Spreading Radius Research Articles

Insight into Mocha Diffusion Occurring during Ethanol Droplet Spreading on Acrylic Paint.

Mocha diffusion, a significant interfacial phenomenon in pottery painting, remains insufficiently understood in the documented literature regarding its dynamics. This study experimentally investigates Mocha patterns by quantitatively dripping ethanol droplets onto an acrylic paint surface. Results indicate that the spreading radius increases with the ethanol mass fraction, while the fractal period decreases. The fractal dimension of all Mocha patterns approximates 1.4087. Marangoni flow, generated by the volatilization of ethanol, is crucial for the growth and fractal formation of the "dendrites" in this spreading. The scaling analysis is used to interpret the spreading dynamics. This work encourages the interface science community to develop a comprehensive theory for the dynamics of Mocha diffusion and highlights the potential of this intriguing decorative technique.

Evaluation of the Epidemic Situation of Anthrax in Armenia Over the Last Decade.

Anthrax is a World Organisation for Animal Health (WOAH)-listed disease that must be reported upon confirmation based on the Terrestrial Animal Health Code. Anthrax poses a serious health issue for unvaccinated livestock, is a threat to humans through interaction with contaminated livestock and animal products and is endemic in many areas throughout the world, including the Transcaucasian Region. Despite several control and eradication efforts that have been implemented by the government of the Republic of Armenia (RA), sporadic cases of anthrax are still reported. We sought to understand the epidemic situation of anthrax in RA during the last 10 years (2012-2023) based on analysis of outbreaks and reported cases in cattle and humans. We collected and evaluated officially reported data from human and animal cases, such as time, location, animal species, disease intensity and spread radius. The data and various parameters were mapped using ArcGIS to prepare a viable risk assessment. Based on the officially available data and reports, there have been 80 human cases and 55 animal cases of anthrax confirmed in RA from 2012 to 2023. We also identified the presence of anthrax spores in soil and environmental samples near animal burial sites in RA in 2015-2017 through polymerase chain reaction (PCR) testing. Upon comparing the human and animal cases by frequency and intensity, the human cases are directly proportional to the animal husbandry practices performed in RA. The detection of the anthrax pathogen at the burial sites highlights the continued threat in these areas. Thus, it is imperative to secure and monitor any areas that have been used for anthrax burial and limit the movement of animals in these areas. In the future, legislation should be updated to prioritise incineration of anthrax-infected carcasses instead of burial to limit further exposure to animals and humans.

Rapid Spreading of Yield-Stress Liquids.

When a liquid drop makes initial contact with any surface, an unbalanced surface tension force drives the contact line, causing spreading. For Newtonian liquids, either liquid inertia or viscosity dictates these early regimes of spreading, albeit with different power-law behaviors of the evolution of the dynamic spreading radius. In this work, we investigate the early regimes of spreading for yield-stress liquids. We conducted spreading experiments with hydrogels and blood with varying degrees of yield stress. We observe that for yield-stress liquids, the early regime of spreading is primarily dictated by their high shear rate viscosity. For yield-stress liquids with low values of high shear rate viscosity, the spreading dynamics mimics that of Newtonian liquids like water, i.e., an inertia-capillary regime exhibited by a power-law evolution of spreading radius with exponent 1/2. With increasing high shear rate viscosity, we observe that a deceptively similar, although slower, power-law spreading regime is obeyed. The observed regime is in fact a viscous-capillary where viscous dissipation dominates over inertia. The present findings can provide valuable insights into how to efficiently control moving contact lines of biomaterial inks, which often exhibit yield-stress behavior and operate at high print speeds, to achieve desired print resolution.

Bounds on the spreading radius in droplet impact: the inviscid case

We consider the classical problem of droplet impact and droplet spread on a smooth surface in the case of an ideal inviscid fluid. We revisit the rim–lamella model of Roisman et al. (Roisman et al . 2002 Proc. R. Soc. Lond. A 458 , 1411–1430 ( doi:10.1098/rspa.2001.0923 )). This model comprises a system of ordinary differential equations (ODEs); we present a rigorous theoretical analysis of these ODEs, and derive upper and lower bounds for the maximum spreading radius. Both bounds possess a W e 1 / 2 scaling behaviour, and by a sandwich result, the spreading radius itself also possesses this scaling. We demonstrate rigorously that the rim–lamella model is self-consistent: once a rim forms, its height will invariably exceed that of the lamella. We introduce a rational procedure to obtain initial conditions for the rim–lamella model. Our approach to solving the rim–lamella model gives predictions for the maximum droplet spread that are in close agreement with existing experimental studies and direct numerical simulations.

