Impact of a suspension drop onto a hot substrate: diminution of splash and prevention of film boiling.

In the present study, the effect of graphite lubricant additives on the dynamics of a single drop impact onto a heated surface has been investigated in the nucleate boiling and thermal atomization regimes. In the nucleate boiling regime the drop impact is accompanied by the nucleation and expansion of multiple vapor bubbles. The drop residence time at the substrate is determined by the time of its mass loss due to splash and evaporation. At higher temperatures, above the Leidenfrost point, impact may lead to drop rebound. In this experimental and theoretical study the effect of additives on the outcome of drop impact, in particular, the addition of solid graphite particles, is investigated. The residence time of the drop has been measured for various initial drop temperatures and suspension concentrations. The addition of the particles leads to some increase of the residence time, while its dependence on the substrate temperature follows the scaling relation obtained in the theory. Moreover, the presence of the particles in the drop leads to suppression of splash and a significant increase of the drop rebound temperature, which is often associated with the Leidenfrost point. These effects are caused by the properties of the deposited layer, and pinning of the contact line of the entire drop and of each vapor bubble, preventing bubble coalescence and drop rebound. The phenomena are also explained by a significant increase of the liquid viscosity caused by the evaporation of the bulk liquid at high wall temperatures.

A method for scattering angle calibration in the rainbow region using a droplet stream.

Accurate quantification of scattering angle versus detector pixel strongly determines the measurement accuracy of rainbow refractometry. This is an emerging measurement technique operating at backscatter angles and characterizing droplets or complex droplets in terms of size and refractive index. A novel method for calibration of the rainbow scattering angle using a monodisperse droplet stream is introduced and the achievable accuracy is estimated. The assumption of a linear pixel-to-angle relation is derived, and a calibration procedure is proposed based on global fit of calibration data to the theoretically known rainbow signal. The accuracy of this method was examined by simulations and experiments, where the uncertainties of a priori parameters of droplets were also considered and validated using shadowgraphy as a ground truth. The results confirm the feasibility of this method with a maximum absolute error of 0.032°and 3.9E-5°/pixel respectively for the intercept and slope of the linear relationship. These values translate into maximum uncertainties in diameter and refractive index of approx. 0.67% and 2.8 × 10-4.

Planar rainbow refractometry.

Rainbow refractometry has been used in the past to measure size and refractive index of spherical particles, typically droplets in a spray. In the present study, conventional optical configurations for point measurements or line measurements have been extended to allow also the particle position in a plane to be determined, and hence, the designation planar rainbow refractometry. However, this extension introduces challenges in accurately calibrating the 2D scattering angles with the image coordinates. This challenge has been met using a novel calibration method, employing a monodispersed droplet stream traversed through the measurement plane. Experiments confirm achievable horizontal and vertical position accuracies of 0.42 mm and 0.36 mm, respectively, and a refractive index uncertainty of 2×10-4.

Geometric optics applied to drops passing through a focused Gaussian beam.

The present study examines the scattered light intensity from a drop passing through a Gaussian beam of a diameter comparable to or smaller than the drop. This is the situation encountered when using the time-shift technique, an optical technique used to characterize drops and aerosols according to the size and the velocity. In simulating the signals received by such an instrument, the computational effort involved when using, for instance, the Generalized Lorenz-Mie Theory or vector ray-tracing, is immense and hardly practical for use in instrument design and/or optimization. In this study theoretical expressions based on geometric optics are derived as an alternative, and they are shown to adequately capture the main features of the time-shift signals. These solutions require little computational effort and can be effectively used to explore the dependencies of the signals on various input factors, thus allowing further instrument development. On the other hand, these relations are also of general interest in the field of light scattering from drops and aerosols.

Ice nucleation in high alternating electric fields: Effect of electric field strength and frequency.

