Academic literature on the topic 'Maximum spreading'

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.

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°.

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.

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.

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*).

This thesis presents a literature review of mathematical models developed to simulate the spreading of agrichemical spray droplets impacting on plant leaf surfaces. New results are derived to predict how far droplets will spread when deposited or sprayed perpendicularly onto a dry, uniform, horizontal, solid surface. The first part of the new research provides equations to predict the extent a sessile droplet will spread on these surfaces as well as its itemized energy budget. The second part examines scaling law formulae to predict the maximum spreading factor for droplets impacting the solid at non-zero velocities.

An experimental study on impaction of a single drop on solid surfaces was conducted to show the effects of particles on the impact process. The parameters were: volume fraction of particles (0 to 0.3), particle size (0.47 to 250 micron), and ratio of particle size to drop size (0.00017 to 0.074). The effect of particle volume fraction on the spreading process depended on impact speed and substrate. At low impact speed, particles had little effect on the spreading except for surfaces where the equilibrium contact angle was low. For high impact speed, the influence of particles on spreading can be described by the effective viscosity. The effect of particle size on the spreading process also depended on impact speed and substrate. At low impact speed, the drop did not have enough kinetic energy to overcome the energy barrier associated with the large particles. For particle-laden liquids, retraction was affected by particle parameters. When pure liquid drops retracted from the maximum spreading ratio, the retraction appeared to be symmetric around the point of impaction while retraction of the particle-laden drop was sometimes asymmetric. Rebounding on the Teflon film depended on impact speed, particle volume fraction, and particle size. The impact speed must reach a critical value for rebounding to occur. Bouncing results suggested that the probability of bouncing decreased as viscosity increased, impact speed increased, and surface tension decreased. The non-wetting behavior and bouncing probably involved an air layer between the surface and the drop. When a low-velocity liquid drop impacts on a surface, ejection of a secondary drop from the top of the impacting drop was sometimes observed. When Renardy et al.'s (2003) criterion for the range of velocities for existence of a capillary wave was applied to for a 3.2-mm water drop; the range was between 0.2 to 1.5 m/s. However, drop ejection was observed at lower impact speed. When apparent viscosity of the particle-laden liquid obtained from Krieger's equation (1972) was used in the pure liquid models for predicting the maximum spreading ratio, good agreement between model predictions and experimental results was obtained when Park et al's model (2003) was used.

A new reliability-based probabilistic model is developed for the estimation of liquefaction-induced lateral ground spreading, taking into consideration the uncertainties within the model functional form and the descriptive variables as well. The new model is also introduced as performance-based probabilistic engineering tool.

How do the things which connect us divide us at the same time? This book tells a different history of globalization by tracing how news circulated in a divided society: Algeria under French rule in the late nineteenth and early twentieth centuries. The years between 1881 and 1940 were those of maximum colonial power in North Africa, a period of intense technological revolution, global high imperialism, and the expansion of settler colonialism. Algerians became connected to international networks of news, and local people followed distant events with great interest. But once news reached Algeria, accounts of recent events often provoked conflict as they moved between different social groups. In a society split between its native majority and a substantial settler minority, distant wars led to riots. Circulation and polarization were two sides of the same coin. Looking at a range of sources in multiple languages across colonial society, this book offers a new understanding of what news is. News was a whole ecosystem in which new technologies such as the printing press, the telegraph, the cinema and the radio interacted with older media like songs, rumours, letters, and manuscripts. The French government watched anxiously over these developments, monitoring Algerians’ reactions to news through an extensive network of surveillance that often ended up spreading news rather than controlling its flow. By tracking what different people thought was new, this history of news helps us reconsider the relationship between time, media, and historical change.