An equivalent surface model bridging intermolecular interactions and the normalization of substrate wettability

A liquid deposited on a solid surface exhibits various wetting properties, primarily influenced by solid–liquid intermolecular interactions. Achieving a well-estimation of wetting behaviors on textured surfaces remains challenging because the influence of surface textures on intermolecular interactions is unclear. Here, an equivalent surface model is proposed to unify the wettability of both plane and textured substrates through intermolecular interactions. We show that by incorporating intermolecular interactions, lattice structures, and surface topographies, the substrate wettability can be tailored in an equivalent plane with the same average Lennard–Jones potential energy field E. The wettability of one substrate (plane or patterned) is transferred from non-wetting, partial wetting to complete wetting by adjusting the potential well depth of E, εa. With enhancing εa, complete wetting is achieved under the critical potential well depth of E, εac. Before εac, the spreading radius grows as R ∼ t1/1.47 until reaches equilibrium. In this scenario, the equilibrium contact angle θ and spreading factor β are strongly dependent on εa, and cos θ is linear to εa. When exceeding εac, complete wetting is achieved, and droplets spread with a precursor film as R ∼ t1/2.3 latterly. This model builds a bridge to link intermolecular interactions and substrate wettability normalization. This strategy offers a framework for substrate surface design and wettability manipulation, catering to applications such as photoresist-drop dispensing in nanoimprint lithography, surface design for grating antifouling, and anti-icing on aircraft surfaces.

Heat transfer during droplet impact on a cold superhydrophobic surface via interfacial thermal mapping

AbstractUndesired heat transfer during droplet impact on cold surfaces can lead to ice formation and damage to renewable infrastructure, among others. To address this, superhydrophobic surfaces aim to minimize the droplet surface interaction thereby, holding promise to greatly limit heat transfer. However, the droplet impact on such surfaces spans only a few milliseconds making it difficult to quantify the heat exchange at the droplet–solid interface. Here, we employ high‐speed infrared thermography and a three‐dimensional transient heat conduction COMSOL model to map the dynamic heat flux distribution during droplet impact on a cold superhydrophobic surface. The comprehensive droplet impact experiments for varying surface temperature, droplet size, and impacting height reveal that the heat transfer effectiveness () scales with the dimensionless maximum spreading radius as , deviating from previous semi‐infinite scaling. Interestingly, despite shorter contact times, droplets impacting from higher heights demonstrate increased heat transfer effectiveness due to expanded contact area. The results suggest that reducing droplet spreading time, as opposed to contact time alone, can be a more effective strategy for minimizing heat transfer. The results presented here highlight the importance of both contact area and contact time on the heat exchange between a droplet and a cold superhydrophobic surface.

Control of chemical release in hydrogel microvalve array for localized chemical stimulations

Chemical stimulation is considered as one of the most promising therapeutic solutions for degenerated retina due to its ability to mimic a natural chemical signaling pathway. However, the majority of demonstrated platforms actuate chemicals using bulky external setups. Hence, developing high-resolution chemical release platforms with remote-controlled actuation mechanism is of great interest to the next generation of chemical prosthetics. Moreover, the effectiveness of chemical stimulation depends on several parameters, such as the chemical dosage, pulse duration, and spread radius. Therefore, to engineer the chemical release profile, the actuation mechanism of these localized chemical release platforms needs to be thoroughly studied to facilitate modifications. In this study, we have presented a high-resolution chemical release platform based on a macroporous silicon membrane structure. Chemical release ports defined in the membrane pores can be remotely actuated through thermo-responsive poly(N-isopropylacrylamide) (PNIPAAm) hydrogel with near-infrared (NIR) light. As plasmonic heating elements, gold nanorod (GNR) was incorporated within PNIPAAm hydrogel. The pore size of the hydrogel was tuned by varying tetrahydrofuran content in the hydrogel polymerization solution. We have shown that the chemical release properties through membrane pores can be controlled as required using this approach. This insight can be used to engineer the relevant chemical release parameters, thereby creating an efficient chemical stimulation platform.

