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Journal articles on the topic 'Maximum spreading'

Author: Grafiati

Published: 6 September 2023

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1

Walsh, B. M., D. T. Welling, Y. Zou, and Y. Nishimura. "A Maximum Spreading Speed for Magnetopause Reconnection." Geophysical Research Letters 45, no. 11 (June 5, 2018): 5268–73. http://dx.doi.org/10.1029/2018gl078230.

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2

Aksoy, Yunus Tansu, Pinar Eneren, Erin Koos, and Maria Rosaria Vetrano. "Spreading of a droplet impacting on a smooth flat surface: How liquid viscosity influences the maximum spreading time and spreading ratio." Physics of Fluids 34, no. 4 (April 2022): 042106. http://dx.doi.org/10.1063/5.0086050.

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Existing energy balance models, which estimate maximum droplet spreading, insufficiently capture the droplet spreading from low to high Weber and Reynolds numbers and contact angles. This is mainly due to the simplified definition of the viscous dissipation term and incomplete modeling of the maximum spreading time. In this particular research, droplet impact onto a smooth sapphire surface is studied for seven glycerol concentrations between 0% and 100%, and 294 data points are acquired using high-speed photography. Fluid properties, such as density, surface tension, and viscosity, are also measured. For the first time according to the authors' knowledge, we incorporate the fluid viscosity in the modeling of the maximum spreading time based on the recorded data. We also estimate the characteristic velocity of the viscous dissipation term in the energy balance equation. These viscosity-based characteristic scales help to formulate a more comprehensive maximum droplet spreading model. Thanks to this improvement, our model successfully fits the data available in the literature for various fluids and surfaces compared to the existing models.

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3

Liu, Xiaohua, Kaimin Wang, Yaqin Fang, R. J. Goldstein, and Shengqiang Shen. "Study of the effect of surface wettability on droplet impact on spherical surfaces." International Journal of Low-Carbon Technologies 15, no. 3 (January 20, 2020): 414–20. http://dx.doi.org/10.1093/ijlct/ctz077.

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Abstract The effect of surface wettability on droplet impact on spherical surfaces is studied with the CLSVOF method. When the impact velocity is constant, with the increase in the contact angle (CA), the maximum spreading factor and time needed to reach the maximum spreading factor (tmax) both decrease; the liquid film is more prone to breakup and rebound. When CA is constant, with the impact velocity increasing, the maximum spreading factor increases while tmax decreases. With the curvature ratio increasing, the maximum spreading factor increases when CA is between 30 and 150°, while it decreases when CA ranges from 0 to 30°.

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4

Zhang, Xuan, Bingqiang Ji, Xin Liu, Siyu Ding, Xiaomin Wu, and Jingchun Min. "Maximum spreading and energy analysis of ellipsoidal impact droplets." Physics of Fluids 33, no. 5 (May 2021): 052108. http://dx.doi.org/10.1063/5.0047583.

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5

Fukai, Jun, Mitsuru Tanaka, and Osamu Miyatake. "Maximum Spreading of Liquid Droplets Colliding with Flat Surfaces." JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 31, no. 3 (1998): 456–61. http://dx.doi.org/10.1252/jcej.31.456.

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6

Liang, Gangtao, Yang Chen, Liuzhu Chen, and Shengqiang Shen. "Maximum Spreading for Liquid Drop Impacting on Solid Surface." Industrial & Engineering Chemistry Research 58, no. 23 (May 22, 2019): 10053–63. http://dx.doi.org/10.1021/acs.iecr.9b02014.

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7

Börnhorst, Marion, Xuan Cai, Martin Wörner, and Olaf Deutschmann. "Maximum Spreading of Urea Water Solution during Drop Impingement." Chemical Engineering & Technology 42, no. 11 (September 4, 2019): 2419–27. http://dx.doi.org/10.1002/ceat.201800755.

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8

Ashikhmin, Alexander, Nikita Khomutov, Roman Volkov, Maxim Piskunov, and Pavel Strizhak. "Effect of Monodisperse Coal Particles on the Maximum Drop Spreading after Impact on a Solid Wall." Energies 16, no. 14 (July 10, 2023): 5291. http://dx.doi.org/10.3390/en16145291.

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The effect of coal hydrophilic particles in water-glycerol drops on the maximum diameter of spreading along a hydrophobic solid surface is experimentally studied by analyzing the velocity of internal flows by Particle Image Velocimetry (PIV). The grinding fineness of coal particles was 45–80 μm and 120–140 μm. Their concentration was 0.06 wt.% and 1 wt.%. The impact of particle-laden drops on a solid surface occurred at Weber numbers (We) from 30 to 120. It revealed the interrelated influence of We and the concentration of coal particles on changes in the maximum absolute velocity of internal flows in a drop within the kinetic and spreading phases of the drop-wall impact. It is explored the behavior of internal convective flows in the longitudinal section of a drop parallel to the plane of the solid wall. The kinetic energy of the translational motion of coal particles in a spreading drop compensates for the energy expended by the drop on sliding friction along the wall. At We = 120, the inertia-driven spreading of the particle-laden drop is mainly determined by the dynamics of the deformable Taylor rim. An increase in We contributes to more noticeable differences in the convection velocities in spreading drops. When the drop spreading diameter rises at the maximum velocity of internal flows, a growth of the maximum spreading diameter occurs. The presence of coal particles causes a general tendency to reduce drop spreading.

