Maximum Spread Research Articles

Droplet Impact on a Micro-structured Hydrophilic Surface: Maximum Spreading, Jetting, and Partial Rebound

• Droplet impact on a hydrophilic microstructured substrate was studied. • Various impact outcomes were observed in our experiments. • The effects of impact velocity and fluid viscosity on impact phenomena were studied. • The scaling law for the maximum spreading diameter was reported. • The satellite droplets produced in jetting and partial rebound were analyzed. In this paper, we perform an experimental study of droplet impact on a partially wetting hydrophilic substrate composed of cylindrical micro-pillars. Water and glycerol are mixed at different ratios to primarily change liquid viscosity and keep surface tension approximately constant. We show that our microstructured hydrophilic surface can exhibit many of the same impact outcomes as hydrophobic surfaces including spreading, recoiling, jetting, and partial rebound. A regime map is constructed to convey the overall effects of the impact velocity and viscosity on the impact outcomes. Our data indicate that the maximum spreading factor β max generally follows the power law with the Weber number We as β max ∼ We 0.25 . However, the scaling relation of β max ∼ We 0.2 Re 0.04 provides a better correlation for β max because the viscous dissipative effect due to flow through the micro-pillars on the substrate becomes increasingly important for more viscous fluids. The rapid jet caused by the collapse of the air cavity in the recoil phase grows in a self-similar pattern. The relationship between the size of the top jet droplet and jet velocity is found to obey the same scaling law originally proposed for the bubble bursting jet. The partial rebound occurs only for low viscosity fluids with relatively high impact velocity. The size of the rebounding droplet emitted by the breakup of inertially stretched thick liquid thread in the partial rebound is found to be nearly independent of the impact velocity. The elapsed time between droplet impingement and partial rebound event scales with the capillary time.

Using Dominated Solutions at Edges to the Diversity and the Uniformity of Non-dominated Solution Distributions in NSGA-II

This paper proposes a method for improving the diversity of the Pareto front and the uniformity of non-dominated solution distributions in a fast elitist non-dominated sorting genetic algorithm (NSGA-II), which is an evolutionary multi-objective optimization algorithm. Conventional NSGA-II has excellent convergence to the Pareto front, but it has been reported that for some test cases, it does not produce a more diverse solution distribution than the strength Pareto evolutionary algorithm 2 (SPEA2). In addition, selection using the crowding distance may cause a bias in the selected solution distribution. To avoid this problem, we propose a method that archives dominated solutions that may be effective in improving diversity in the conventional search process when used for genetic operations, and mates these archived solutions with non-dominated solutions at the edge of rank 1 for each objective function. We experimentally compare this approach with the conventional method on the typical ZDT suite of multi-objective test problems and a two-objective constrained knapsack problem. By evaluating the performance based on Pareto front diagrams, the number of non-dominated solutions, the maximum spread and hypervolume values, we show that the proposed method is effective at improving the diversity at both ends of the Pareto optimal front and the solution distribution.

Pancake-shaped freezing of a droplet impacting a supercooled surface: Evidence for a threshold temperature

The residual diameter of a droplet at a temperature of 25 °C impacting a cold surface was investigated using high-speed photography. The temperature of the impacted surface was varied from −50 to 25 °C. A threshold temperature was found below which the impacting droplet freezes near the maximum spreading diameter, resulting in pancake-shaped freezing. However, above the threshold temperature, the lamella retracts before freezing. The maximum spreading diameter remains nearly unchanged for surfaces with various temperatures for the same Weber number. Variations of the threshold temperature required for pancake-shaped freezing as a function of the Weber number were determined. The threshold temperature decreases as the Weber number increases. A model for predicting the threshold temperature is proposed and compared with experimental observations. It is shown that it is the freezing time of the lamella tip that determines the threshold temperature.