Icing is a severe problem for many technical systems such as aircraft or systems for high-voltage power transmission and distribution. Ice nucleation in water droplets is affected by several influencing factors like impurities or the liquid temperature, which have been widely investigated. However, although an electric field affects nucleation, this influence has been far less investigated and is still not completely understood. The present work is focused on the influence of high alternating electric fields on ice nucleation in sessile water droplets, which is examined for a systematic variation of the electric field frequency and strength. All experiments used to determine the influence of a single parameter like the electric field strength or frequency are performed with the same set of droplets to ensure well-defined conditions and a high repeatability of the procedure. For each parameter variation a large number of nucleation events is observed and analyzed. Droplet survival curves and the nucleation site density are used to analyze the experiments and to determine the influence of the electric field on ice nucleation. Especially for high electric field strengths, a significant influence on nucleation is observed. Some droplets freeze earlier, which leads to a higher median nucleation temperature. On the other hand, the lowest temperature required to freeze all droplets is almost constant compared to the reference case without an electric field. It is shown that not all droplets are affected by the electric field in the same way, but the influence of the electric field on ice nucleation is rather of singular nature. In addition, the frequency of the applied electric field has an impact on the nucleation behavior. The present experimental data quantitatively demonstrate the effect of an electric field on ice nucleation and improves our understanding of heterogeneous nucleation of supercooled water subjected to high alternating electric fields.

Simulation of the optical caustics associated with the primary rainbow for oblate spheroidal drops illuminated by a Gaussian beam.

A vector ray-tracing model (VRT) has been developed to compute the optical caustics associated with the primary rainbow for an oblate spheroidal water drop illuminated by a Gaussian beam. By comparing the optical caustic structures (in terms of limiting rainbow and hyperbolic umbilic fringes) for a water drop with a Gaussian beam (GB) illumination with that for the same drop, but with parallel beam (PB) illumination, the influence of the Gaussian beam on the optical caustics is investigated. For a water drop with GB illumination and different drop/beam ratios (i.e., the ratio between the drop equatorial radius and the Gaussian beam waist), the location of cusp points and the curvature of the limiting rainbow fringe are also studied. We anticipate that these results not only confirm the approach to compute optical caustics for oblate spheroidal drops illuminated by a shaped beam, but may also lead to a new method for measuring the aspect ratio of spheroidal drops.

Parametric Sequential Method for MRI-Based Wall Shear Stress Quantification.

Wall shear stress (WSS) has been suggested as a potential biomarker in various cardiovascular diseases and it can be estimated from phase-contrast Magnetic Resonance Imaging (PC-MRI) velocity measurements. We present a parametric sequential method for MRI-based WSS quantification consisting of a geometry identification and a subsequent approximation of the velocity field. This work focuses on its validation, investigating well controlled high-resolution in vitro measurements of turbulent stationary flows and physiological pulsatile flows in phantoms. Initial tests for in vivo 2D PC-MRI data of the ascending aorta of three volunteers demonstrate basic applicability of the method to in vivo.

Ice nucleation forced by transient electric fields.

Icing affects many technical systems, like aircraft or high-voltage power transmission and distribution in cold regions. Ice accretion is often initiated by ice nucleation in sessile supercooled water droplets and is influenced by several influencing factors, of which the impact of electric fields on ice nucleation is still not completely understood. Especially the influence of transient electric fields is rarely or not at all investigated, even though it is of great interest, e.g., for high-voltage transmission lines or for the food industry. In the present study the impact of transient electric fields on ice nucleation in supercooled sessile water droplets is experimentally investigated under well-defined conditions. A set of droplets is cooled down to a certain temperature and is subsequently exposed to electric fields generated from standard lightning or standard switching impulse voltages, which are commonly used for testing of high-voltage equipment. The nucleation behavior of individual droplets is captured using a high-speed camera and the effect of the transient electric field on ice nucleation is analyzed by considering both the singular and the stochastic nature of nucleation. While the singular nature of nucleation is referred to during analysis of the relative number of droplets remaining liquid long times after the impulse voltage, its stochastic nature is accounted for in the analysis of the temporal evolution of the relative number of frozen droplets. It is shown that low electric field strengths (E[over ̂]≤6.52kV/cm) only have a negligible impact on ice nucleation, independent of the supercooling. In contrast, high electric field strengths (E[over ̂]≥9.78kV/cm) promote significantly ice nucleation. It is also shown that depending on the supercooling, the freezing delay of the different droplets in the ensemble may vary over several magnitudes for the same conditions. It is demonstrated that the electric field appears to indirectly affect the nucleation rate by generating droplet oscillations, finally promoting ice nucleation. The experiments clearly demonstrate the possibility to actively force ice nucleation by applying transient electric fields. These results improve the understanding of ice accretion on high-voltage insulators and may also lend insight into freezing processes in food industry. We expect that these results will be a valuable contribution in formulating and/or validating new nucleation models.

