scholarly journals Jet Dynamics Associated with Drop Impact on Micropillared Substrate

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 155
Author(s):  
Brooklyn Asai ◽  
Anayet Ullah Siddique ◽  
Hua Tan
Keyword(s):  
Time Dependence ◽  
Power Law ◽  
High Speed ◽  
Scaling Laws ◽  
Scaling Law ◽  
Droplet Impact ◽  
Dimensionless Time ◽  
Cavity Collapse ◽  
Bubble Bursting ◽  
Jet Breakup

The jetting phenomenon associated with droplet impact upon a hydrophilic micropillared substrate was analyzed in detail using a high-speed camera. Viscosities of the fluids were varied using differing concentrations of glycerol in deionized water. This paper aims to connect similarities between this form of capillary jetting and another well-known jetting phenomenon from the bubble bursting. Both experience a cavity collapse when opposing fluid fronts collide which causes a singularity at the liquid surface, thus leading to the occurrence of jetting. Following processes used to define scaling laws for bubble bursting, a similar approach was taken to derive scaling laws for the dimensionless jet height, jet radius, base height, and radius of the jet base with respect to dimensionless time for the jetting phenomenon associated with the droplet impact. The development of a top droplet before the breakup of the jet also allows the examination of a scaling law for the necking diameter. We find that with the proper scaling factors, the evolution of the jet profile can collapse into a master profile for different fluids and impact velocities. The time dependence of the necking diameter before the jet breakup follows the power law with an exponent of ~2/3. Contrastingly, for other jet parameters such as the radius and height, the power law relationship with time dependence was not found to have a clear pattern that emerged from these studies.

Generation and breakup of Worthington jets after cavity collapse. Part 2. Tip breakup of stretched jets

2010 ◽  
Vol 663 ◽  
pp. 331-346 ◽  
Author(s):  
J. M. GORDILLO ◽  
STEPHAN GEKLE
Keyword(s):  
High Speed ◽  
Local Strain ◽  
External Noise ◽  
Creeping Flow ◽  
Liquid Density ◽  
Dimensionless Time ◽  
Cavity Collapse ◽  
Flow Limit ◽  
Theoretical Predictions ◽  
High Reynolds

The capillary breakup of the high-speed Worthington jets ejected after a cavity collapse in water occurs due to the high-Reynolds-number version of the capillary end-pinching mechanism first described, in the creeping flow limit, by Stone & Leal (J. Fluid Mech., vol. 198, 1989, p. 399). Using potential flow numerical simulations and theory, we find that the resulting drop ejection process does not depend on external noise and can be described as a function of a single dimensionless parameter, WeS = ρ R30S20/σ, which expresses the ratio of the capillary time to the inverse of the local strain rate, S0. Here, ρ and σ indicate the liquid density and the interfacial tension coefficient, respectively, and R0 is the initial radius of the jet. Our physical arguments predict the dimensionless size of the drops to scale as Ddrop/R0 ~ We−1/7S and the dimensionless time to break up as TS0 ~ We2/7S. These theoretical predictions are in good agreement with the numerical results.

scholarly journals Solid-phase crystallization under continuous heating: Kinetic and microstructure scaling laws

2008 ◽  
Vol 23 (2) ◽  
pp. 418-426 ◽  
Author(s):  
J. Farjas ◽  
P. Roura
Keyword(s):  
Grain Size ◽  
Kinetic Parameters ◽  
Scaling Laws ◽  
Solid Phase ◽  
Scaling Law ◽  
Continuous Heating ◽  
Dimensionless Time ◽  
Solid Phase Crystallization ◽  
Average Grain Size ◽  
Length Scaling

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors. Concerning the kinetics, it is shown that the extended volume evolves with time according to αex = [exp(κCt′)]m+1, where t′ is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters.