Multi‐objective quantum atom search optimization algorithm for electric vehicle charging station planning

This paper presents an effective planning methodology for electric vehicle (EV) fast-charging stations (CS) using a multi-objective binary version of the atom search optimization (ASO) algorithm. The proposed method uses quantum operations to binarize the algorithm and achieve a higher convergence rate than the existing binary ASO algorithm. Additionally, a modified atom selection function is used to improve the searching capability of the ASO algorithm. Furthermore, the nondominated sorting procedure and pareto concepts are infused to solve the CS location problem (CSLP) considering the EV travel time, CS costs, and grid power loss as independent multi-objectives. The efficacy of the proposed multi-objective quantum ASO (MO-QASO) algorithm is evaluated using performance metrics namely, inverted generational distance (IGD), spacing (SP), and maximum spread (MS). The MO-QASO simulation results are compared with the results of other heuristic algorithms. MO-QASO achieves the best IGD (0.0021), SP (0.0002), and MS (0.9982) values, verifying the convergence and diversity of the algorithm. Importantly, the best CS planning solution obtained from MO-QASO is similar to the true solution obtained from the exhaustive search method. The MO-QASO efficiency is further validated by solving a CSLP from literature. Thus, the MO-QASO algorithm is a promising optimization tool for solving CSLP.

Vertical Dense Effluent Discharge Modelling in Shallow Waters

Vertical dense effluent discharges are popular in outfall system designs. Vertical jets provide the opportunity to be efficient for a range of ambient currents, where the jet is pushed away so as not to fall on itself. This study focuses on the worst-case scenario of the dilution and mixing of such jets: vertical dense effluent discharges with no ambient current, in shallow water, where the jet impinges the water surface. This scenario provides conservative design criteria for such outfall systems. The numerical modelling of such jets has not been investigated before and this study provides novel insights into simulations of vertical dense effluent discharges in shallow waters. Turbulent vertical discharges with Froude numbers ranging from 9 to 24 were simulated using OpenFOAM. A Reynolds stress model (RSM) was applied to characterize the geometrical (i.e., maximum discharge rise Zm and lateral spread Rsp) and dilution μmin properties of such jets. Three flow regimes were reproduced numerically, based on the experimental data: deep, intermediate, and impinging flow regimes.

Dynamic behavior of impinging drops on water repellent surfaces: Machine learning-assisted approach to predict maximum spreading

The study of drop dynamic undergoing collision with solid surfaces seems quite necessary due to its practical applications ranging from coating industries to anti-icing and self-cleaning surfaces. Therefore, we experimentally studied the dynamic of impinging drop on water-repellent surfaces for a wide range of drop properties and initial velocities in terms of weber number (We). We considered the maximum spreading diameter to quantify the spreading dynamic. We modified one of the existing energy-balance models to analytically predict the observed maximum spreading diameters. We showed that above a critical We number (roughly 60–80), the maximum spreading diameter of superhydrophobic surfaces starts to deviate from those of hydrophobic surfaces. Therefore, we incorporated an adjusting factor into the energy-balance model to consider the transition from hydrophobicity to superhydrophobicity. Moreover, we developed a machine learning approach to predict the maximum spreading diameter as a function of drop properties and surface characteristics. Using the machine learning approach, it was found that beyond a critical contact angle (CAadv ∼ 150°–160°) the maximum spreading diameter does not depend on the contact angle anymore. Moreover, for low We numbers, the maximum spreading diameter decrease with increasing the contact angle, while for high We numbers they are directly proportional.

Dynamic and kinematic characteristics of unsteady motion of a water-in-oil emulsion droplet in collision with a solid heated wall under conditions of convective heat transfer

The paper presents the experimental results of spreading, fingering and corona-like splashing of water-in-oil emulsion droplets based on n-decane, isoparaffin oil and distilled water in the range of Weber numbers We = 100–900, wall temperatures Tw = 20–80 °C and in collision with a smooth solid surface. The spreading features and separate convective rolling structures in emulsion droplets are examined at the late stages of wetting. The effect of Tw on the viscous dissipation energy and the maximum spreading coefficient is established. The validity of the assumptions explaining the contradictory behavior of the maximum spreading diameter of emulsion droplets with increasing temperature is studied. The assumption of unstable behavior of the emulsion droplet rim during spreading is proposed. The maximum emulsion corona diameter and height decrease linearly with the Tw growth due to the longer corona lifetime. The maximum corona diameter increases following the power law with increasing the Brinkman number due to an increase in the liquid viscosity and a decrease in Tw. The results help to predict the corona's behavior by determining the relationship between the viscous dissipation of the spreading liquid and the energy transferred to the liquid from the wall due to molecular (thermal) conduction.