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9

Grevemeyer, Ingo, Nicholas W. Hayman, Dietrich Lange, Christine Peirce, Cord Papenberg, Harm J. A. Van Avendonk, Florian Schmid, Laura Gómez de La Peña, and Anke Dannowski. "Constraining the maximum depth of brittle deformation at slow- and ultraslow-spreading ridges using microseismicity." Geology 47, no. 11 (September 23, 2019): 1069–73. http://dx.doi.org/10.1130/g46577.1.

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Abstract The depth of earthquakes along mid-ocean ridges is restricted by the relatively thin brittle lithosphere that overlies a hot, upwelling mantle. With decreasing spreading rate, earthquakes may occur deeper in the lithosphere, accommodating strain within a thicker brittle layer. New data from the ultraslow-spreading Mid-Cayman Spreading Center (MCSC) in the Caribbean Sea illustrate that earthquakes occur to 10 km depth below seafloor and, hence, occur deeper than along most other slow-spreading ridges. The MCSC spreads at 15 mm/yr full rate, while a similarly well-studied obliquely opening portion of the Southwest Indian Ridge (SWIR) spreads at an even slower rate of ∼8 mm/yr if the obliquity of spreading is considered. The SWIR has previously been proposed to have earthquakes occurring as deep as 32 km, but no shallower than 5 km. These characteristics have been attributed to the combined effect of stable deformation of serpentinized mantle and an extremely deep thermal boundary layer. In the context of our MCSC results, we reanalyze the SWIR data and find a maximum depth of seismicity of 17 km, consistent with compilations of spreading-rate dependence derived from slow- and ultraslow-spreading ridges. Together, the new MCSC data and SWIR reanalysis presented here support the hypothesis that depth-seismicity relationships at mid-ocean ridges are a function of their thermal-mechanical structure as reflected in their spreading rate.

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10

Li, Siqi, Hourong Yu, and Haisheng Fang. "Experimental study of liquid droplets impact on powder surface: The application of effective dimensionless parameters in analysis." E3S Web of Conferences 341 (2022): 01011. http://dx.doi.org/10.1051/e3sconf/202234101011.

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Spreading dynamics of liquid droplets impacting onto powder bed are experimentally studied using high-speed photography. Dimensionless numbers—We, Re, the modified We* and Re∗ corrected by substrate deformation—are used to analyze the impact behaviors of droplets. The spreading time and the maximum spreading factor are further analyzed. The spreading time is accurately described by a universal scaling law that is obtained from the modified dimensionless time vs. the effective Weber number (We∗), and the maximum spreading factor is found to follow the modified classic scaling law βmax = f(We*, Re*).

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11

Wei, Yu, and Marie-Jean Thoraval. "Maximum spreading of an impacting air-in-liquid compound drop." Physics of Fluids 33, no. 6 (June 2021): 061703. http://dx.doi.org/10.1063/5.0053384.

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12

Ryu, Sung Uk, and Sang Yong Lee. "Maximum spreading of electrically charged droplets impacting on dielectric substrates." International Journal of Multiphase Flow 35, no. 1 (January 2009): 1–7. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2008.09.003.

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13

Liu, Xin, Jingchun Min, and Xuan Zhang. "Dynamic behavior and maximum spreading of droplets impacting concave spheres." Physics of Fluids 32, no. 9 (September 1, 2020): 092109. http://dx.doi.org/10.1063/5.0020110.

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14

Abouelsoud, Mostafa, Vinod A. Thale, Ahmed N. Shmroukh, and Bofeng Bai. "Spreading and retraction of the concentric impact of a drop with a sessile drop of the same liquid: Effect of surface wettability." Physics of Fluids 34, no. 11 (November 2022): 112108. http://dx.doi.org/10.1063/5.0117964.

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The concentric impact on a sessile drop is relevant in many applications, including spray coating and icing phenomena. Herein, the spreading and retraction phases yielded during the impact of a coaxial drop with a sessile drop on a solid substrate were empirically and analytically examined. We analyzed the effects of surface wettability on the impact outcomes utilizing five distinctive surfaces (i.e., smooth glass, aluminum, copper, Teflon, and coated glass). The results showed that the merged drop takes longer to attain its maximum spreading diameter at a relatively higher contact angle of the sessile drop with the solid surface. Furthermore, based on energy balance, a model for predicting the maximum spreading diameter of the drop with varying surface wettability was presented. This model considers the assumption of viscous energy loss during the merging of falling and sessile drops and at the maximum spreading diameter. Additionally, the maximum retraction height during the impact on the coated glass surface was investigated. Our model results matched well with the experimental data.

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15

Wang, Fei, Lin Wang, and Guoding Chen. "Analysis of Oil Droplet Deposition Characteristics and Determination of Impact State Criterion in Aero-Engine Bearing Chamber." Processes 8, no. 6 (June 25, 2020): 741. http://dx.doi.org/10.3390/pr8060741.