On the scaling of jetting from bubble collapse at a liquid surface

2017 ◽  
Vol 822 ◽  
pp. 791-812 ◽  
Author(s):  
Sangeeth Krishnan ◽  
E. J. Hopfinger ◽  
Baburaj A. Puthenveettil
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Liquid Surface ◽  
Limited Range ◽  
Capillary Waves ◽  
Bubble Collapse ◽  
Jet Formation ◽  
Cavity Depth ◽  
Jet Breakup ◽  
Jet Velocity

We present scaling laws for the jet velocity resulting from bubble collapse at a liquid surface which bring out the effects of gravity and viscosity. The present experiments conducted in the range of Bond numbers $0.004<Bo<2.5$ and Ohnesorge numbers $0.001<Oh<0.1$ were motivated by the discrepancy between previous experimental results and numerical simulations. We show here that the actual dependence of $We$ on $Bo$ is determined by the gravity dependency of the bubble immersion (cavity) depth which has no power-law variation. The power-law variation of the jet Weber number, $We\sim 1/\sqrt{Bo}$, suggested by Ghabache et al. (Phys. Fluids, vol. 26 (12), 2014, 121701) is only a good approximation in a limited range of $Bo$ values ($0.1<Bo<1$). Viscosity enters the jet velocity scaling in two ways: (i) through damping of precursor capillary waves which merge at the bubble base and weaken the pressure impulse, and (ii) through direct viscous damping of the jet formation and dynamics. These damping processes are expressed by a dependence of the jet velocity on Ohnesorge number from which critical values of $Oh$ are obtained for capillary wave damping, the onset of jet weakening, the absence of jetting and the absence of jet breakup into droplets.

Scaling Laws for the Peak Overpressure of a Cannon Blast

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Robert A. Carson ◽  
Onkar Sahni
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Near Field ◽  
Scaling Law ◽  
Radial Distance ◽  
Polar Angle ◽  
Model Parameters ◽  
Far Field ◽  
Simulation Data ◽  
Angle Dependence

For large cannons, blast overpressure can have a detrimental effect on the crew in the near field (i.e., within a distance of 50 tube diameters or calibers from the muzzle center) as well as on the support personnel and equipment in the far field (i.e., at a distance greater than 50 calibers). Therefore, an efficient method to determine the peak overpressure due to a cannon blast is highly desired. In this study, we investigate scaling laws for the peak overpressure, due to the primary blast of a large cannon, with the aim that they can be applied as an efficient method to evaluate the peak overpressure in the far field. We explore two types of scaling laws; each type is based on a power-law model involving a prefactor and an exponent as model parameters. The two types of the power-law models differ in the way they incorporate the polar angle dependence. The first type was proposed by Fansler and Schmidt (1983, “The Prediction of Gun Muzzle Blast Properties Utilizing Scaling,” U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, Report No. ARBRL-TR-02504). They developed a muzzle-center based scaling law (MCSL) in which the polar angle dependence was incorporated through a reference length scale to define a nondimensional or scaled radial distance from the muzzle center and the model parameters were independent of the polar angle. They calibrated the parameters by employing least-squares fit to a wide range of experimental data. In this study, we recalibrated or updated the parameters for the current cannon by using the numerical simulation data for the cannon blast in the near field. Additionally, we developed a second type of scaling law in which the radial distance is defined from the blast center (in contrast to the muzzle center) and scaled using the inner tube diameter. In this model, the angular dependence is incorporated directly into the model parameters. For this model too, we calibrated the parameters by using the numerical simulation data. We observe that both the modified version of the muzzle-center based scaling law as well as the blast-center based scaling law (BCSL) show a significantly closer fit to the numerical and experimental data and achieve a similar level of accuracy. This indicates that the current form or structure of the two types of power-law based scaling models is able to fit well with the near-field data; however, the current methodology requires a calibration process for a given cannon of interest. In the future, with far field data, we plan to evaluate predictions in the far field.

scholarly journals Compound jetting from bubble bursting at an air-oil-water interface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Bingqiang Ji ◽  
Zhengyu Yang ◽  
Jie Feng
Keyword(s):  
Scaling Laws ◽  
Surface Microlayer ◽  
Size Change ◽  
Cavity Collapse ◽  
Bubble Bursting ◽  
Sea Surface Microlayer ◽  
Wide Range ◽  
Aqueous Surface ◽  
Multi Phase ◽  
Tip Radius