Hydrodynamic analysis of the energy dissipation of droplets on vibrating superhydrophobic surfaces

In this paper, experimental and numerical methods are presented to describe the hydrodynamic process of the vibration-induced detachment of a droplet from a superhydrophobic surface. We conduct the investigation of the droplet dynamics under various vibration and impact parameters, from an energy conversion perspective. In particular, the energy dissipation that occurs following the droplet impact is analyzed quantitatively. We identify three viewpoints on vibration-induced droplets. Firstly, the phase angle is the dominant factor in characterizing the droplet morphology evolution and energy dissipation on a vibrating surface. The law governing the initial phase angle is affected by the vibration frequency, while the intensity is affected by the vibration amplitude. Secondly, the energy dissipation is positively correlated with the maximum spreading diameter and impact velocity. A larger initial diameter tends to produce a longer contact time. Finally, the central jet formation depends heavily on the upward velocity of the concave liquid, under the peculiar morphology of a vibration-induced droplet. For all these effects, up to 60% of the total energy is squandered during impact, while the surface energy remains almost constant. Much of the droplet's kinetic energy is lost in resisting the viscous force of the substrate.

Thermographic Observation and Hydrodynamic Patterns of Inclined Ethanol Droplet Train Impingement on a Non-Uniformly Heated Glass Surface

Droplet train impingement is a fundamental approach to mimic the complicated interactions between the fluid and the substrate in advanced thermal engineering applications in industry. Differently from previous studies, the main original contribution of this study is to perform an inclined droplet train impingement on a non-uniformly heated surface. Ethanol was used as the liquid for droplet train impingement applications, while glass substrate was selected as the target surface. The inclined flow angle was 63 degrees. Both optical and thermographic observations were performed on the target surface by focusing on the droplet impact area. Three experimental sets were created with the Weber numbers 667.57, 841.90, and 998.01. A surface temperature range was selected between 85.00 °C and 200.00 °C, which was above the boiling point of the ethanol. The maximum spreading length was measured at 0.97 mm at the surface temperature of 82.00 °C for the experiment with the Weber number of 998.01, whilst the minimum spreading length was found at 0.18 mm at the highest surface temperature for the experiment with the Weber number of 667.57. A uniform splashing direction was observed above 170.00 °C for all experiments, which meant that the sign of the transition regime appeared.

Droplet bouncing on topological nonwetting surfaces via laser fabrication

PurposeThe purpose of this paper is to show that the droplet impact phenomenon is important for the advancement of industrial technologies in many fields such as spray cooling and ink jet printing. Droplet bouncing on the nonwetting surfaces is a special phenomenon in the impact process which has attracted lots of attention.Design/methodology/approachIn this work, the authors fabricated two kinds of representative nonwetting surfaces including superhydrophobic surfaces (SHS) and a slippery liquid-infused porous surface (SLIPS) with advanced UV laser processing.FindingsThe droplet bouncing behavior on the two kinds of nonwetting surfaces were compared in the experiments. The results indicate that the increasing Weber number enlarges the maximum droplet spreading diameter and raises the droplet bounce height but has no effect on contact time.Originality/valueIn addition, the authors find that the topological SHS and SLIPS with the laser-processed microwedge groove array produce asymmetric droplet bouncing with opposite offset direction. Microdroplets can be continuously transported without any additional driving force on such a topological SLIPS. The promising method for manipulating droplets has potential applications for the droplet-based microfluidic platforms.