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The research of oil/air two-phase flow and heat transfer is the fundamental work of the design of lubrication and heat transfer in aero-engine bearing chamber. The determination of impact state criterion of the moving oil droplets with the wall and the analysis of oil droplet deposition characteristics are important components. In this paper, the numerical analysis model of the impact between the moving oil droplet and the wall is established by using the finite volume method, and the simulation of oil droplet impingement on the wall is carried out. Then the effects of oil droplet diameter, impact velocity, and incident angle on the characteristic parameters of impact state are discussed. The characteristic parameters include the maximum spreading length, the maximum spreading width, and the number of splashing oil droplets. Lastly the calculation results are verified through comparing with the experimental results in the literature. The results show as follows: (1) The maximum spreading width of oil droplet firstly increases and then slows down with the incident angle and the oil droplet diameter increasing; (2) when the oil droplet diameter becomes small, the influence of the incident angle on the maximum spreading length of oil droplet is obvious and vice versa; (3) with the impact velocity and diameter of oil droplet increasing, the maximum spreading width of oil droplet increases firstly and then slows down, and the maximum spreading length increased gradually; (4) the number of splashing oil droplets increases with the incident angle and impact velocity increasing; and (5) compared with the experimental data in literature, the critical dimensionless splashing coefficient K c proposed in this paper can better distinguish the impact state of oil droplet.

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16

Vuolo, Maria Raffaella, Marco Acutis, Bhishma Tyagi, Gabriele Boccasile, Alessia Perego, and Simone Pelissetti. "Odour Emissions and Dispersion from Digestate Spreading." Atmosphere 14, no. 4 (March 24, 2023): 619. http://dx.doi.org/10.3390/atmos14040619.

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Odour emissions from digestate applied on 21 October 2020 in a 2.4 ha field in the Po Valley (Casalino, 28060, Novara, Italy) were measured using dynamic olfactometry and a six-specialist odour panel, and two application techniques were compared. The measured odour emissions were 3024 and 1286 ou m−2 h−1, corresponding to the digestate application with surface spreading and direct injection, respectively. The odour dispersion for the different emission values was modeled to a distance of approx. 500 m from the center of the field and 15 m from the ground using a Lagrangian puff model (SCICHEM) in different meteorological conditions. The meteorological variables were measured at the closest station during the whole month in which the digestate application took place, mimicking a “worst-case scenario” characterized by the frequent applications along the considered period. The maximum odour concentrations within one square km area from the center of the field occurred in calm wind and stable atmospheric conditions. This study also evaluated the effect of a barrier downwind from the source. In the worst-case scenario (spreading technique with maximum emissions, no barriers), the average and maximum estimated odour concentrations were 3.2 and 18.9 ou m−3, respectively. The calculated probabilities of exceeding the threshold value of 1 ou m−3 were 36% and 47% for the whole period and the episodes of calm winds, respectively, and 14% on average for the episode of maximum wind gust. In the best emission scenario (direct injection), the average and maximum odour concentrations were 1.5 and 8.6 ou m−3, respectively, while the probabilities of exceeding 1 ou m−3 were 26% and 36% for the whole period and the episodes of calm winds, respectively, and 0.016% for the maximum wind gust episode. In the presence of a solid barrier downwind from the source and for the wind gust episode, the peak values of the concentrations and exceedance probabilities at the sampling height were found to be reduced by a factor close to 2.5 and 5 × 105, respectively. The study also evaluated the concentration field’s vertical distribution, showing that the odour plume’s vertical and horizontal dispersion slightly increased with the barrier. This is not a cause of concern unless the emitted substances causing odour nuisance are also atmospheric pollutants with potential harm to far-field ecosystems and human settlements at low concentration levels.

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17

Yang, Yanjie, Xiaoqian Chen, and Yiyong Huang. "Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface." Applied Sciences 9, no. 11 (May 29, 2019): 2214. http://dx.doi.org/10.3390/app9112214.

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The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ

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18

Chen, Xinxing, Aidan P. O’Mahony, and Tracie Barber. "Spreading behavior of cell-laden droplets in 3D bioprinting process." Journal of Applied Physics 133, no. 1 (January 7, 2023): 014701. http://dx.doi.org/10.1063/5.0130063.

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3D droplet-based bioprinting technology is an innovative and time-saving additive manufacturing method, which enables spatial patterning of biological materials and biochemical and living cells for multiple clinical and research applications. Understanding the criteria that control droplet spreading behavior during droplet impact is of great importance in controlling printing resolution and optimizing the printing performance. In this experimental work, the spreading of 3D printed cell-laden droplets was studied with side and bottom view images. The droplets contain [Formula: see text] cells/ml input cell concentration and corresponding [Formula: see text] cell volume fraction and impact onto a flat hydrophilic substrate, a pre-printed droplet, and a pre-printed thin liquid film. The cell-laden droplet impact morphology, the maximum spreading factor, and the cell distribution under different printing conditions ([Formula: see text]) in a 3D bioprinting process were characterized. It was found that on the hydrophilic flat substrate, the cells homogeneously distributed into a disk structure. The maximum spreading factor, [Formula: see text], can be well described by the correlation formulas based on the energy balance and volume conservation. A power-law scaling formula was found to describe the maximum spreading in terms of the Weber number for cell-laden droplet impact on both pre-printed droplets and thin liquid films, where [Formula: see text]. Input cell concentration, up to [Formula: see text] cells/ml, was found to have negligible effect on the maximum droplet spreading factor in a 3D bioprinting process.