AbstractBursting of bubbles at a liquid surface is ubiquitous in a wide range of physical, biological, and geological phenomena, as a key source of aerosol droplets for mass transport across the interface. However, how a structurally complex interface, widely present in nature, mediates the bursting process remains largely unknown. Here, we document the bubble-bursting jet dynamics at an oil-covered aqueous surface, which typifies the sea surface microlayer as well as an oil spill on the ocean. The jet tip radius and velocity are altered with even a thin oil layer, and oily aerosol droplets are produced. We provide evidence that the coupling of oil spreading and cavity collapse dynamics results in a multi-phase jet and the follow-up droplet size change. The oil spreading influences the effective viscous damping, and scaling laws are proposed to quantify the jetting dynamics. Our study not only advances the fundamental understanding of bubble bursting dynamics, but also may shed light on the airborne transmission of organic matters in nature related to aerosol production.

Chip Flow and Scaling Laws in High Speed Metal Cutting

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Guy Sutter ◽  
Alain Molinari ◽  
Gautier List ◽  
Xuefeng Bi
Keyword(s):  
High Speed ◽  
Metal Cutting ◽  
Scaling Laws ◽  
Scaling Law ◽  
Chip Morphology ◽  
Cutting Conditions ◽  
High Speed Machining ◽  
Workpiece Material ◽  
Machined Surface ◽  
Perfectly Plastic

Chip formation in machining plays an important role in the cutting process optimisation. Chip morphology often reflects the choice of cutting conditions, the tool wear and by consequences the integrity of the machined surface and tool life. In this study, photographs of the chip morphology during high speed machining of a middle hard steel (C20 similar to AISI 1020) are taken by using a ballistic setup. From these recordings, the evolution of the chip morphology is presented and analysed in terms of cutting conditions. A simplified modeling is then proposed by considering the workpiece material as elastic perfectly plastic. The existence of a scaling law governing the chip morphology in high speed machining is demonstrated. The cutting velocity is shown to have a weak effect at high speed machining as opposed to the well known strong influence of the velocity in the range of low cutting speeds.

Towards a Universal Scaling for Broadband Turbulent Noise in Internal Flow Devices

2013 ◽  
Author(s):  
Arjen de Jong ◽  
Joachim Golliard
Keyword(s):  
High Speed ◽  
Scaling Laws ◽  
Scaling Law ◽  
Power Spectra ◽  
Internal Flow ◽  
Acoustic Power ◽  
Broadband Noise ◽  
Current Work ◽  
Sound Power ◽  
Noise Sources

An investigation is performed on the scalability of broadband noise sources from separated flows in internal pipe systems. Broadband sources from for example wellhead chokes, bends and valves can potentially excite subsea manifolds through fluid acoustic coupling and fluid structural coupling. The focus of the current work is evaluation and improvement of scaling laws for collapse of sound power spectra. The approach proposed here is to use steady-state Computational Fluid Dynamics [CFD] to better estimate the properties of the flow in order to improve the scaling law and obtain a universal broadband spectrum. Steady Reynolds Averaged Navier-Stokes [RANS] simulations of several bend and orifice geometries have been performed. A surface acoustic power model based on modeled turbulent quantities is implemented. Based on the RANS data, more advanced models for scaling have been developed. Experimental sound power spectra from literature of the simulated geometries are scaled using different methodologies in both amplitude and frequency. When a new scaling based on CFD modeled surface acoustic power was used, a universal collapse among geometries occurred. Using CFD, the velocity in the high-speed sound-producing region is obtained, as well as a more accurate length scaling in order to improve the frequency scaling. A vast improvement in collapse over different geometries is achieved. The current work indicates that a universal collapse might indeed be present. The methodology does not require high fidelity calculations and is thus easy to implement. By comparing original and new scaling laws, it turns out that the ratio of fluctuating drag over steady drag can vary among geometries.