Economy and mankind are inextricably interlinked. Just as the economy or the production of material wealth is unimaginable without a man, so human existence and development are impossible without the wealth created in the economy. Shortly, both the goal and the means of achieving and realization of the economy are still the human resources. People have long ago noticed that it was the economy that created livelihoods, and the delays in their production led to the catastrophic events such as hunger, poverty, civil wars, social upheavals, revolutions, moral degeneration, and more. Therefore, the special interest of people in understanding the regulatory framework of the functioning of the economy has existed and exists in all historical epochs [A. Sisvadze. Economic theory. Part One. 2006y. p. 22]. The system of economic disciplines studies economy or economic activities of a society. All of them are based on science, which is currently called economic theory in the post-socialist space (the science of economics, the principles of economics or modern economics), and in most countries of the world - predominantly in the Greek-Latin manner - economics. The title of the present book is also Modern Economics. Economics (economic theory) is the science that studies the efficient use of limited resources to produce and distribute goods and services in order to satisfy as much as possible the unlimited needs and demands of the society. More simply, economics is the science of choice and how society manages its limited resources. Moreover, it should be emphasized that economics (economic theory) studies only the distribution, exchange and consumption of the economic wealth (food, beverages, clothing, housing, machine tools, computers, services, etc.), the production of which is possible and limited. And the wealth that exists indefinitely: no economic relations are formed in the production and distribution of solar energy, air, and the like. This current book is the second complete updated edition of the challenges of the modern global economy in the context of the coronary crisis, taking into account some of the priority directions of the country's development. Its purpose is to help students and interested readers gain a thorough knowledge of economics and show them how this knowledge can be applied pragmatically (professionally) in professional activities or in everyday life. To achieve this goal, this textbook, which consists of two parts and tests, discusses in simple and clear language issues such as: the essence of economics as a science, reasons for origin, purpose, tasks, usefulness and functions; Basic principles, problems and peculiarities of economics in different economic systems; Needs and demand, the essence of economic resources, types and limitations; Interaction, mobility, interchangeability and efficient use of economic resources. The essence and types of wealth; The essence, types and models of the economic system; The interaction of households and firms in the market of resources and products; Market mechanism and its elements - demand, supply and price; Demand and supply elasticity; Production costs and the ways to reduce them; Forms of the market - perfect and incomplete competition markets and their peculiarities; Markets for Production Factors and factor incomes; The essence of macroeconomics, causes and importance of origin; The essence and calculation of key macroeconomic indicators (gross national product, gross domestic product, net national product, national income, etc.); Macroeconomic stability and instability, unemployment, inflation and anti-inflationary policies; State regulation of the economy and economic policy; Monetary and fiscal policy; Income and standard of living; Economic Growth; The Corona Pandemic as a Defect and Effect of Globalization; National Economic Problems and New Opportunities for Development in the conditions of the Coronary Crisis; The Socio-economic problems of moral obsolescence in digital technologies; Education and creativity are the main solution way to overcome the economic crisis caused by the coronavirus; Positive and negative effects of tourism in Georgia; Formation of the middle class as a contributing factor to the development of tourism in Georgia; Corporate culture in Georgian travel companies, etc. The axiomatic truth is that economics is the union of people in constant interaction. Given that the behavior of the economy reflects the behavior of the people who make up the economy, after clarifying the essence of the economy, we move on to the analysis of the four principles of individual decision-making. Furtermore, the book describes how people make independent decisions. The key to making an individual decision is that people have to choose from alternative options, that the value of any action is measured by the value of what must be given or what must be given up to get something, that the rational, smart people make decisions based on the comparison of the marginal costs and marginal returns (benefits), and that people behave accordingly to stimuli. Afterwards, the need for human interaction is then analyzed and substantiated. If a person is isolated, he will have to take care of his own food, clothes, shoes, his own house and so on. In the case of such a closed economy and universalization of labor, firstly, its productivity will be low and, secondly, it will be able to consume only what it produces. It is clear that human productivity will be higher and more profitable as a result of labor specialization and the opportunity to trade with others. Indeed, trade allows each person to specialize, to engage in the activities that are most successful, be it agriculture, sewing or construction, and to buy more diverse goods and services from others at a relatively lower price. The key to such human interactions is that trade is mutually beneficial; That markets are usually the good means of coordination between people and that the government can improve the results of market functioning if the market reveals weakness or the results of market functioning are not fair. Moroever, it also shows how the economy works as a whole. In particular, it is argued that productivity is a key determinant of living standards, that an increase in the money supply is a major source of inflation, and that one of the main impediments to avoiding inflation is the existence of an alternative between inflation and unemployment in the short term, that the inflation decrease causes the temporary decline in unemployement and vice versa. The Understanding creatively of all above mentioned issues, we think, will help the reader to develop market economy-appropriate thinking and rational economic-commercial-financial behaviors, to be more competitive in the domestic and international labor markets, and thus to ensure both their own prosperity and the functioning of the country's economy. How he/she copes with the tasks, it is up to the individual reader to decide. At the same time, we will receive all the smart useful advices with a sense of gratitude and will take it into account in the further work. We also would like to thank the editor and reviewers of the books. Finally, there are many things changing, so it is very important to realize that the XXI century has come: 1. The century of the new economy; 2. Age of Knowledge; 3. Age of Information and economic activities are changing in term of innovations. 1. Why is the 21st century the century of the new economy? Because for this period the economic resources, especially non-productive, non-recoverable ones (oil, natural gas, coal, etc.) are becoming increasingly limited. According to the World Energy Council, there are currently 43 years of gas and oil reserves left in the world (see “New Commersant 2007 # 2, p. 16). Under such conditions, sustainable growth of real gross domestic product (GDP) and maximum satisfaction of uncertain needs should be achieved not through the use of more land, labor and capital (extensification), but through more efficient use of available resources (intensification) or innovative economy. And economics, as it was said, is the science of finding the ways about the more effective usage of the limited resources. At the same time, with the sustainable growth and development of the economy, the present needs must be met in a way that does not deprive future generations of the opportunity to meet their needs; 2. Why is the 21st century the age of knowledge? Because in a modern economy, it is not land (natural resources), labor and capital that is crucial, but knowledge. Modern production, its factors and products are not time-consuming and capital-intensive, but science-intensive, knowledge-intensive. The good example of this is a Japanese enterprise (firm) where the production process is going on but people are almost invisible, also, the result of such production (Japanese product) is a miniature or a sample of how to get the maximum result at the lowest cost; 3. Why is the 21st century the age of information? Because the efficient functioning of the modern economy, the effective organization of the material and personal factors of production largely depend on the right governance decision. The right governance decision requires prompt and accurate information. Gone are the days when the main means of transport was a sailing ship, the main form of data processing was pencil and paper, and the main means of transmitting information was sending letters through a postman on horseback. By the modern transport infrastructure (highways, railways, ships, regular domestic and international flights, oil and gas pipelines, etc.), the movement of goods, services and labor resoucres has been significantly accelerated, while through the modern means of communication (mobile phone, internet, other) the information is spreading rapidly globally, which seems to have "shrunk" the world and made it a single large country. The Authors of the book: Ushangi Samadashvili, Doctor of Economic Sciences, Associate Professor of Ivane Javakhishvili Tbilisi State University - Introduction, Chapters - 1, 2, 3, 4, 5, 6, 9, 10, 11,12, 15,16, 17.1,18 , Tests, Revaz Shengelia, Doctor of Economics, Professor of Georgian Technical University, Chapters_7, 8, 13. 14, 17.2, 17.4; Zhuzhuna Tsiklauri - Doctor of Economics, Professor of Georgian Technical University - Chapters 13.6, 13.7,17.2, 17.3, 18. We also thank the editor and reviewers of the book.