Behavior of charged and uncharged drops in high alternating tangential electric fields.

The interaction of drops and electric fields occurs in many applications like electrowetting, electrospinning, atomization, but also causes unwanted effects like the aging of high-voltage composite insulators. Water drops are influenced by electric fields due to the polar properties of the water molecules. The behavior of the drops depends on several parameters like the orientation and strength of the electric field, drop volume, and frequency of the applied field. In addition, electric charges can influence the behavior of drops significantly. However, the impact of electric charges, including the interaction with the drop as well as the electric field strength, is far from being well understood. In this work, the impact of electric charges on the behavior of single sessile drops is investigated experimentally under well-defined conditions. The effects of the drop volume, electric field strength, field frequency, and electric charge of the drop are studied. The necessary amount of charge to change the behavior of drops, depending on the applied electric field and drop volume, is determined and different drop behavior regimes are identified. Depending on the boundary conditions, the drop oscillates with the same or double the frequency of the applied voltage. The different regimes are investigated for the first three oscillation modes. The obtained results will help to improve the understanding and to manipulate the behavior of uncharged and charged drops in strong electric fields.

Impact of electric charge and motion of water drops on the inception field strength of partial discharges.

Strong electric fields may deform drops and induce their oscillation or motion on the substrate. Moreover, they can initiate partial discharges (PDs) because of the enhancement of the electric field in the vicinity of the three-phase contact lines. The partial discharges affect the drop spreading which can result in unusual drop shapes. In addition, the partial discharges can also deteriorate the surface properties of the substrate, e.g., of high-voltage composite insulators. In this study the occurrence of partial discharges due to stationary or oscillating sessile drops under the influence of an alternating electric field is investigated using a generic insulator model under well-defined conditions. Drops of a yield stress fluid (a gelatin-water mixture) are used to determine the PD inception field strength for stationary drop shapes. The influence of the volume as well as the distance between the individual drops for two drop configurations on the PD inception threshold is determined. The inception field strength of the partial discharges is measured for various drop volumes, drop charges, as well as for different resonance modes of drop oscillations. Besides the electrical measurement, the location of the partial discharges is optically determined by a UV camera. The detailed knowledge of the influencing factors of the partial discharges improves the understanding of the drop behavior under the impact of strong electric fields.

Simulation of light scattering from a colloidal droplet using a polarized Monte Carlo method: application to the time-shift technique.

This study is devoted to the development and application of a Monte Carlo ray-tracing model to simulate light scattering when a colloid suspension droplet passes through a highly focused Gaussian laser sheet. Within this study, a colloidal suspension droplet refers to a spherical droplet containing multiple spherical inclusions. Such scattering scenarios arise when using the time-shift measurement technique for particle sizing. The incident laser sheet is treated as a large number of polarized light rays: the Stokes vector of each light ray is tracked, achieved by multiplication of the rotation matrix and the Mueller matrix after each scattering event. For the Monte Carlo simulation of light scattering, a very important issue is to generate the deflection angle and azimuthal angle after each scattering event. The scattering from embedded inclusions is computed using the Lorenz-Mie theory and by employing the rejection sampling technique to update the new propagation direction. Multi-reflection and refraction within the droplet is accounted for, as is total reflection at the drop interface. For this, the Mueller matrix formulation is invoked at the drop surface to update the Stokes vector. To validate this simulation code, the scattering diagram from a nanoparticle is computed with this Monte Carlo method and compared with the scattering diagram computed with the Lorenz-Mie theory, the agreement is excellent. This Monte Carlo code is then applied to simulate signals arising from a time-shift device, when a colloid suspension droplet passes through a focused polarized laser sheet, with the objective of measuring the concentration of colloidal particles in the droplet. Measurements verify the ability of the code to properly simulate this light scattering scenario.