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Non-Axisymmetric Bouncing Dynamics on a Moving Superhydrophobic Surface

The phenomenon of droplet impact on moving surfaces is widely observed in fields such as transportation, rotating machinery, and inkjet printing. Droplets exhibit non-axisymmetric behavior due to the motion of solid surfaces which significantly determines core parameters such as contact time, maximum spreading radius, and bounding velocity, thereby affecting the efficiency of related applications. In this study, we focus on the kinetics and morphology of the non-axisymmetric bouncing behaviors for droplets impacting on a moving superhydrophobic surface (SHPS) within the normal (Wen) and tangential (Wet) Weber numbers. Considering the influences of the moving surface on the contact area and contact time, the previous scaling formula for the horizontal velocity of droplets has been improved. Based on the velocity superposition hypothesis, we establish a theoretical model for the ratio of the maximum spreading radius at both ends depending on Wen and Wet. This research provides both experimental and theoretical evidence for understanding and controlling the non-axisymmetric behavior of droplets impacting on moving surfaces.

Analysis of the spreading radius in droplet impact: The two-dimensional case

We study droplet impact problems in a 3D cylindrical or equivalent 2D Cartesian geometry. Such structures do have an approximate experimental realization, and they are often simulated as a testbed for computational methods. We focus on droplet impact on a smooth homogeneous surface as well as head-on collision of two droplets. We perform an energy-budget analysis and introduce a correlation, which predicts the maximum spreading radius as a function of Reynolds number and Weber number. We show how the dissipation term in this analysis can be decomposed into boundary-layer dissipation in the droplet lamella (where applicable) and head loss. We use existing results in the literature (simulations and experiments) as well as our own simulation results to validate the correlation. Dissipation by head loss is a key term in the analysis: only by modeling it accurately, one can obtain good agreement between the simulations and the theory.

Experimental study on spread radius and burning rate of spill fires on a fine sand substrate

Experimental study on spread radius and burning rate of spill fires on a fine sand substrate

Impinging blood droplets on different wettable surfaces: Impact phenomena, contact line motion, post-impact oscillation and dried stains

Understanding the underlying hydrodynamics of impinging blood droplets and finding out the physical parameters determining the bloodstain characteristics are of great importance in blood related forensic investigations. In this work, the impact of non-Newtonian blood droplets on solid surfaces ranging from lyophilic to superlyophobic was systematically investigated and compared to that of Newtonian droplets with a similar dynamic shear viscosity. We show that impinging blood droplets behave as low-viscosity Newtonian droplets in the short-time spreading, which is dominated by capillary and inertial forces, but their non-Newtonian viscoelasticity would notably affect the droplet retraction and post-impact oscillation occurring in large timescales. Whereas the strong liquid–solid adhesion and the non-Newtonian elongational viscosity hinder droplet recoiling and thus alter the impact phenomena on lyophobic and superlyophobic surfaces, the shear and elongational viscosities are coupled to result in higher damping coefficients of oscillating blood droplets after deposition, in comparison to that of impinging Newtonian droplets. The size of the dried bloodstain was found to be different from both the maximum spreading radius of the droplet that can reach during impact and the final radius of the deposited droplet after oscillation, and their correlations are highly dependent on the impact velocity and surface wettability. Moreover, the morphologic characteristics of the bloodstains would also be changed by varying either the impact velocity or the surface wettability. We envision that these findings can not only find applications in the bloodstain pattern analysis, but also provide useful information for medical diagnosis based on blood droplet test.

Early stage of bubble spreading in a viscous ambient liquid

We investigate numerically the spreading dynamics of a bubble coming into contact with a smooth solid substrate in a viscous liquid. The substrate is partially wettable, and the singularity of the moving contact line is relieved by adopting the Navier-slip model. The Stokes equations are solved by employing a boundary element method coupled with adaptive mesh refinement. This allows us to realize sufficiently small slip lengths down to $O(10^{-5})$ in dimensionless form, which is crucial to resolve the local interface structures at the early stage of spreading. The results show that the early-stage spreading of the bubble is always characterized by the growth and propulsion of a dewetting liquid rim close to the contact line, while the macroscopic interface remains unchanged. The evolution of the contact line and the morphology of the rim depends on the wettability and the slip length, and a parametric investigation is performed. Based on mass conservation, a relation between the rim size and the spreading radius is established. We also propose an analytical prediction of the temporal variation in the contact line radius at the early stage of spreading, which is found to follow a logarithmically corrected linear relation rather than a pure power law. Moreover, the early stages of bubble spreading are qualitatively similar for two-dimensional and axisymmetric configurations.