AbstractThe working condition of water valve is an important sign of the success for navigation lock design, and the valve cavitation characteristics and suppression technology is the key technical challenge in the design of high head navigation lock, in the view of the “flat bottom & top spreading” with the condition of “less project quantities, convenient construction” simple type corridor with the head of 19 m in Qianwei ship lock, the method of combining the physical model test and prototype observation are both adopt to this research. Through the physical model test, the cavitation position, cavitation characteristics and the effect of natural ventilation on cavitation suppression are comprehensively determined by analyzing the change law of cavitation noise intensity from several cavitation noise sensors under different opening conditions during the opening process, also the visual observation of flow state and auditory observation. Prototype observation focuses on the effect of self-aerated technology of valve lintel. When the air pipe outside the value lintel position is closed, there are evident in the cavitation pulse signal, and the maximum strength can reach to 182Pa, the “crackling” of cavitation collapse could be clearly felt at the top of the value, occasionally with 2–3 times slight “muffled thunder”, The results show that the valve section has stronger cavitation during the opening process of value. On the contrary, when self-aerated of valve lintel was realized, the maximum ventilatory capacity was 0.169 m3/s, which was close to the 0.170 m3/s calculated by the physical model in the design stage, and no cavitation pulse signal was detected among the valve wells on both sides, and the process line was “stable” with the maximum noise intensity only about 10 Pa, no sound of cavitation collapse was heard at the top of the valve section during the whole valve opening process. The comparison of value steeve vibration also verifies the effect of self-aerated technology of valve lintel at the same times. The results show that self-aerated technology of valve lintel can significantly inhibit the cavitation of valve segment of this form.

