Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle’s mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on “scattering fingerprints” of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures – the intermediate scattering function and dynamic structure factor – and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and X-ray scattering scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

Modelling the Energy Spectra of Radio Relics

Radio relics are diffuse synchrotron sources that illuminate shock waves in the intracluster medium. In recent years, radio telescopes have provided detailed observations about relics. Consequently, cosmological simulations of radio relics need to provide a similar amount of detail. In this methodological work, we include information on adiabatic compression and expansion, which have been neglected in the past in the modelling of relics. In a cosmological simulation of a merging galaxy cluster, we follow the energy spectra of shock accelerated cosmic-ray electrons using Lagrangian tracer particles. On board of each tracer particle, we compute the temporal evolution of the energy spectrum under the influence of synchrotron radiation, inverse Compton scattering, and adiabatic compression and expansion. Exploratory tests show that the total radio power and, hence, the integrated radio spectrum are not sensitive to the adiabatic processes. This is attributed to small changes in the compression ratio over time.

Oscillatory active microrheology of active suspensions

Using the method of Brownian dynamics, we investigate the dynamic properties of a 2d suspension of active disks at high Péclet numbers using active microrheology. In our simulations the tracer particle is driven either by a constant or an oscillatory external force. In the first case, we find that the mobility of the tracer initially appreciably decreases with the external force and then becomes approximately constant for larger forces. For an oscillatory driving force we find that the dynamic mobility shows a quite complex behavior—it displays a highly nonlinear behavior on both the amplitude and frequency of the driving force. In the range of forces studied, we do not observe a linear regime. This result is important because it reveals that a phenomenological description of tracer motion in active media in terms of a simple linear stochastic equation even with a memory-mobility kernel is not appropriate, in the general case.

Aerial tracer particle distribution system for surface image velocimetry

A novel aerial tracer particle distribution system has been developed. This system is mounted on an Unmanned Aerial Vehicle (UAV) and flown upstream from where surface velocimetry measurements are conducted. This enables surface velocimetry techniques to be applied in rivers and channels lacking sufficient natural tracer particles or surface features. Lack of tracers is a common problem during low flows, in lowland rivers, or in artificial channels. This is particularly problematic for analysis conducted using Particle Image Velocimetry (PIV) techniques where dense tracer particles are required. Techniques for colouring tracer particles with biodegradable dye have also been developed, along with methods for extracting them from Red Green Blue (RGB) imagery in the Hue Saturation Value (HSV) colour space. The use of coloured tracer particles enables flow measurements in situations where sunglint, surface waves, moving shadows, or dappled lighting on riverbeds can interfere with and corrupt results using surface velocimetry techniques. These developments further expand the situations where surface velocimetry can be applied, as well as improving the accuracy of the results.

Direct velocity measurements in high-temperature non-ideal vapor flows

Direct velocity measurements in a non-ideal expanding flow of a high temperature organic vapor were performed for the first time using the laser Doppler velocimetry technique. To this purpose, a novel seeding system for insemination of high-temperature vapors was specifically conceived, designed, and implemented. Comparisons with indirectly measured velocity, namely inferred from pressure and temperature measurements, are also provided. Nozzle flows of hexamethyldisiloxane (MM, C$$_6$$ 6 H$$_{18}$$ 18 OSi$$_2$$ 2 ) at temperature up to $$220\,^\circ \mathrm {C}$$ 220 ∘ C and pressure up to 10 bar were taken as representative of non-ideal compressible-fluid flows. The relative high temperature, high pressure and the need of avoiding contamination pose strong constraints on the choice of both seeding system design and tracer particle, which is solid. A liquid suspension of tracer particles in hexamethyldisiloxane is injected through an atomizing nozzle in a high-temperature settling chamber ahead of the test section. The spray droplets evaporate, while the particles are entrained in the flow to be traced. Three different test cases are presented: a subsonic compressible nozzle flow with a large uniform region at Mach number 0.7, a high velocity gradient supersonic flow at Mach number 1.4 and a near-zero velocity gradient flow at Mach number 1.7. Temperature, pressure and direct velocity measurements are performed to characterize the flow. Measured velocity is compared with both computational fluid dynamics (CFD) calculations and velocity computed from pressure and temperature measurements. In both cases, the thermodynamic model applied was a state-of-the-art Helmoltz energy equation of state. A maximum velocity deviation of 6.6% was found for both CFD simulations and computed velocity. Graphical abstract

Optimization of the Tracer Particle Addition Method for PIV Flowmeters

When a PIV flowmeter is used to measure a large flow of natural gas, the flow field fluctuation and particle distribution have a significant influence on the measurement accuracy and the particle injection mode plays a key role in the flow field fluctuation and particle distribution. To improve the measurement accuracy of PIV flowmeters, the method of filling tracer particles in single pipes, multiple pipes, and L pipes of a natural gas DN100 pipeline under high-pressure working conditions was compared and analyzed through numerical calculation and testing. The results show that the disturbance distance of filling particles in L pipes was the shortest, but the particle distribution area was small, whereas the flow metering error was large. By shortening the intersection distance between the L tube injection flow field and the main flow field, the problem that the particles failed to fill the test area was effectively solved, and the peak turbulence intensity at the intersection of the flow field decreased from 13.4% to 8%. Furthermore, the optimized structure was used to measure a flow of 100–600 m3/h with different flow rates. The relative error between the flowmeter and the ultrasonic flowmeter was approximately 2%, and the metering deviation was significantly improved.