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19

Gordillo, José Manuel, Guillaume Riboux, and Enrique S. Quintero. "A theory on the spreading of impacting droplets." Journal of Fluid Mechanics 866 (March 5, 2019): 298–315. http://dx.doi.org/10.1017/jfm.2019.117.

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Here we provide a self-consistent analytical solution describing the unsteady flow in the slender thin film which is expelled radially outwards when a drop hits a dry solid wall. Thanks to the fact that the fluxes of mass and momentum entering into the toroidal rim bordering the expanding liquid sheet are calculated analytically, we show here that our theoretical results closely follow the measured time-varying position of the rim with independence of the wetting properties of the substrate. The particularization of the equations describing the rim dynamics at the instant the drop reaches its maximal extension which, in analogy with the case of Savart sheets, is characterized by a value of the local Weber number equal to one, provides an algebraic equation for the maximum spreading radius also in excellent agreement with experiments. The self-consistent theory presented here, which does not make use of energetic arguments to predict the maximum spreading diameter of impacting drops, provides us with the time evolution of the thickness and of the velocity of the rim bordering the expanding sheet. This information is crucial in the calculation of the diameters and of the velocities of the droplets ejected radially outwards for drop impact velocities above the splashing threshold.

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20

温, 原. "The Maximum Spreading Factor of the Droplet Impacting the Horizontal Surface." International Journal of Mechanics Research 08, no. 01 (2019): 1–12. http://dx.doi.org/10.12677/ijm.2019.81001.

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21

Choudhury, Raihan, Junho Choi, Sangsun Yang, Yong-Jin Kim, and Donggeun Lee. "Maximum spreading of liquid drop on various substrates with different wettabilities." Applied Surface Science 415 (September 2017): 149–54. http://dx.doi.org/10.1016/j.apsusc.2016.12.195.

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22

WENG, WEN GUO, SHUN JIANG NI, HONG YONG YUAN, and WEI CHENG FAN. "MODELING THE DYNAMICS OF DISASTER SPREADING FROM KEY NODES IN COMPLEX NETWORKS." International Journal of Modern Physics C 18, no. 05 (May 2007): 889–901. http://dx.doi.org/10.1142/s0129183107010619.

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In this paper, we present the dynamics of disaster spreading from key nodes in complex networks. The key nodes have maximum and minimum out-degree nodes, which show important in spreading disaster. This paper considers directed Erdös–Rényi, scale-free and small-world networks. Using the model considering the common characteristics of infrastructure and lifeline networks, i.e., self-healing function and disaster spreading mechanism, we carry out simulations for the effects of the recovery time parameter and the time delay on the recovery rate and the number of damaged nodes. Simulation results show some typical disaster spreading characteristics, e.g., a non-equilibrium phase transition in the parameter space, disturbance from the maximum out-degree nodes resulting in more damaged effect, etc.

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23

Pan, Qingmin, Deyu Tu, Baohong Tong, Yongguang Hu, and Tao Wang. "Numerical Analysis of Spreading Process of Ellipsoidal Spraying Droplet Impacting on Superhydrophobic Surface." Agricultural Science 2, no. 2 (November 5, 2020): p160. http://dx.doi.org/10.30560/as.v2n2p160.

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Agricultural spray deposition is especially important for pesticide application because low efficiency can lead to environmental pollution, poor biological efficiency and economic loss. The deposition of pesticide spray on the leave surfaces is related to the impact kinetic behavior of droplets. But after considering the deformation of the droplet, how impingement will affect the deposition is an interesting research. In this study, a superhydrophobic surface was used to replace the plant surface that the pesticide droplets may affect. An interface tracking method was proposed to characterize the impingement dynamics behaviors of different ellipsoid droplets impacting on the surface. The maximum spreading coefficient and time of ellipsoidal droplets increased with the raise of their size. A lower sized droplet has a faster spreading rate, while the center of a higher sized droplet is thinner. As the velocity of pesticide increases, maximum spreading coefficient of droplet increases with a decrease in the maximum spreading time of droplet. The simulation results can contribute to provide theoretical basis for improving spray efficiency.

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24

Arizona, Rafil, Teguh Wibowo, Indarto Indarto, and Deendarlianto Deendarlianto. "The effects of surface tension on the spreading ratio during the impact of multiple droplets onto a hot solid surface." MATEC Web of Conferences 197 (2018): 08016. http://dx.doi.org/10.1051/matecconf/201819708016.

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The impact between multiple droplets onto hot surface is an important process in a spray cooling. The present study was conducted to investigate the dynamics of multiple droplet impact under various surface tensions. Here, the ethylene glycol with compositions of 0%, 5%, and 15% was injected through a nozzle onto stainless steel surface as the multiple droplet. The solid surface was heated at the temperatures of 100 °C, 150 °C, and 200 °C. To observe the dynamics of multiple droplets, a high speed camera with the frame rate of 2000 fps was used. A technique of image processing was developed to determine the maximum droplet spreading ratio. As the result, the surface tension contributes significantly to maximum spreading ratio. As the droplet surface tension decreases, the maximum spreading ratio increases. The maximum spreading ratio appears when the percentage of the ethylene glycol is 15% at the temperature of 150°C. From the visual observation, it is shown that a slower emergence of secondary droplets (droplet splashing) is carried out under a lower surface tension. Hence, surface tension plays an important role on the behavior of emerging secondary droplets. Furthermore, results of the experiments are useful for the validation of available previous CFD models.