A data-driven stochastic program for bi-level network design with hazardous material (hazmat) transportation is proposed in this chapter. In order to regulate the risk associated with hazmat transportation and minimize total travel cost on interested area under stochasticity, a multi-objective stochastic optimization model is presented to determine generalized travel cost for hazmat carriers. Since the bi-level program is generally non-convex, a data-driven bundle method is presented to stabilize solutions of the proposed model and reduce relative gaps between iterations. Numerical comparisons are made with existing risk-averse models. The results indicate that the proposed data-driven stochastic model becomes more resilient than others in minimizing total travel cost and mitigating risk exposure. Moreover, the trade-offs among maximum risk exposure, generalized travel costs, and maximum equitable risk spreading over links are empirically investigated in this chapter.

The influence of Pinus Pinaster needles packing ratio on fire spread at laboratory scale is investigated experimentally and compared to other wildland fuels. The packing ratio was varied from up to 10% by changing the fuel bed load and thickness. An optimum ratio of 5.5% is obtained corresponding to a maximum rate of spread. This optimum ratio is close to that found by Rothermel for crib fuels. However, the rate of spread increases again for higher porosity, which suggests the existence of a second optimum ratio. Two optimum ratios were also observed by Rothermel for excelsior fuels and recently by He et al for experiments using laser-cut cardboard. Recently, two optimum ratios corresponding to a minimum ignition time were observed using Pinus Halepensis needles. The minimum ignition time for spreading fuels correspond to a maximum rate of spread. These ratios have been attributed to a maximum heat flux absorption by the fuel. The heat flux absorption effect on the rate of spread is discussed by using the fuel optical length. The obtained optimum ratio corresponds to a small optical length (12 mm), which means that the heat flux is absorbed by the surface of the fuel bed. The second optimum ratio may correspond to an optical length much larger than the fuel bed thickness (around 50 mm). This corresponds to a bulk absorption of the heat flux. Further analyses of the mass-loss rate are provided to discuss thermochemical effects.

Neurodegenerative diseases (NDs) are characterized by specific dysfunction and damage of neurons related to pathologically changed proteins that deposit in the patient brain but also in peripheral organs. These proteins can be used for therapy or used as biomarkers. Except for a plethora of alterations revealed for dissimilar neurodegeneration-related proteins, amyloid-β, prion protein, TAR DNA-binding protein 43 (TDP-43, transactive response DNA binding protein 43 kDa), tau and α-synuclein, or fused in sarcoma protein (FUS), molecular classification of NDs depend on the full morphological assessment of protein deposits, their spreading in the brain, and their correspondence to clinical signs with specific genetic modifications. The current chapter represents the etiology of neurodegeneration, classification of NDs, concentrating on the maximum applicable biochemical and anatomical characteristics and most imperative NDs.

Play is a spontaneous and free activity of the child and its role in learning processes has been recognized by pedagogical studies from Piaget onwards. Game-based learning places the pupil at the center of the teaching-learning process, creating a motivating and challenging environment in which the pupil can learn freely, proceeding by trial and error, learning to evaluate their choices and those of other players and monitor a number of variables. Game-based learning therefore stands as an individualized and inclusive learning environment, which allows all students to achieve maximum educational success. In more recent years, the spread of online games, the use of coding as a teaching tool, and distance learning experiences have contributed to spreading game-based didactics. In this chapter, the author proposes a path of coding games for the development of problem solving in primary school with interdisciplinary links and to the mathematics curriculum.

With the advancement of technology, new modes of communication have emerged and are being used in the field of academics. Traditional media played a pivotal role in spreading knowledge in all sections of societies in the world. Traditional media proved to be a powerful tool in the process of making learning and teaching more effective, interesting, and simple to insure everyone benefits to the maximum. Social media are newly-emerged communication networks which are in use not only for sharing information but also for education, knowledge transfer, and for building a global community of academicians. Different tools of social media are in use in different streams of education. Over the years, it has been realized that both traditional and social media have much potential and use in education at all three levels e.g. primary, secondary, and higher education. But, the integration of traditional and social media still has a long way to go in terms of acceptance. This chapter highlights some major points related to changing academic environment, with the use of technology in classes, students vs. teachers’ perspectives on learning and teaching, academics, and use of media – Traditional vs. New media in classes and integrating traditional and social media within the academic environment.