Ecological multi-objective joint optimized scheduling of cascade hydropower plants based on improved marine predators algorithm

The joint operation of large cascade hydropower plants changes the natural hydrological regime of the river, thereby reducing the stability of the basin ecosystem. To coordinate the power generation of cascade hydropower plants' demand and ecological environment demand, this paper establishes an ecological multi-objective optimized scheduling model (EMOOSM) for cascade hydropower plants, aiming at the maximum power generation of cascade hydropower plants and the minimum inappropriate ecological water volume. To solve the complex EMOOSM, a marine predators algorithm was introduced, which was improved and extended to the multi-objective solution level. Multi-objective improved marine predators algorithm (MOIMPA) based on Cauchy variation preserves non-dominated solutions by adding an external archive set and maintaining them with a crowdedness-based fast sorting strategy. The optimal dispatching results of a cascade hydropower plant in China's Pearl River system show that MOIMPA can effectively deal with conflicting power generation and ecological goals. The recommended scheme determined according to the fuzzy set theory and the principle of maximum satisfaction can adapt to the change law of ecological demand and reasonably adjust the inappropriate ecological water volume in the stage according to the different ecological sensitivity in the dispatching period. The recommended scheme in the normal year reduces the inappropriate ecological water volume caused by the operation of the cascade reservoir by 1.7156 × 105 m3 at the expense of only 1.12% of the power generation, effectively balancing the power generation and ecological benefits of the cascade hydropower plant operation. Compared with the results of other algorithms, the Pareto solution set obtained by MOIMPA has a better diversity metric (DM) indicator, maximum spread (MS) indicator, and hypervolume (HV) indicator. The research results provide a theoretical basis and reference for the ecological operation research of cascade hydropower plants.

Impact dynamics of air-in-liquid compound droplets

Compound droplets are utilized in applications ranging from preparation of emulsion to biological cell printing and additive manufacturing. Here, we report on the impact dynamics of an air-in-liquid hollow compound droplet on a solid substrate. Contrary to the impact of pure droplets and compound droplets with liquids of similar densities, a compound droplet with an encapsulated air bubble demonstrates the formation of a counterjet in addition to the lamella. We experimentally investigate the influence of the size of the air bubble, liquid viscosity, and height of impact on the evolution of counterjet and the spreading characteristics of the lamella. For a given hollow droplet, the volume of the counterjet is observed to depend on the volume of air and liquid in the droplet and is independent of the viscosity of the liquid and impact velocity of the droplet. We observe that the spread characteristics, counterintuitively, do not vary significantly compared to that of a pure droplet having an identical liquid volume as the hollow droplet. We propose a model to predict the maximum spread during the impact of a hollow droplet based on the energy interaction between the spreading liquid and the liquid in the counterjet during the impact process.

Simulation of coalescence dynamics of droplets on surfaces with different wettabilities

The head-on-collision coalescence dynamics for droplets on surfaces with different wettabilities was numerically investigated by using the method of coupled level set and volume of fluid, and a high-speed video experiment was used to validate the simulation results. The simulated coalescence behavior of droplets is consistent with the experiment results. We compared droplets with different Weber numbers (3.67 ≤ We ≤ 50) coalescing on solid surfaces of different wettabilities and contact angles (80° ≤ α ≤ 160°). The result is a regional division diagram that relates Weber number and contact angle based on different coalescence phenomena. The factors causing droplet deposition, air entrapment, bounce, and partial bounce during collision coalescence are described based on an analysis of interactions involving inertial forces, surface tension, and wall adhesion forces. Furthermore, the effect of Weber number and contact angle on droplet coalescence behavior is elaborated by analyzing the relationship between coalescence time and wettability radius under different Weber numbers and contact angles. Finally, through an energy analysis, we explain the maximum spreading radius and oscillation of droplets with different Weber numbers on solid surfaces with different wettabilities and in the process of head-on-collision coalescence.

Droplet impacts on cold surfaces

We study drop impact for the case where the impacted surface is cooled below the freezing temperature of the liquid droplet. The freezing is found to affect the spreading dynamics of the impacting drops and, thus, the degree of surface coverage. The cooling of the surface leads to the arrest of the three-phase contact line, impeding droplet spreading and, thus, drastically reducing the maximum spreading diameter. Besides the surface temperature, the impact speed is also an important parameter: the higher the impact speed, the more the droplet spreads before arrest. Based on experimental observations of droplet impacts using two different liquids and two different substrates, we show using a combination of experiments and a one-dimensional freezing model, that droplet arrest occurs when a solid layer of the liquid forms on the substrate: droplet arrest occurs when this solid layer reaches a well-defined critical thickness. We then devise a simple model that efficiently predicts the maximum spreading diameter of droplets impinging, at different velocities, and freezing onto surfaces maintained at different temperatures below the liquid freezing point.