scholarly journals The velocity-curvature power law in Drosophila larval locomotion

2016 ◽  
Author(s):  
Myrka Zago ◽  
Francesco Lacquaniti ◽  
Alex Gomez-Marin
Keyword(s):  
Power Law ◽  
Scaling Laws ◽  
Scaling Law ◽  
Fruit Fly ◽  
Pattern Generation ◽  
Geometric Constraints ◽  
Muscle Properties ◽  
Wide Range ◽  
The Law ◽  
Almost All

AbstractWe report the discovery that the locomotor trajectories generated by crawling fruit fly larvae follow the same power law relationship between speed and curvature previously found in the human motor control of hand-drawing, walking, eye movements and speech. Using high resolution behavioral tracking of individual flies in different sensory environments, we tested the power law by making maggots trace different trajectory types in naturalistic conditions, from reaching-like movements to scribbles. In all these conditions, we found that the law holds, and also that the exponent of the larval scaling law approaches 3/4, rather than the usual 2/3 exponent found in almost all human situations. This is consistent with recent findings on humans drawing ellipses on water, where dynamic effects related to medium viscosity have been shown to increase the exponent that would emerge from purely kinematic-geometric constraints. To our knowledge, the speed-curvature power law has only been studied in human and non-human primates, our work then being the first demonstration of the speed-curvature scaling principle in other species. As there are still different competing hypotheses for the origin of such law in humans (one invoking complex cortical computations in primates; another postulating its emergence from the coupling of viscoelastic muscle properties with simple central pattern generation) our findings in the larva demonstrate that the law is possible in an animal with a nervous system orders of magnitude simpler than that of humans, thus supporting the latter view. Given that our discovery is in Drosophila (amenable to precise genetic manipulations, electron microscopy reconstruction of neural circuits, imaging in behaving animals, electrophysiology, and other techniques) this opens great potential for uncovering the mechanistic implementation of the velocity-curvature power law. Such scaling laws might exist because natural selection favors processes that remain behaviorally efficient across a wide range of contexts in distantly related species. Our work is an effort to search for shared principles of animal behavior across phyla.

High-resolution seismic signals from band-limited data using scaling laws of wavelet transforms

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA143-WA152 ◽  
Author(s):  
K. R. Devi ◽  
Herb Schwab
Keyword(s):  
High Resolution ◽  
Power Law ◽  
Seismic Data ◽  
Wavelet Transforms ◽  
Scaling Laws ◽  
Scaling Law ◽  
Well Log ◽  
Seismic Signals ◽  
Local Scaling ◽  
Seismic Wavelet

Time-scale spectra, obtained from seismic data wavelet transforms, are useful in analyzing local scaling properties of seismic signals. In particular, the wavelet transform modulus maxima (WTMM) spectra, obtained by following the local extrema of wavelet transforms along a constant phase line, describe characteristics of discontinuities such as interfaces. They also show a smooth behavior as a function of scale and thus allow us to derive local scaling laws. We use scaling behavior of WTMM spectra to enhance the bandwidth of seismic data. An analysis of well-log scaling behaviors and the seismic data shows that, whereas the WTMM spectrum of well logs at each interface exhibits a power-law behavior as a function of scale, the corresponding seismic signal spectrum shows a more complicated behavior, arising from seismic wavelet effects. Under the assumption that local well-log power-law behavior holds in general, a scaling law for seismic signals can be derived in terms of parameters that describe subsurface scaling effects and the seismic wavelet. A stable estimation of these parameters can be carried out simultaneously, as a function of time and over the seismic bandwidth, using the modified scaling law. No well-log information is needed to derive the seismic wavelet. Then wavelet transforms can be corrected for seismic wavelet effects and a high-resolution signal reconstructed. This reconstructed high-resolution signal can be used to map features that might not be obvious in the original seismic data, such as small faults, fractures, and fine-scale variations within channel margins.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

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