This chapter studies the application of information technology in tourism promotion, particularly through Internet. In the context of tourism management, this chapter penetrates different usage of Web technology to disseminate maximum level of information for tourism promotion. This chapter is designed to determine the conditions of Websites as well as application of different application of Web technology like Virtual Reality (VR), CRS, etc. used in tourism promotion to identify the obstacles faced in this type of promotion via Web. The chapter adopts a survey from 200 respondents. Collected data is analyzed through different statistical tools like correlation analysis, simple average method, and Cronbach Alfa for reliability of the data. The results show that tourism promotion through the Web helps to increase competition as well as tourism demand if Web design helps to disseminate information about the tourism offers to the tourists' desire. Both sexes consider the Website design as a means helps to ensure the information veracity of tourism offers. The chapter recommends continuing development of the role of tourism promotion through the Internet in spreading information about tourism offers, so as to achieve the greatest possible benefits. This study also indicates how to develop and upgrade Web for promotion of tourism information and offer better tourism service excellence, while promoting less popular tourist spots.

The malignant cells that cannot be controlled from spreading throughout the body is Cancer. Among which the cancer occurs in bone is their type. It is malignant disease occur in bone of human body where their growth cant be controlled from growing. This bone cancer is very critical of all the cancer types since the malignant cells are not identified at their earlier stage and it is the major challenge. Bone cancer is highly common for children and teenagers. For earlier detection of this cancer the correlation of medical imaging has been adapted with image processing and machine learning techniques where maximum accuracy can be obtained similarly even for bone cancer. This paper proposes the detection of bone cancer from the dataset taken from clinical dataset. Here the proposed design comprises of 2 phases in predicting the disorder with higher accuracy. The first stage is extracting the feature of segmented bone image using Gray-Level Co-occurrence Matrix (GLCM) method is applied to extract the features in terms of statistical texture-based and the second phase is classification of extracted feature using K-NN with decision tree algorithm. The simulation results show the enhanced classification results and extracted output with higher accuracy.

With the advancement of technology, new modes of communication have emerged and are being used in the field of academics. Traditional media played a pivotal role in spreading knowledge in all sections of societies in the world. Traditional media proved to be a powerful tool in the process of making learning and teaching more effective, interesting, and simple to insure everyone benefits to the maximum. Social media are newly-emerged communication networks which are in use not only for sharing information but also for education, knowledge transfer, and for building a global community of academicians. Different tools of social media are in use in different streams of education. Over the years, it has been realized that both traditional and social media have much potential and use in education at all three levels e.g. primary, secondary, and higher education. But, the integration of traditional and social media still has a long way to go in terms of acceptance. This chapter highlights some major points related to changing academic environment, with the use of technology in classes, students vs. teachers' perspectives on learning and teaching, academics, and use of media – Traditional vs. New media in classes and integrating traditional and social media within the academic environment.

Abstract We present a simple analytical model for the estimation of the maximum splat diameter of an impacting droplet on a subcooled target. This work is an extension of the isothermal model of Pasandideh-Fard et al. (1996). The model uses an energy conservation argument, applied between the initial and final drop configurations, to approximately capture the dynamics of spreading. The effects of viscous dissipation, surface tension, and contact angle are taken into account. Tests against limited experimental data at high Reynolds and Weber numbers indicate that an accuracy of the order of 5% is achieved with no adjustable parameters required. Agreement with experimental data in the limit We → ∞ is also very good. We additionally propose a simple model for the estimation of the thickness of the freezing layer developed at the droplet-substrate contact during droplet spreading. This model accounts for the effect of thermal contact resistance and its predictions compare favorably with experimental data.

Abstract Plasma-sprayed, molten molybdenum particles (~55 µm diameter) were photographed during impact on grit-blasted glass surfaces that were maintained at either room temperature or at 350°C. Droplets approaching the surface were sensed using a photodetector and after a known delay, a fast charge-coupled device (CCD) camera was triggered to capture time-integrated images of the spreading splat from behind the glass. A rapid two-color pyrometer was used to collect the thermal radiation from the spreading droplets to follow the evolution of their temperature and calculate the splat cooling rates. It was found that as the surface roughness increased, the maximum spread diameters of the molten molybdenum droplets decreased, while the splat cooling rates increased. Impact on non-heated and heated roughened glass with similar roughness values produced splats with approximately the same maximum spread diameters, skewed morphologies, and cooling rates. On smooth glass, the splat morphologies were circular, with larger maximum spread diameters and smaller cooling rates on non-heated smooth glass. An established model was used to estimate the splat-substrate thermal contact resistances. On highly roughened glass, the thermal contact resistance decreased as the glass roughness increased, suggesting that splat-substrate contact was improved as the molten metal penetrated the spaces between the large asperities.