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Song, Yajie, Qi Wang, Yushan Ying, Zhuo You, Songbai Wang, Jiang Chun, Xuehu Ma, and Rongfu Wen. "Droplet Spreading Characteristics on Ultra-Slippery Solid Hydrophilic Surfaces with Ultra-Low Contact Angle Hysteresis." Coatings 12, no. 6 (May 31, 2022): 755. http://dx.doi.org/10.3390/coatings12060755.

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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.

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26

Guo, Jingzhong, Longzhe Jin, Yuanzhong Yang, Ruoyu Cui, Naseer Muhammad Khan, Ming Li, Qipeng Zhang, and Xinran Yue. "Study on Dynamic Contact Behavior of Multi-Component Droplet and Dust Surface." Coatings 13, no. 7 (June 24, 2023): 1146. http://dx.doi.org/10.3390/coatings13071146.

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The dynamic contact behavior between multi-component droplets and the surface of iron ore dust was taken as the research object, analysis of the maximum spreading coefficient, maximum acting diameter, maximum acting area, and maximum bouncing height of solid-liquid contact, from a microscopic perspective, using high-speed photography and image analysis and processing technology. The experimental results indicate that (1) with the particle size of dust particles decreases, the solid-liquid contact behavior sequentially manifests as spread immediately after broken, retraction, negative bounce, primary bounce, and secondary bounce. (2) When the surface tension of the droplets decreases from 55.5 to 34.8 mN/m, the maximum spreading diameter of the droplet has increased by 30% to 40%, the maximum bounce heights (coefficients) decreased by 100%, 57.14%, and 53.57%, respectively, the maximum spreading coefficient of the droplet exhibits no obvious pattern. (3) With decreasing droplet surface tension, the unidirectional acting diameter and the maximum acting area increase when the dust surface size is over 100 μm. When the surface particle size is less than 100 μm, there is no significant change in the unidirectional acting diameter and maximum acting area despite decreasing surface tension. Thus, droplet diffusion is mainly influenced by particle size. These findings contribute to enhancing the theory of water mist dust removal and improving dust removal efficiency.

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27

Song, Yun Chao, Chun Hai Wang, and Zhi Ning. "Study on Spreading of Liquid Droplet Impacting on a Solid Dry Surface." Applied Mechanics and Materials 66-68 (July 2011): 888–93. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.888.

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A numerical computation and theoretical model are presented on spreading of a single droplet impacting on a solid surface at low Weber number. The numerical simulation uses combined Level Set-VOF method and a precise wetting model. The singularity at the moving contact line was analyzed and removed by present wetting model. A theoretical model based on the energy balance was developed to predict the maximum spreading ratio, accounting for wetting effect by a correction factor. The droplets shapes, the dimensionless spreading radius and the dimensionless height of droplet calculated by present numerical method were compared with the experimental data. The theoretical model is used to predict the maximum spreading ratio. The numerical and theoretical results agree well with the experimental data. Present theoretical model indicates that capillary effects may be neglected if 6We(We/3+4)>>Re.

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28

Pei Wei-Dong, Liu Zhong-Xin, Chen Zeng-Qiang, and Yuan Zhu-Zhi. "Study of epidemic spreading on scale-free networks with finite maximum dissemination." Acta Physica Sinica 57, no. 11 (2008): 6777. http://dx.doi.org/10.7498/aps.57.6777.

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29

Ahmed, Abrar, Brian A. Fleck, and Prashant R. Waghmare. "Maximum spreading of a ferrofluid droplet under the effect of magnetic field." Physics of Fluids 30, no. 7 (July 2018): 077102. http://dx.doi.org/10.1063/1.5032113.

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30

Alexander, Kaitlin, Katrin J. Meissner, and Timothy J. Bralower. "Sudden spreading of corrosive bottom water during the Palaeocene–Eocene Thermal Maximum." Nature Geoscience 8, no. 6 (May 11, 2015): 458–61. http://dx.doi.org/10.1038/ngeo2430.

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31

Lee, Jae Bong, Dominique Derome, Robert Guyer, and Jan Carmeliet. "Modeling the Maximum Spreading of Liquid Droplets Impacting Wetting and Nonwetting Surfaces." Langmuir 32, no. 5 (January 25, 2016): 1299–308. http://dx.doi.org/10.1021/acs.langmuir.5b04557.

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32

Lin, Shiji, Binyu Zhao, Song Zou, Jianwei Guo, Zheng Wei, and Longquan Chen. "Impact of viscous droplets on different wettable surfaces: Impact phenomena, the maximum spreading factor, spreading time and post-impact oscillation." Journal of Colloid and Interface Science 516 (April 2018): 86–97. http://dx.doi.org/10.1016/j.jcis.2017.12.086.

