-temporal transmission characteristics of the applied forcing. In summary, the obtained results demonstrate the applicability of DPTV measurement technique for the flow characterization above a plasma actuator array using the presented modifications.

The flow convergence method includes calculation of the proximal isovelocity surface area (PISA) and is widely used to classify mitral regurgitation (MR) with echocardiography. It constitutes a primary decision factor for determination of treatment and should therefore be a robust quantification method. However, it is known for its tendency to underestimate MR and its dependence on user expertise. The present work systematically compares different pulsatile flow profiles arising from different regurgitation orifices using transesophageal echocardiographic (TEE) probe and particle image velocimetry (PIV) as a reference in an in-vitro environment. It is found that the inter-observer variability using echocardiography is small compared to the systematic underestimation of the regurgitation volume for large orifice areas (up to 52%) where a violation of the flow convergence method assumptions occurs. From a flow perspective, a starting vortex was found as a dominant flow pattern in the regurgant jet for all orifice shapes and sizes. A series of simplified computational fluid dynamics (CFD) simulations indicate that selecting a suboptimal aliasing velocity during echocardiography measurements might be a primary source of potential underestimation in MR characterization via the PISA-based method, reaching up to 40%. In this study, it has been noted in clinical observations that physicians often select an aliasing velocity higher than necessary for optimal estimation in diagnostic procedures.

The flow within adhering droplets subjected to external shear flows has a significant influence on the stability and eventual detachment of the droplets from the surface. Most commonly, the velocity field inside adhering droplets is measured by means of particle image velocimetry (PIV), which requires a correction step for distortion caused by refraction of light at the gas-liquid interface. Current methods for distortion correction based on ray tracing are limited to low external flow velocities. However, the ray-tracing method can be extended to arbitrarily deformed droplet shapes if the instantaneous three-dimensional droplet interface is availble. In the present work, a previously introduced method for the image-based reconstruction of gas-liquid interfaces by means of deep learning is adapted to determine the instantaneous interface of adhering droplets in external shear flows. In this regard, a purposefully developed optical measurement technique based on the shadowgraphy method is employed that encodes additional three-dimensional (3D) information of the interface in the images via glare points from lateral light sources. On the basis of the images recorded in the experiments, the volumetric shape of the droplet is reconstructed by a neural network that was trained on the spatio-temporal dynamics of the gas-liquid interface from a synthetic dataset obtained by numerical simulation. The results for experiments with adhering droplets at different velocities of external flow demonstrate that the combination of the learned droplet geometry with the depth encoding through the glare points facilitates a robust and flexible reconstruction. The proposed method reconstructs the instantaneous three-dimensional interface of adhering droplets at both high resolution and spatial accuracy and thereby enables the distortion correction of PIV measurements at high external flow velocities.

Particle image (PI) overlap presents a significant challenge in single-camera particle tracking and sizing techniques such as Defocusing Particle Tracking Velocimetry (DPTV) and Interferometric Particle Imaging (IPI). In DPTV, overlap obscures PI boundaries, complicating the detection and accurate estimation of PI diameter and center position, which increases uncertainty in the reconstructed particle positions. In IPI, overlap reduces the usable area of the interference pattern, limiting the accuracy of particle size determination. This study introduces a statistical model to quantify PI overlap independently from the optical setup, source density, or PI size. The model assumes uniformly distributed, uniformly sized circular PIs and is validated against experimental data featuring non-uniform sizes and mild astigmatism (up to aspect ratios of 1.66), demonstrating strong agreement. The present study reveals that the seeding density $\mathcal{S}$ serves as a strong universal scaling parameter for PI overlap. Key overlap metrics, including the number of overlaps per PI, the fraction of overlap-free PIs, and the usable PI area are analyzed as functions of the seeding density $\mathcal{S}$. The results reveal a critical threshold at $\mathcal{S} = 0.25$, where each PI experiences, on average, one overlap. The study provides practical guidance for experimental design by linking overlap metrics to controllable parameters such as source density, defocus length, and aperture diameter. The presented models serve as lookup tools to help experimenters maintain PI overlap within acceptable limits, enabling more reliable and quantitatively robust measurements in DPTV and IPI applications.