Universal scaling of droplet retraction dynamics on vibrating surfaces

Over the past decade, extensive efforts have been made in the study of droplet impact, especially on stationary surfaces, owing to its direct applications in thermal cooling, self-cleaning, and power generation. However, many practical applications, such as ultrasonic cleaning, aerosolized drug delivery, and vibration-assisted welding, involve the direct interaction of droplets with vibrating surfaces, on which droplets undergo spreading and retraction. Distinct from stationary surfaces where the retraction behaviors, such as the retraction velocity and rate, are mainly governed by the surface wettability and droplet inertia, the retraction behaviors on vibrating surfaces become complicated due to the vibration velocity, which dictates the outcomes of droplet impact, such as the pinning, bouncing, gyrating, and jetting. Here, we revealed the synergistic effect of droplet inertia and vibration velocity on droplet retraction. We found that the droplet retraction behaviors on both stationary and vibrating surfaces could be characterized by a universal scaling law, allowing us to analyze and predict the maximum droplet retraction velocities. Moreover, we found that the maximum retraction rate increased with the maximum spreading radius at low Weber numbers. We demonstrated that the droplet retraction dynamics at both low Weber numbers and high Weber numbers could be unified into one integrated model, which indicates the decisive role of the maximum droplet spreading in droplet retraction dynamics.

Experimental investigation on the spreading progress after droplets impacting on to a vertical vibrating plate at low frequencies

The impingement of fuel droplets on the piston surface would greatly affect the combustion process and emission generation of direct injection diesel engines. In this paper, to mimic the interaction between the droplets and vibrating engine body, the dynamic behaviors of droplets impacting on a vertically vibrating plate were explored experimentally. The main target of this paper is the spreading process from the droplet attaching the plate to it reaching the maximum diameter. Several groups of impacting heights and plate vibrating frequencies were set to obtain a broad range of Weber numbers. The temporal evolutions of the inner lamella and rim after impact were traced by high-speed photography. The results show that the maximum spread time of the inner lamella maintains a relatively stable value, and the whole spreading time depend on the growth time of the rim. The fluctuation range of the growth time of the rim increases under increased vibrating frequency, while decreases with the increase of impacting height. The fluctuation range of the thickness of rim would be smaller with higher impacting height, and the relationship between growth time of rim and impact phase is cosinoidal at the same impacting Weber number. The effect of acceleration plays a key role in the development of the liquid layer. In addition, the maximum spread radius would be smaller for droplets with an impacting height of 15 cm, because the ring-shaped rim would receive more resistance from viscous forces and surface tension than fingers. Finally, an empirical formula based on Srivastava’s model was built to accurately predict the maximum spread factor of droplets after impacting on the vibrating plate, in which the influence of the impact phase, vibration frequency, vibration amplitude and Weber number were incorporated.

Analysis of Soil and Crop Parameters for the Development of Power Tiller-Operated Groundnut Digger

Groundnut (Arachis hypogea L.) is a major oilseed crop and holds an important place in the Indian agricultural economy. Odisha occupies 6th place in the major groundnut-producing states of the country with a total production of 0.388 MT and is grown in both Kharif and Rabi seasons. Harvesting is one of the major unit operations in groundnut cultivation and is mechanically harvested by tractor-operated diggers but their use is limited because of small land holdings and high capital costs and is not economical for small and marginal farmers of the state. However, the groundnut diggers to match with power tillers are not commercially available, therefore, efforts were made to develop a single-row groundnut digger operated by a power tiller. The study was conducted to relate the soil and crop parameters for the digger design, which influences the harvesting of groundnut. The design of a power tiller-operated groundnut digger to harvest a single row of groundnut requires the data of soil parameters (soil type, bulk density, cone index and soil moisture content) and crop parameters (plant population, plant height, pod zone, pod spreading radius, taproot length, taproot diameter, pod-vine ratio), suitable for different groundnut varieties. It was found that the majority of groundnut varieties were grown in sandy soils and harvested at 12-15 % soil moisture for more yield with a minimum power requirement. It was observed that for all types of groundnut varieties the plant population, plant height, pod zone depth, pod spreading radius, taproot length, taproot diameter and the number of pods per plant varies from 24-29/m2, 31-49.18 cm, 5.79-6.86 cm, 5.87-9.15 cm, 11.70-13.78 cm, 4.64-5.84 cm and 11-27/plant, respectively.