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33

CHAKRABORTY, ABHIJIT, and S. S. MANNA. "DISEASE SPREADING MODEL WITH PARTIAL ISOLATION." Fractals 21, no. 03n04 (September 2013): 1350015. http://dx.doi.org/10.1142/s0218348x13500151.

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The effect of partial isolation has been studied in disease spreading processes using the framework of susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models. The partial isolation is introduced by imposing a restriction: each infected individual can probabilistically infect up to a maximum number n of his susceptible neighbors, but not all. It has been observed that the critical values of the spreading rates for endemic states are non-zero in both models and decrease as 1/n with n, on all graphs including scale-free graphs. In particular, the SIR model with n = 2 turned out to be a special case, characterized by a new bond percolation threshold on square lattice.

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Zhang, Fangfang, Xiangyu Li, Huajie Li, Jingdan Tang, Zhen Shen, Guopei Li, Tingxiang Jin, and Pei Yuan. "Impingement dynamics of droplets on mildly heated walls at initial and later stages." Physics of Fluids 34, no. 3 (March 2022): 037113. http://dx.doi.org/10.1063/5.0082244.

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The impingement dynamics of water droplets on a heated wall at initial and later stages are experimentally investigated. First, the effects of the wall temperature and the Weber number on the water droplet spreading characteristics are considered. A constant contact radius evaporation mode is observed during most of the evaporation. The wall temperature has little influence on the spreading characteristics at the initial stages. The Weber number greatly influences the spreading characteristics, such as the spreading dynamic behavior, maximum spreading time, spreading height, diameter, and contact angle, at the initial stages. At the later stages of spreading, the heating temperature has a relatively greater impact on the rate of linear change of the residual volume, whereas the impact of the Weber number on that is relatively small. Subsequently, the effect of evaporation on the impingement dynamics is investigated. The spreading characteristics of the water droplet are compared with those of an ionic liquid droplet (which does not experience evaporation), whereby the spreading factor increases and the volume remains unchanged with the increasing contact time in the absence of the evaporation effect.

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Yang, Song, Yu Hou, Yuheng Shang, and Xin Zhong. "BPNN and CNN-based AI modeling of spreading and icing pattern of a water droplet impact on a supercooled surface." AIP Advances 12, no. 4 (April 1, 2022): 045209. http://dx.doi.org/10.1063/5.0082568.

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A water droplet impacting on a supercooled surface normally experiencing spreading and freezing is a complex process involving fluid flow, heat transfer, and phase change. We established two models to, respectively, predict the spreading dynamics of a water droplet impact on a supercooled surface and classify the icing patterns to predict the corresponding surface supercooling degree. Six important factors are used to characterize droplet spreading, including Reynolds number, Weber number, Ohnesorge number, surface supercooling degree, the maximum spreading factor, and the dimensionless maximum spreading time. A Back Propagation Neural Network model, including four inputs and two outputs, is established, containing a hidden layer with 15 neurons to perform the non-linear regression training on the spreading factors of 778 groups of an impact water droplet. The trained model is adopted to predict the spreading factors of 86 groups of a water droplet impact on the supercooled surface. The second model is developed to discern and classify the experimentally captured three different icing patterns. Different clustering methods are performed on 116 icing images, including gray-scale and red-green-blue (RGB) clustering. Then, two convolution neural network models of VGG-19 (Visual Geometry Group-19) and VGG-16 are established to classify, train, and test the icing images by gray-scale and RGB clustering methods. The K = 2 gray-scale clustering and the VGG-19 model exhibits the highest accuracy at 90.57%. The two models developed in this study can, respectively, predict the essential factors characterizing spreading dynamics of an impact droplet on a cold surface and predict surface supercooling degree based on an icing pattern.

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Fernández, Joseph John, Shiho Kobayashi, and Gavin P. Lamb. "Lateral spreading effects on VLBI radio images of neutron star merger jets." Monthly Notices of the Royal Astronomical Society 509, no. 1 (October 7, 2021): 395–405. http://dx.doi.org/10.1093/mnras/stab2879.

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ABSTRACT Very long baseline interferometry radio images recently proved to be essential in breaking the degeneracy in the ejecta model for the neutron star merger GW170817. We discuss the properties of synthetic radio images of merger jet afterglows by using semi-analytical models of laterally spreading or non-spreading jets. The image centroid initially moves away from the explosion point in the sky with apparent superluminal velocity. After reaching a maximum displacement, its motion is reversed. This behaviour is in line with that found in full hydrodynamic simulations. We show that the evolution of the centroid shift and the image size are significantly different when lateral spreading is considered. For Gaussian jet models with plausible model parameters, the morphology of the laterally spreading jet images is much closer to circular. The maximum displacement of the centroid shift and its occurrence time are smaller/earlier by a factor of a few for spreading jets. Our results indicate that it is crucial to include lateral spreading effects when analysing radio images of neutron star merger jets. We also obtain the viewing angle θobs by using the centroid shift of radio images provided the ratio of the jet core size θc and θobs is determined by afterglow light curves. We show that a simple method based on a point-source approximation provides reasonable angular estimates ($10{-}20{{\ \rm per\ cent}}$ errors at most). By taking a sample of laterally spreading structured Gaussian jets, we obtain θobs ∼ 0.32 for GW170817, consistent with previous studies.