Fiber optic measurement techniques such as Raman Distributed Temperature Sensing (DTS) are beneficial for applications in boreholes, as they provide continuous measurements over long distances with all measurement equipment outside of the borehole. Efforts have been made for at least a decade to utilize these temperature measurements for indirect velocity measurements. Active DTS measurements refer to a setup, where the fiber is embedded in a hybrid cable, which itself is heated by Joule heating. Such Active DTS processing takes advatange of known heat transfer phenomena to determine velocitiy information.When the heated cable is placed in a saturated porous medium, groundwater fluxes perpendicular to the cable's axis were quantified with low uncertainties in a controlled lab experiment [1]. Heated fiber placed in the free flow of a borehole was applied to identify active zones of groundwater flow and highly fractured zones [2]. A very similar setup of a heated fiber in a borehole was applied to measure vertical flow exploiting the heat transfer law of a cylinder in flow parallel to its axis [3]. Utilization of this heat-transfer law was shown to be difficult as a thermal boundary layer builds up in the flow direction, thus influencing the downstream sections. This effect may be modelled, but additionally, the boundary layer mixes behind every centralizer and therefore enhances the heat transfer locally. The latter cannot easily be modeled and was removed using a postprocessing filter [3]. Even though only limited quantitative comparability with reference flowmeter measurements was possible the results rendered the approach a promising strategy, since the correct order of magnitude and moreover similar trends have been identified.Inspired by the heat transfer of a cylinder in cross flow as state of the art in aerodynamics velocimetry [5], it has been demonstrated that the convective heat transfer of a heated cable in free flow can be better utilized if the cable axis is positioned perpendicular to the flow to take advantage of the heat transfer law of a cylinder in cross flow [4].The objective of our research is to build an active DTS-based free stream flowmeter to monitor pump flows in arbitrarily deep boreholes. The system shall be scalable with an arbitrary number of point measurement flowmeters, which are connected to a single glass fiber and one heating cable. At the current state of the research, the flowmeter consists of a point flowmeter, which is a helically wound, heated glass fiber. The sensitivity in the predicted measurement range was verified and the temperature distribution along the cable cross-section was investigated. Presently, the major challenge is a precise reproducible DTS temperature measurement. Therefore, water baths and a new prototype were built to achieve measurement uncertainties within the range of the water bath reference sensors (cp. [7]).[1] Simon et al. https://doi.org/10.1016/j.jhydrol.2023.129755 [2] Banks et al. https://doi.org/10.1111/gwat.12157[3] Read et al. https://doi.org/10.1002/2014WR015273[4] Rautenberg et al. https://doi.org/10.1007/s00348-023-03741-5[5] Örlü, Vinuesa, Chapter 9 Thermal Anemometry https://doi.org/10.1201/9781315371733-12 [6] Giesen et al. https://doi.org/10.3390/s120505471

This work investigates the feasibility of a post-processing-based approach for phase separation in defocusing particle tracking velocimetry for dispersed two-phase flows. The method enables the simultaneous 3D localization determination of both tracer particles and particles of the dispersed phase, using a single-camera setup. The distinction between phases is based on pattern differences in defocused particle images, which arise from distinct light scattering behaviors of tracer particles and bubbles or droplets. Convolutional neural networks, including Faster R-CNN and YOLOv4 variants, are trained to detect and classify particle images based on these pattern features. To generate large, labeled training datasets, a generative adversarial network based framework is introduced, allowing the generation of auto-labeled data that more closely reflects experiment-specific visual appearance. Evaluation across six datasets, comprising synthetic two-phase and real single- and two-phase flows, demonstrates high detection precision and classification accuracy (95-100%), even under domain shifts. The results confirm the viability of using CNNs for robust phase separation in disperse two-phase DPTV, particularly in scenarios where traditional wavelength-, size-, or ensemble correlation-based methods are impractical.

Interferometric particle imaging (IPI) enables the sizing of small transparent particles, from a few microns to several millimeters, across a large field of view, which is not feasible with typical imagingbased methods. However, current IPI setups typically require two separate optical accesses-one for coupling the illuminating laser beam into the measurement volume, and another to allow the scattered light to exit toward the camera-thereby limiting their applicability in constrained environments. This work presents a generalized IPI approach suitable across all scattering regimes-including backscatter for single-optical-access configurations-and is applicable to both droplets and bubbles. This study demonstrates how the scattering angle influences signal-to-noise ratio (SNR), measurable size range, and uncertainty. Polarization significantly affects signal quality, particularly in backscatter. Variations in light intensity with angular variations can introduce position-dependent uncertainties, and the sensitivity of the size measurement (transfer function) varies with scattering angle. Experimental validation with bubbles confirms the feasibility of backscatter IPI despite lower SNR. For droplets, the reduction in SNR is less pronounced; however, the transfer function behaves differently compared to bubbles, making both evaluation and uncertainty estimation more complex. Additional effects like glare-point splitting can add redundancy but increase complexity. Overall, this study demonstrates that IPI in backscatter is not only feasible but also a key step toward single-sided optical access, expanding the method's practical applicability of the IPI method.