DNS of a turbulent boundary layer using inflow conditions derived from 4D-PTV data

Unsteady, 3D particle tracking velocimetry (PTV) data are applied as an inlet boundary condition in a direct numerical simulation (DNS). The considered flow case is a zero pressure gradient (ZPG) turbulent boundary layer (TBL) flow over a flat plate. The study investigates the agreement between the experimentally measured flow field and its simulated counterpart with a hybrid 3D inlet region. The DNS field inherits a diminishing contribution from the experimental field within the 3D inlet region, after which it is free to spatially evolve. Since the measurement does not necessarily provide a spectrally complete description of the turbulent field, the spectral recovery of the flow field is analyzed as the TBL evolves. The study summarizes the pre-processing methodology used to bring the experimental data into a form usable by the DNS as well as the numerical method used for simulation. Spectral and mean flow analysis of the DNS results show that turbulent structures with a characteristic length on the order of one average tracer particle nearest neighbor radius $${\bar{r}}_{\text {NN}}$$ r ¯ NN or greater are well reproduced and stay correlated to the experimental field downstream of the hybrid inlet. For turbulent scales smaller than $${\bar{r}}_{\text {NN}}$$ r ¯ NN , where experimental data are sparse, a relatively quick redevelopment of previously unresolved turbulent energy is seen. The results of the study indicate applicability of the approach to future DNS studies in which specific upstream or far field boundary conditions (BCs) are required and may provide the utility of decreasing high initialization costs associated with conventional inlet BCs. Graphic abstract

Approximate Bayesian framework for 3D reconstruction in a volumetric PIV/PTV measurement

Non-invasive flow velocity measurement techniques like volumetric Particle Image Velocimetry (PIV) (Elsinga et al., 2006; Adrian and Westerweel, 2011) and Particle Tracking Velocimetry (PTV) (Maas, Gruen and Papantoniou, 1993) use multi-camera projections of tracer particle motion to resolve three-dimensional flow structures. A key step in the measurement chain involves reconstructing the 3D intensity field (PIV) or particle positions (PTV) given the projected images and known camera correspondence. Due to limited number of camera-views the projected particle images are non-unique making the inverse problem of volumetric reconstruction underdetermined. Moreover, higher particle concentration (>0.05 ppp) increases erroneous reconstructions or “ghost” particles and decreases reconstruction accuracy. Current reconstruction methods either use voxel-based representation for intensity reconstruction (e.g. MART (Elsinga et al., 2006)) or a particle-based approach (e.g. IPR (Wieneke, 2013)) for 3D position estimation. The former method is computationally intensive and has a lesser positional accuracy due to stretched shape of the reconstructed particle along the line of sight. The latter compromises triangulation accuracy (Maas, Gruen and Papantoniou, 1993) due to overlapping particle images for higher particle concentrations. Thus, each method has its own challenges and the error in 3D reconstruction significantly affects the accuracy of the velocity measurement. Though, other methods like maximum-a-posteriori (MAP) estimation have been previously developed (Levitan and Herman, 1987; Bouman and Sauer, 1996) for computed Tomography data, it has not been explored for PIV/ PTV 3D reconstruction. Here, we use a MAP estimation framework to model and solve the inverse problem. The cost function is optimized using a stochastic gradient ascent (SGA) algorithm. Such an optimization can converge to a better local maximum and also use smaller image patches for efficient iterations.

Main results of the first Lagrangian Particle Tracking Challenge

This work presents the main results of the first Lagrangian Particle Tracking challenge, conducted within the framework of the European Union’s Horizon 2020 project HOMER (Holistic Optical Metrology for Aero-Elastic Research), grant agreement number 769237. The challenge, jointly organised by the research groups of DLR, ONERA and TU Delft, considered a synthetic experiment reproducing the wall-bounded flow in the wake of a cylinder which was simulated by LES. The participants received the calibration images and sets of particle images acquired by four virtual cameras, and were asked to produce as output the particles positions, velocities and accelerations (when possible) at a specific time instant. Four different image acquisition strategies were addressed, namely two-pulse (TP), four-pulse (FP) and time-resolved (TR) acquisitions, each with varying tracer particle concentrations (or number of particles per pixel, ppp). The participants’ outputs were analysed in terms of percentages of correctly reconstructed particles, missed particles, ghost particles, correct tracks and wrong tracks, as well as in terms of position, velocity and acceleration errors, along with their distributions. The analysis of the results showed that the best-performing algorithms allow for a correct reconstruction of more than 99% of the tracer particles with positional errors below 0.1 pixels even at ppp values exceeding 0.15, whereas other algorithms are more prone to the presence of ghost particles already for ppp < 0.1. While the velocity errors remained contained within a small percentage of the bulk velocity, acceleration errors as large as 50% of the actual acceleration magnitude were retrieved.