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Li, Qian-Ping, Yi Ouyang, Xiao-Dong Niu, Youhua Jiang, Ming-Fu Wen, Ze-Qin Li, Mu-Feng Chen, De-Cai Li, and Hiroshi Yamaguchi. "Maximum Spreading of Impacting Ferrofluid Droplets under the Effect of Nonuniform Magnetic Field." Langmuir 38, no. 8 (February 18, 2022): 2601–7. http://dx.doi.org/10.1021/acs.langmuir.1c03272.

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Bamaarouf, O., A. Ould Baba, S. Lamzabi, A. Rachadi, and H. Ez-Zahraouy. "Effects of maximum node degree on computer virus spreading in scale-free networks." International Journal of Modern Physics B 31, no. 26 (October 17, 2017): 1750182. http://dx.doi.org/10.1142/s021797921750182x.

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The increase of the use of the Internet networks favors the spread of viruses. In this paper, we studied the spread of viruses in the scale-free network with different topologies based on the Susceptible–Infected–External (SIE) model. It is found that the network structure influences the virus spreading. We have shown also that the nodes of high degree are more susceptible to infection than others. Furthermore, we have determined a critical maximum value of node degree [Formula: see text], below which the network is more resistible and the computer virus cannot expand into the whole network. The influence of network size is also studied. We found that the network with low size is more effective to reduce the proportion of infected nodes.

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An, Sang Mo, and Sang Yong Lee. "Maximum spreading of a shear-thinning liquid drop impacting on dry solid surfaces." Experimental Thermal and Fluid Science 38 (April 2012): 140–48. http://dx.doi.org/10.1016/j.expthermflusci.2011.12.003.

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Huang, Hai-Meng, and Xiao-Peng Chen. "Energetic analysis of drop’s maximum spreading on solid surface with low impact speed." Physics of Fluids 30, no. 2 (February 2018): 022106. http://dx.doi.org/10.1063/1.5006439.

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Ukiwe, Chijioke, and Daniel Y. Kwok. "On the Maximum Spreading Diameter of Impacting Droplets on Well-Prepared Solid Surfaces." Langmuir 21, no. 2 (January 2005): 666–73. http://dx.doi.org/10.1021/la0481288.

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Vadillo, D. C., A. Soucemarianadin, C. Delattre, and D. C. D. Roux. "Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces." Physics of Fluids 21, no. 12 (December 2009): 122002. http://dx.doi.org/10.1063/1.3276259.

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43

Ellison, G. N. "Maximum thermal spreading resistance for rectangular sources and plates with nonunity aspect ratios." IEEE Transactions on Components and Packaging Technologies 26, no. 2 (June 2003): 439–54. http://dx.doi.org/10.1109/tcapt.2003.815088.

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Lee, Jae Bong, Dominique Derome, Ali Dolatabadi, and Jan Carmeliet. "Energy Budget of Liquid Drop Impact at Maximum Spreading: Numerical Simulations and Experiments." Langmuir 32, no. 5 (January 25, 2016): 1279–88. http://dx.doi.org/10.1021/acs.langmuir.5b03848.

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HUI, ZI, XU CAI, JEAN-MARC GRENECHE, and QIUPING A. WANG. "IMPACTS OF SPATIAL STRUCTURE ON EPIDEMIC SPREADING." International Journal of Modern Physics C 23, no. 12 (December 2012): 1250082. http://dx.doi.org/10.1142/s0129183112500829.

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The epidemic spreading on spatial-driven network is studied with the spatial susceptible-infected-susceptible (SIS) model. The network is constructed by random addition of nodes on the plan. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power α. The spreading rate between two nodes is inversely proportional to their spatial distance. The effective spreading time increases with the increasing of α. The proportional coefficient is found to have a α-dependent threshold with a maximum situated in the interval 1.5 < α < 2.

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Zhang, Shaosong, and Jun Zhang. "A New Approach to Estimate Directional Spreading Parameters of a Cosine-2s Model." Journal of Atmospheric and Oceanic Technology 23, no. 2 (February 1, 2006): 287–301. http://dx.doi.org/10.1175/jtech1846.1.

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Abstract For accurate and consistent estimates of the directional spreading parameter and mean wave direction of directional seas based on a cosine-2s directional spreading model, a new approach is proposed, employing a maximum likelihood method (MLM) to estimate the directional spreading function and then the angular Fourier coefficients. Because an MLM is more tolerant of errors in the estimated cross-spectrum than a directional Fourier transfer used in the conventional approach, the proposed approach is able to estimate the directional spreading parameter more accurately and consistently, which is examined and confirmed by applying the proposed approach and conventional approach, respectively, to the time series generated by numerical simulation and recorded in field measurements.

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Chen, Chun-Kuei, Sheng-Qi Chen, Wei-Mon Yan, Wen-Ken Li, and Ta-Hui Lin. "Experimental study on two consecutive droplets impacting onto an inclined solid surface." Journal of Mechanics 37 (2021): 432–45. http://dx.doi.org/10.1093/jom/ufab012.