The present work introduces a deep learning approach for the three-dimensional reconstruction of the spatio-temporal dynamics of the gas-liquid interface in two-phase flows on the basis of monocular images obtained via optical measurement techniques. The dynamics of liquid droplets impacting onto structured solid substrates are captured through high-speed imaging in an extended shadowgraphy setup with additional reflective glare points from lateral light sources that encode further three-dimensional information of the gas-liquid interface in the images. A neural network is learned for the physically correct reconstruction of the droplet dynamics on a labelled dataset generated by synthetic image rendering on the basis of gas-liquid interface shapes obtained from direct numerical simulation. The employment of synthetic image rendering allows for the efficient generation of training data and circumvents the introduction of errors resulting from the inherent discrepancy of the droplet shapes between experiment and simulation. The accurate reconstruction of the gas-liquid interface during droplet impingement on the basis of images obtained in the experiment demonstrates the practicality of the presented approach based on neural networks and synthetic training data generation. The introduction of glare points from lateral light sources in the experiments is shown to improve the reconstruction accuracy, which indicates that the neural network learns to leverage the additional three-dimensional information encoded in the images for a more accurate depth estimation. Furthermore, the physically reasonable reconstruction of unknown gas-liquid interface shapes indicates that the neural network learned a versatile model of the involved two-phase flow phenomena during droplet impingement.

Lagrangian defocusing particle tracking velocimetry (DPTV) measurements are conducted in a thin, wall-parallel volume above a plasma actuator array that is applied to mimic the effect of wall oscillations by inducing alternating, wall-parallel forcing in opposite directions into the air above the actuator surface. The aim of the experiments is to capture the plasma-induced flow structures in otherwise quiescent air in order to increase the understanding of different actuation parameters. For this purpose, high-speed particle image velocimetry equipment with one camera is used in a DPTV setup, where the out-of-plane particle coordinate is obtained through the diameter of a defocused particle image. On this basis, an approach for continuous particle tracking in several consecutive frames is presented, allowing to derive three component, three dimensional velocity and acceleration data. Light reflections that occur on the adjacent actuator surface give raise to particular challenges concerning the measurement uncertainty estimation as well as the calibration procedure for the evaluation of the wall-normal coordinate of tracer particles. To overcome the latter, a calibration approach is presented for which solid particles are applied to the actuator surface and their particle image diameter is captured at different camera positions in a separate measurement. The estimation of in-plane and out-of-plane displacement measurement uncertainties is conducted following a newly-developed procedure where the deviation of particle displacements from a straight track is evaluated for measurements in quasi-quiescent air. The obtained results show the suitability of DPTV measurement technique for the practical application of the characterization of flow structures above a plasma actuator array. The measurement accuracy is found to be limited due to the available illumination, which depends on the used components. The measured flow fields together with optical and electrical measurement data allow for a further analysis of the present forcing strategy. Particularly, by recording phase-resolved, three-dimensional flow velocity and acceleration fields in the vicinity of the wall, the spatio-temporal occurrence and homogeneity of the near-wall forcing effects can be analyzed in future investigations.

A new flow measuring technique is introduced to measure liquid flow velocities under harsh circumstances in environments with dirt, high pressures and elevated temperatures as in boreholes within the earth’s crust. A glass fiber embedded in a cable with heating wires measures the temperature within the heated cable with fiber-optic temperature sensing. Similar to hot-wire anemometry (HWA), the velocity dependence of convective heat transfer is exploited to measure the velocity around the cable as a cylinder in crossflow. In the first experiment, a borehole-mimicking test rig and a realistic prototype of a borehole probe were built and the flow along the borehole axis was investigated. The concept of this new measurement technique was proven, since the expected Nusselt-Reynolds characteristic of a cylinder in crossflow has been successfully measured. Furthermore, a temperature profile model across the cables cross section has been developed to account for the unexpectedly low ranges of Nusselt number. The model accuracy has been addressed with a second experiment, where a straight segment of a custom-built heated cylinder was placed in a water channel perpendicular to the flow direction. The upstream flow speed during this set of measurements was recorded using particle image velocimetry (PIV), while multiple temperature sensors in the channel, on the probe’s sheath and within the probe delivered the information for the heat transfer model.