MR-based wall shear stress measurements in fully developed turbulent flow using the Clauser plot method.

In arterial blood flow wall shear stress (WSS) quantifies the frictional force that flowing blood exerts on a vessel wall. WSS can be directly estimated from phase-contrast (PC) MR velocity measurements and has been suggested as a biomarker in cardio-vascular diseases. We present and investigate the application of the Clauser plot method for estimating WSS in fully developed turbulent stationary flow using PC velocity measurements. The Clauser plot method estimates WSS from the logarithmic region of boundary layer in fully developed turbulent stationary flow. The Clauser plot method was evaluated using 2D PC-MR phantom measurements at 3 T for different in-plane resolutions at various Reynolds numbers. WSS values derived from the Clauser plot were compared to results from Laser Doppler Velocimetry (LDV) measurements and theoretical results calculated using the friction factor formula for smooth pipe flow. For all Reynolds numbers, WSS values derived from the Clauser plot were in good agreement with results from LDV measurements and values using the friction factor formula (relative deviations ∼5%). Furthermore, Clauser plot derived results were almost independent of spatial resolution, in contrast to WSS results obtained with our in-house software tool for MR-based WSS quantification showing relative deviations of more than 100%. In fully developed turbulent flow, the Clauser plot method provides highly consistent WSS independent of the underlying spatial resolution. Therefore, it renders a valuable approach for MR-based WSS estimates in controllable flow settings. Although its direct in vivo applicability is severely limited because of the different flow character, it may serve as helpful approach for validation of MR-based WSS quantification algorithms prior to their clinical application.

Model for computing optical caustic partitions for the primary rainbow from tilted spheriodal drops.

A model is proposed to compute the salient optical caustic partitions occurring in the primary rainbow for oblate spheroidal drops. By computing the boundary limits of outgoing rays, the optical caustic structures (termed rainbow and hyperbolic umbilic fringes) for tilted drops are calculated and compared with those for aligned (untilted) drops. The curvature of the rainbow fringe and the shifts of cusp caustics are discussed as well. The observed properties of the caustics can potentially be used for drop measurements. The model could also be applied to compute the optical caustics for drops with arbitrary shape, arbitrary orientation, and shaped beam illumination.

Spontaneous rise in open rectangular channels under gravity.

Fluid movement in microfluidic devices, porous media, and textured surfaces involves coupled flows over the faces and corners of the media. Spontaneous wetting of simple grooved surfaces provides a model system to probe these flows. This numerical study investigates the spontaneous rise of a liquid in an array of open rectangular channels under gravity, using the Volume-of-Fluid method with adaptive mesh refinement. The rise is characterized by the meniscus height at the channel center, outer face and the interior and exterior corners. At lower contact angles and higher channel aspect ratios, the statics and dynamics of the rise in the channel center show little deviation with the classical model for capillarity, which ignores the existence of corners. For contact angles smaller than 45°, rivulets are formed in the interior corners and a cusp at the exterior corner. The rivulets at long times obey the one-third power law in time, with a weak dependence on the geometry. The cusp behaviour at the exterior corner transforms into a smooth meniscus when the capillary force is higher in the channel, even for contact angles smaller than 45°. The width of the outer face does not influence the capillary rise inside the channel, and the channel size does not influence the rise on the outer face.

Ice Layer Spreading along a Solid Substrate during Solidification of Supercooled Water: Experiments and Modeling.