Impact Dynamics of Non-Newtonian Droplets on Superhydrophobic Surfaces

Droplet impact behavior on a solid surface is critical for many industrial applications such as spray coating, food production, printing, and agriculture. For all of these applications, a common challenge is to modify and control the impact regime and contact time of the droplets. This challenge becomes more critical for non-Newtonian liquids with complex rheology. In this research, we explored the impact dynamics of non-Newtonian liquids (by adding different concentrations of Xanthan into water) on superhydrophobic surfaces. Our experimental results show that by increasing the Xanthan concentration in water, the shapes of the bouncing droplet are dramatically altered, e.g., its shape at the separation moment is changed from a conventional vertical jetting into a "mushroom"-like one. As a result, the contact time of the non-Newtonian droplet could be reduced by up to ∼50%. We compare the impact scenarios of Xanthan liquids with those of glycerol solutions having a similar apparent viscosity, and results show that the differences in the elongation viscosity induce different impact dynamics of the droplets. Finally, we show that by increasing the Weber number for all of the liquids, the contact time is reduced, and the maximum spreading radius is increased.

Measuring the Adhesion Force and the Spreading Radius between Droplets and a Solid Surface during Short-Time Spreading

When a droplet contacts a solid surface, the liquid spreads over the solid surface to minimize the total surface energy. This phenomenon is widespread in industrial production and nature, so research on droplet spreading is of great significance. Here, the adhesion force and the spreading radius during droplet spreading can be quantified using a highly sensitive photoelectric method. It is possible to study droplet spreading from two dimensions at the microscale. The adhesion force is measured by an optical lever, and the spreading radius is measured by an ultrafast electrical method. The measurement method allows the force resolution and the space-time resolution to reach the nanonewton lever and the nanosecond lever, respectively. We obtain the maximum spreading radius and the maximum adhesion force during short-time spreading through our technique. Moreover, we numerically simulate the droplet spreading process through the lattice Boltzmann solver and confirm the observed results. This study provides a new experimental technique for studying droplet spreading dynamics from multiple perspectives, which can deepen our understanding of droplet spreading and provide guidance for the development of new techniques.

Sieve Search Centroiding Algorithm for Star Sensors.

The localization of the center of the star image formed on a sensor array directly affects attitude estimation accuracy. This paper proposes an intuitive self-evolving centroiding algorithm, termed the sieve search algorithm (SSA), which employs the structural properties of the point spread function. This method maps the gray-scale distribution of the star image spot into a matrix. This matrix is further segmented into contiguous sub-matrices, referred to as sieves. Sieves comprise a finite number of pixels. These sieves are evaluated and ranked based on their degree of symmetry and magnitude. Every pixel in the image spot carries the accumulated score of the sieves associated with it, and the centroid is its weighted average. The performance evaluation of this algorithm is carried out using star images of varied brightness, spread radius, noise level, and centroid location. In addition, test cases are designed around particular scenarios, like non-uniform point spread function, stuck-pixel noise, and optical double stars. The proposed algorithm is compared with various long-standing and state-of-the-art centroiding algorithms. The numerical simulation results validated the effectiveness of SSA, which is suitable for small satellites with limited computational resources. The proposed algorithm is found to have precision comparable with that of fitting algorithms. As for computational overhead, the algorithm requires only basic math and simple matrix operations, resulting in a visible decrease in execution time. These attributes make SSA a fair compromise between prevailing gray-scale and fitting algorithms concerning precision, robustness, and processing time.

A general urban spreading pattern of COVID-19 and its underlying mechanism

Currently, the global situation of COVID-19 is aggravating, pressingly calling for efficient control and prevention measures. Understanding the spreading pattern of COVID-19 has been widely recognized as a vital step for implementing non-pharmaceutical measures. Previous studies explained the differences in contagion rates due to the urban socio-political measures, while fine-grained geographic urban spreading pattern still remains an open issue. Here, we fill this gap by leveraging the trajectory data of 197,808 smartphone users (including 17,808 anonymous confirmed cases) in nine cities in China. We find a general spreading pattern in all cities: the spatial distribution of confirmed cases follows a power-law-like model and the spreading centroid human mobility is time-invariant. Moreover, we reveal that long average traveling distance results in a high growth rate of spreading radius and wide spatial diffusion of confirmed cases in the fine-grained geographic model. With such insight, we adopt the Kendall model to simulate the urban spreading of COVID-19 which can well fit the real spreading process. Our results unveil the underlying mechanism behind the spatial-temporal urban evolution of COVID-19, and can be used to evaluate the performance of mobility restriction policies implemented by many governments and to estimate the evolving spreading situation of COVID-19.