Flame Spread Pulsation Characteristics of Transformer Oil Vertical Spill Fire

Abstract To investigate the effects of fuel discharge rate and initial fuel temperature on flame pulsation characteristics of vertical spill fire, a series of experiments under continuous leakage conditions are conducted on a specially designed experimental setup, for which transformer oil is selected as the fuel. Results show that the vertical spill fire burning area can be divided into three parts. Both the main flame and the flash flame are involved in the flame pulsation behavior, and the essence of the flame pulsation of the vertical spill fire is the periodic alternation of the diffusion flame and the premixed flame. Flame pulsation frequency shows a linear negative correlation with the fuel leakage rate, it decreases from 3.56 Hz (4.98 ml m−1s−1) to 2.439 Hz (15.93 ml m−1s−1), and it has a positive correlation with the initial fuel temperature. As the fuel discharge rate increases, the pulsation amplitude increases while the flame transient spread rate decreases, both of them have no significant correlation with the initial fuel temperature. The ratio of the average flame pulsation amplitude to the maximum pulsation amplitude is between 0.57 and 0.76. The flame transient spread rate shows a negative correlation with the fuel discharge rate, the maximum flame spread velocity reaches 3.17 m/s and 2.85 m/s in the growing phase and shrinking phase respectively. Due to the entrainment effect of the flame plume, the flame transient spread rate in the shrinking phase is higher than that in the growing phase. Analyzed the diffusion process of fuel vapor and the heat transfer mechanism of vertical spill fire, the control of fuel leakage rate and initial temperature on the flame pulsation characteristics is mainly manifested in its influence on the fuel evaporation and diffusion process and the length of preheating area. This work provides data supplement on the flame spread of liquid fuel spill fire.

Application of MOMSA algorithm for optimal operation of Karun multi objective multi reservoir dams with the aim of increasing the energy generation

Multi-reservoir system operation is a challenging and complex task, because of the curse of uncertainties, nonlinearities, dimensionalities and conflicts among the various contradictory objectives. Contemporaneous optimization of such competing objectives needs improving the capability of existing optimization algorithms. This study reports the first application of the recently-introduced multi-objective moth swarm algorithm (MOMSA) in optimization of long-term operation of the large Karun multi-purpose multi-reservoir system. In this algorithm, the decision variables were defined in such a way that the algorithm synchronization capability has improved. Furthermore, a robust mechanism (crowding distance mechanism) with high exploratory capability was employed to select the most efficient solutions within the population. To evaluate the algorithm's efficiency, the results of MOMSA were compared with two well-known multi-objective algorithms of the non-dominated sorting genetic algorithm-II (NSGA-II) and the strength Pareto evolutionary algorithm-II (SPEA-II). To compare the capability of these algorithms, a set of statistical indices including the generational distance (GD), the spacing (S), the spread (Δ), and the maximum spread (MS), along with four reservoir's performance evaluation indicators of the reliability (Rel), the vulnerability (Vul), the resiliency (Res), and the sustainability index were employed. The results demonstrated the superior performance of the MOMSA in solving the Karun multi-reservoir system problem with GD = 259.64, S = 3574.69, Δ = 0.755 and MS = 18420.8. The MOMSA, with the optimized average annual energy production of 15669.7 GW, outperformed the NSGA-II (7569.1 GW) and SPEA-II (9026.3 GW) algorithms. Furthermore, the developed algorithm could supply the downstream demands with a sustainability index of 86.73%, while the corresponding values for the NSGA-II, the SPEA-II and the real operating conditions were 22.73%, 46.09% and 78.87%, respectively. In addition, among the utilized algorithms, the MOMSA demonstrated the best results for flood control purpose. The superior performance of MOMSA will ensure it as a robust algorithm in the optimization of complex and large-scale problems.

Adaptive influence maximization under fixed observation time-step

The influence maximization problem aims to find some seeds which can cause the maximum influence spread results in a social network. Most researches focus on the non-adaptive strategies, in which all seeds are selected at once. For the non-adaptive strategies, the seeds may influence other seeds in the influence spread process and make the waste of budget. This paper considers the adaptive strategies and studies the adaptive influence maximization and adaptive stochastic influence maximization in the general feedback model. These problems select seeds adaptively, and it completes each selection after the fixed observation time-step. In this paper, we utilize the adaptive greedy to solve these problems and propose a theoretical analysis by introducing a comparative factor. In addition, we present the feasible approximation algorithm using the reverse sampling technique. Finally, we carry out experiments on three networks to show the efficiency of adaptive strategies.