The thermal influence of a solid wall on the solidification of a sessile supercooled water drop is experimentally investigated. The velocity of the initial ice layer propagating along the solid substrate prior to dendritic solidification is determined from videos captured using a high-speed video system. Experiments are performed for varying substrate materials and liquid supercooling. In contrast to recent studies at moderate supercooling, in the case of metallic substrates only a weak influence of the substrate's thermal properties on the ice layer velocity is observed. Using the analytical solution of the two-phase Stefan problem, a semiempirical model for the ice layer velocity is developed. The experimental data are well described for all supercooling levels in the entire diffusion limited solidification regime. For higher supercooling, the model overestimates the freezing velocity due to kinetic effects during molecular attachment at the solid-liquid interface, which are not accounted for in the model. The experimental findings of the present work offer a new perspective on the design of anti-icing systems.

Transient effects in ice nucleation of a water drop impacting onto a cold substrate.

The impact of water drops onto a solid surface at subfreezing temperatures has been experimentally studied. Drop nucleation has been observed using a high-speed video system. The statistics of nucleation allows the estimation of the average number of nucleation sites per unit area of the wetted part of the substrate. We have discovered that the nucleation rate in the impacting drop is not constant. The observed significant increase of the nucleation rate at small times after impact t<50 ms can be explained by the generation of nanobubbles at early times of drop impact. These bubbles serve as additional nucleation sites and enhance the nucleation rate.

Reynolds number influence on the formation of vortical structures on a pitching flat plate.

The impact of chord-based Reynolds number on the formation of leading-edge vortices (LEVs) on unsteady pitching flat plates is investigated. The influence of secondary flow structures on the shear layer feeding the LEV and the subsequent topological change at the leading edge as the result of viscous processes are demonstrated. Time-resolved velocity fields are measured using particle image velocimetry simultaneously in two fields of view to correlate local and global flow phenomena in order to identify unsteady boundary-layer separation and the subsequent flow structures. Finally, the Reynolds number is identified as a parameter that is responsible for the transition in mechanisms leading to LEV detachment from an aerofoil, as it determines the viscous response of the boundary layer in the vortex-wall interaction.

Modeling photon transport in turbid media for measuring colloidal concentration in drops using the time-shift technique.

Colloidal drops-suspensions, dispersions, emulsions-are widespread in the process industry but are difficult to characterize by size, velocity, and concentration of particulate matter in the drop. The present study investigates the use of the time-shift (TS) technique for such measurements. Numerically, a model based on ray tracing is developed, incorporating interactions with randomly placed monodispersed scattering centers within the spherical drop. The model creates a random walk propagation trajectory, known from radiative transfer problems. The model approximates Mie scattering from each internal particle with a Gaussian distribution. Experiments are performed using a conventional TS instrument, first with water as a reference and for validation, and then with different concentrations of a milk/water emulsion. Comparison of the modeled and received signals exhibits very good agreement, confirming the possibility of measuring the colloidal concentration in drops using the TS technique.

Solidification of supercooled water in the vicinity of a solid wall.

An experimental approach utilizing a Hele-Shaw cell for the investigation of the solidification of a supercooled liquid in contact with a solid wall is presented. The setup is based on an idea presented by Marín et al. [A. G. Marín et al., Phys. Rev. Lett. 113, 054301 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.054301], who investigated the planar freezing of a sessile drop without supercooling. This apparatus overcomes optical distortions present when observing the freezing of sessile drops, arising due to reflections and refraction of light on the drop surface. The facility is used to investigate the freezing process of water drops, supercooled down to -20^{∘}C, and to qualitatively demonstrate that the growth behavior is uninfluenced by the use of the Hele-Shaw cell. Different features during freezing, which are known for sessile water drops, are also observed with the Hele-Shaw cell. The growth morphology within the first phase of solidification is categorized according to the initial drop supercooling. Furthermore, freezing velocities within this phase are related to data available in the literature for the growth of single ice dendrites.