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Abstract The present study is concerned with the experimental impingement of two consecutive droplets on an inclined solid surface. Attention is mainly paid to the effects of impingement timing with various oblique angles (Φ) of the surface on the impact phenomena, which mainly affect the maximum droplet spreading diameter. The investigation considers four impingement scenarios differentiated by impingement timing, namely Case 1: single-droplet impingement; Case 2 of Δt1: the moment when the leading droplet starts spreading along the oblique surface; Case 3 of Δt2: the moment when the leading droplet reaches its maximum spreading; and Case 4 of Δt3: the moment when the leading droplet starts retracting. It is observed that deformation behavior of two successive droplets impacting on the inclined surface experiences a complex asymmetric morphology evolution due to the enhancement of gravity effect and various conditions of the impingement timing. The merged droplet becomes slender with increasing oblique surface angle in the final steady shape, causing the decrease in the value of front and back contact angles. The impingement timing has a significant influence on the change of the maximum height of the merged droplet. The coalesced droplet spreads to the maximum dimensionless width diameter at Δt = Δt2 and the oblique angle of Φ = 45°, but reaches the maximum dimensionless height for Δt = Δt2 at Φ = 30°. The front contact angles converge to a fixed value eventually for all conditions of impingement timing, and the values become lower with the increasing surface inclination.

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48

Han, Fangwei, Jian Li, Yingying Peng, and Yue Zhao. "Exploration of the Relationships between the Spraying Condition and Wetting Behavior on Coal Surface of Dust Suppression Droplet: Improving the Utilization Rate." Geofluids 2022 (December 21, 2022): 1–13. http://dx.doi.org/10.1155/2022/3464456.

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Dust suppression through water-based media is an important technical means, which is of great significance to industrial process safety and environmental protection. In order to improve the utilization rate of droplets, the dynamic spreading process of droplets impacting the coal surface was studied by the coupled level-set and volume-of-fluid methods (CLSVOF) method. The spread area was calculated by the binary method to characterize the wetting effect. Dimensionless spread area per unit volume (DSAPUV) was proposed to represent the utilization of droplets. The results show that the droplet spreading fracture process can be divided into three stages: initial deformation period, spreading fracture period, and stable period. When the particle size was not being changed, the area of dimensionless spread does not increase consistently with velocities, but there exists an optimal critical velocity of impingement, which is 17 m/s for the maximum dimensionless spread area reached by droplets with a diameter of 30 μm and 19 m/s for the maximum dimensionless spread area reached by droplets with a diameter of 50 μm. Droplet size is directly proportional to the dimensionless spread area. The maximum dimensionless spread areas of the droplets were all reached during spreading, and the time required increased gradually with increasing particle sizes. It was found that the effect of droplet size on the utilization of droplets was obvious when their size ranged from 10 μm to 50 μm, and their velocity ranged from 15 m/s to 20 m/s.

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Liang, He, Peiyi Yang, Wenzhong Wang, Yanfei Liu, Xiangyu Ge, and Baohong Tong. "Spreading Behavior of Single Oil Droplet Impacting Surface with/without a Thin Liquid Film." Lubricants 11, no. 1 (January 12, 2023): 31. http://dx.doi.org/10.3390/lubricants11010031.

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When oil droplets impact a solid surface for oil-air lubrication, they may spread out to produce a thin oil layer on the surface, which serves as a significant source of lubrication. A test rig was constructed in this research to observe the spreading behavior of oil droplets impacting surfaces from both frontal and lateral views. From the frontal view, laser-induced fluorescence techniques are used to measure the thickness of the oil layer quantitatively during the spreading of oil droplets. While the lateral view can observe the shape evolution of the droplets. Oil droplet spreading patterns on the sheet with dry surfaces and with different thin liquid film thicknesses were studied, and the effect of viscosity and the thickness of the thin liquid film on spreading radius and spreading thickness is considered. The experimental findings demonstrate that the maximum spreading factor, the spreading central layer thickness, and the apparentness of retraction all increase as viscosity increases. The retraction is obviously impacted by thin liquid films, and the retraction weakens as the thin liquid film thickness increases.

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Martinez, Patricio, Bo Cheng Jin, and Steven Nutt. "Droplet Spreading on Unidirectional Fiber Beds." Journal of Composites Science 5, no. 1 (January 6, 2021): 13. http://dx.doi.org/10.3390/jcs5010013.

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This study reports a method to analyze parametric effects on the spread flow kinetics of fluid droplets on unidirectional fiber beds. The investigation was undertaken in order to guide the design of droplet arrays for production of an out-of-autoclave (OoA) prepreg featuring discontinuous resin distribution, referred to here as semi-preg. Volume-controlled droplets of a resin facsimile fluid were deposited on carbon fiber beds and the flow behavior was recorded. The time to full sorption (after deposition) and the maximum droplet spread distance were measured. Experiments revealed that fluid viscosity dominated time to full sorption—doubling the viscosity resulted in an 8- to 20-fold increase in sorption time, whereas doubling fabric areal weight increased the time only by a factor of three. Droplet spread distance was nearly invariant with fiber bed architecture and fluid viscosity. A series of droplet arrays were designed, demonstrating how the results can be leveraged to achieve different resin distributions to produce semi-preg optimized for OoA cure.

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