Mapping Spatio-temporal Variations of Surface Water Area of Tanks in Coimbatore Corporation Using Google Earth Engine

Surface water is one of the most significant elements of the earth's ecosystem. It is the basic information for analysing the changes in the environment. Therefore it is important to monitor water resources accurately. Nowadays remote sensing plays a major role in extraction of water spread area. In this study, change in water spread area of tanks was mapped for Coimbatore corporation from 2000 to 2021. The analysis was performed in Google earth engine platform using Landsat ETM+ and Landsat OLI datasets. The images for pre monsoon and post monsoon season were scrutinized and classified using random forest classifier in Google earth engine. The area of each tanks and their deviations were calculated for the study period. Results of the study showed that the lowest water spread area was observed in the period from 2000 to 2005 for both pre monsoon and post monsoon season. The tank has maximum water spread area during post monsoon season. The difficulties that has been confronted during the research is the unavailability of images due to cloud cover. The study shows that the random forest classifier can be effectively used to extract water features and water spread area.

A Machine Learning Approach for Predicting the Maximum Spreading Factor of Droplets upon Impact on Surfaces with Various Wettabilities

Drop impact on a dry substrate is ubiquitous in nature and industrial processes, including aircraft de-icing, ink-jet printing, microfluidics, and additive manufacturing. While the maximum spreading factor is crucial for controlling the efficiency of the majority of these processes, there is currently no comprehensive approach for predicting its value. In contrast to the traditional approach based on scaling laws and/or analytical models, this paper proposes a data-driven approach for estimating the maximum spreading factor using supervised machine learning (ML) algorithms such as linear regression, decision tree, random forest, and gradient boosting. For this purpose, a dataset of hundreds of experimental results from the literature and our own—spanning the last thirty years—is collected and analyzed. The dataset was divided into training and testing sets, each representing 70% and 30% of the input data, respectively. Subsequently, machine learning techniques were applied to relate the maximum spreading factor to relevant features such as flow controlling dimensionless numbers and substrate wettability. In the current study, the gradient boosting regression model, capable of handling structured high-dimensional data, is found to be the best-performing model, with an R2-score of more than 95%. Finally, the ML predictions agree well with the experimental data and are valid across a wide range of impact conditions. This work could pave the way for the development of a universal model for controlling droplet impact, enabling the optimization of a wide variety of industrial applications.

Contact time of a droplet impacting hydrophobic surfaces

A droplet impacting hydrophobic surfaces is explored via lattice Boltzmann method simulations. Dynamics of the spreading and retraction processes of the impacting droplet with different surface wettability (θ = 106°–145°) at various Weber numbers (We = 15–35) and Reynolds numbers (Re = 235–359) are investigated. It indicates that the spreading time, the time interval from a droplet just touching the surface to reaching the maximum spreading diameter, is a fixed value that is not related to the above factors. The retraction time, the time interval from a droplet reaching the maximum spreading diameter to rebounding the surface, is just closely dependent on the surface wettability. Therefore, the contact time, the sum of the spreading time and the retraction time, is mainly related to the retraction process and dependent on the surface wettability. The time is commonly normalized as the non-dimensional time, τ = t/(ρR03/σ)1/2, where R0 is the initial droplet radius and σ is the surface tension. The emphasis of this work is placed on establishing a relationship of the contact time with the surface wettability. Based on simulation research and theoretical modeling, the surface wettability is incorporated into the scaling law of contact time, and a modified scaling law, tc ∼ (R0/V0)We1/2(1 − cosθ)−1/2, where V0 denotes the initial impact velocity, is established for a droplet impacting hydrophobic surfaces of θ = 106°–145°and We = 15–35. It is demonstrated that the scale relationship can be well applied to calculate the contact time of a droplet impacting hydrophobic surfaces for moderate Weber numbers.