The present study addresses a detailed experimental and numerical investigation on the impact of water dropletson smooth heated surfaces. High-speed infrared thermography is combined with high-speed imaging to couple the heat transfer and fluid dynamic processes occurring at droplet impact. Droplet spreading (e.g. spreading ratio) and detailed surface temperature fields are then evaluated in time and compared with the numerically predicted results. The numerical reproduction of the phenomena was conducted using an enhanced version of a VOF- based solver of OpenFOAM previously developed, which was further modified to account for conjugate heat transfer between the solid and fluid domains, focusing only on the sensible heat removed during droplet spreading. An excellent agreement is observed between the temporal evolution of the experimentally measured and the numerically predicted spreading factors (differences between the experimental and numerical values were always lower than 3.4%). The numerical and experimental dimensionless surface temperature profiles along the droplet radius were also in good agreement, depicting a maximum difference of 0.19. Deeper analysis coupling fluid dynamics and heat transfer processes was also performed, evidencing a strong correlation between maximum and minimum temperature values and heat transfer coefficients with the vorticity fields in the lamella, which lead to particular mixing processes in the boundary layer region. The correlation between the resulted temperature fields and the droplet dynamics was obtained by assuming a relation between the vorticity and the local heat transfer coefficient, in the first fluid cell i.e. near the liquid-solid interface. The two measured fields revealed that local maxima and minima in the vorticity corresponded to spatially shifted local minima and maxima in the heat transfer coefficient, at all stages of the droplet spreading. This was particularly clear in the rim region,which therefore should be considered in future droplet spreading models.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.5024

A unique non-dimensional scheme has been employed to analytically determine the steady-state temperature field within a cubic heat spreader of unity aspect-ratio undergoing centralized, uniform heat flux with square footprint. This ‘square-on-square’ boundary value problem was solved using method of Fourier expansion. Plots of the heat spreader non-dimensional maximum temperature and non-dimensional thermal spreading resistance are provided for various Biot numbers, heat spreader thicknesses and a newly-defined ‘area ratio’ — the ratio of heater cross-sectional area to heat spreader cross-sectional area (i.e. footprint). The proposed solution is advantageous for determining optimal heat spreading configurations with low Biot numbers — typical of many electronics packaging applications and heat spreaders of very high effective thermal conductivity. The presented results indicate that the non-dimensional, maximum temperature increases as the area ratio decreases and that a limiting, non-dimensional thermal spreading resistance exists for relatively thick heat spreaders regardless of area ratio or Biot number. A critical, non-dimensional thickness was also found in which the non-dimensional, maximum temperature becomes near unity regardless of Biot number or area ratio.

Abstract Development of methods to spray form materials by precisely controlled deposition of droplets can result in new manufacturing processes which offer improved metallurgical performance and reduced production costs. These processes require a more detailed knowledge of the fluid mechanics, heat transfer and solidification that occur during droplet spreading. Previous work using computer simulations of this process have been difficult to implement and have required long running times. This paper examines the use of an alternative, simplified, method developed by Madjeski for solving for the problem of droplet spreading and solidification. These simplifications reduce the overall splat spreading and solidification problem to a closed-form differential equation. This differential equation is then solved under various conditions as reported from recent publications of experimental and numerical results of drop analysis. The results from the model are compared in terms of maximum splat diameter, minimum splat thickness, and time for the droplet spreading to reach 95% of the maximum diameter. The results indicate that the accuracy of the model can be improved by accounting for energy losses in the initial rate of droplet spreading. The model results show that the predictions of experimental results are improved to within 30% over a wide range of conditions.

The impact process of a molten metal droplet impinging on a solid substrate surface is encountered in several technological applications such as ink-jet printing, spray cooling, coating processes, spray deposition of metal alloys, thermal spray coatings, manufacturing processes and fabrication and in industrial applications concerning thermal spray processes. Deposition of a molten material or metal in form of a droplet on a substrate surface by propelling it towards it forms the core of the spraying process. During the impact process, the molten metal droplet spreads radially and simultaneously starts losing heat due to heat transfer to the substrate surface. The associated heat transfer influences impingement behavior. The physics of droplet impingement is not only related to the fluid dynamics, but also to the respective interfacial properties of solid and liquid. For most applications, maximum spreading diameter of the splat is considered to be an important factor for droplet impingement on solid surfaces. In the present study, we have developed a model for droplet impingement based on energy conservation principle to predict the maximum spreading radius and the radius as a function of time. Further, we have used the radius as a function of time in the heat transfer equations and to study the evolution of splat-temperature and predict the spreading factor and the spreading time and mathematically correlate them to the spraying parameters and material properties.