Spreading Regime Research Articles

Spreading of graphene oxide suspensions droplets on smooth surfaces

Understanding and predicting the spreading of droplets on solid surfaces is crucial in many applications such as printed electronics and spray coating where the fluid is a suspension and in general non-Newtonian. However, many models that predict the maximum spreading diameter usually only apply to Newtonian fluids. Here, we study experimentally and theoretically the maximum spreading diameter of graphene oxide suspension droplets impacting on a smooth surface for a wide range of concentrations and impact velocities (5≤We≤700, 30≤Re≤2000). As the particle concentration increases the rheological behavior changes from a viscous fluid to a shear-thinning yield stress fluid and the maximum spreading diameter decreases. The rheology for all concentrations is well described by a Herschel–Bulkley model that allows us to determine the characteristic viscosity and corresponding Reynolds number Re during spreading. Analogous to Newtonian fluids, the spreading ratio follows the Re1/5 scaling in the viscous spreading regime. Furthermore, we use this characteristic viscosity to develop an energy balance model that takes into account the viscous dissipation and change in surface energies to find the maximum spread diameter for a given impact velocity. The model contains one non-dimensional parameter α that encodes both the dynamic contact angle during spreading and the droplet shape at maximum spread. Our model is in good agreement with our data at all concentrations and agrees well with literature data on Newtonian fluids. Furthermore, the model gives the correct limits in the viscous and capillary regime and can be solved analytically for Newtonian fluids.

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.

Vibration-triggered spreading of nanofluid drops

This study explores the effects of nanoparticles on the dynamics of drop spreading under external vibration, presenting an advance in the understanding of nanofluid behavior on vibrating substrates. This work introduces insights into nanoparticle-mediated drop spreading, offering implications for improving particulate coatings, mini-mixers, and particle segregation technologies. By employing a twofold approach that combines oscillating drop dynamics with internal flow pattern analysis, we find how even small concentrations of hydrophilic or hydrophobized silica nanoparticles inside water sessile droplets significantly alter the spreading process on silanized glass surfaces. Our study allows distinct drop spreading regimes to be identified based on nanoparticle concentration and vibration amplitude, for both hydrophilic and hydrophobized nanoparticles. Through a comprehensive analysis, we demonstrate that the vibration-triggered spreading of nanofluids can lead to a stable and controlled manipulation of complex liquids.

Viscoplastic elliptical objects impacting a solid surface

This theoretical and numerical study focuses on the physical mechanism driving the spreading of viscoplastic elliptical millimetric/centimetric objects after they impact a solid surface under no-slip conditions. The two-dimensional impacting objects are described as Bingham fluids. The two-dimensional numerical simulations are based on a variational multi-scale approach devoted to multiphase non-Newtonian fluid flows. The obtained results are analyzed considering the spreading dynamics, energy budgets and scaling laws. They show that, under negligible capillary effects, the impacting kinetic energy of the elliptical objects is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: inertio-viscous, inertio-plastic, and mixed inertio-visco-plastic. These regimes are strongly affected by the initial aspect ratio of the impacting objects, which reveals the possibility of using morphology to control spreading. Finally, the results are summarized in a diagram linking the object's maximum spreading and spreading time with different spreading regimes through a single dimensionless parameter called impact number.

Geochemical Signatures of Mafic Volcanic Rocks in Modern Oceanic Settings and Implications for Archean Mafic Magmatism

Abstract Greenstone belts are dominated by mafic volcanic rocks with geochemical characteristics that indicate a range of possible geodynamic influences. Many analogies with modern tectonic settings have been suggested. Increasing exploration of the modern oceans and comprehensive sampling of volcanic rocks from the sea floor are now providing unique opportunities to characterize different melt sources and petrogenesis that can be more closely compared to greenstone belts. In this study, we have compiled high-quality geochemical analyses of more than 2,850 unique samples of submarine mafic volcanic rocks (<60 wt % SiO2) from a wide range of settings, including mid-ocean ridges, ridge-hotspot intersections, intraoceanic arc and back-arc spreading centers, and ocean islands. The compiled data show significant geochemical variability spanning the full range of compositions of basalts found in greenstone belts. This diversity is interpreted to be due to variable crustal thickness, dry melting versus wet melting conditions, mantle mixing, and contamination. In particular, different melting conditions have been linked to mantle heterogeneity, complex mantle flow regimes, and short-lived tectonic domains, such as those associated with diffuse spreading, overlapping spreading centers, and triple junctions. These are well documented in the microplate mosaics of the Western Pacific. Systematic differences in mafic volcanic rock compositions in modern oceanic settings are revealed by a combination of principal components analysis and unsupervised hierarchical clustering of the compiled data. Mafic volcanic rocks from most arc-back arc systems have strongly depleted mantle signatures and well-known subduction-related chemistry such as large ion lithophile element (LILE) enrichment in combination with strong negative Nb-Ta anomalies and low heavy rare earth elements (HREEs). This contrasts with mafic volcanic rocks in Archean greenstone belts, which show no, or at least weaker, subduction-related chemistry, a less depleted mantle, less wet melting, and variable crustal contamination. The differences are interpreted to be the result of the lower mantle temperatures, thinner crust, and subduction-related processes of present-day settings. However, mafic rocks that are geochemically identical to those in Archean greenstone belts occur in many modern back-arc basins, including the Lau basin, East Scotia ridge, Bransfield Strait, and Manus basin, which are characterized by fertile mantle sources, high heat flow, and complex spreading regimes typical of small-scale microplate mosaics. These types of settings are recognized as favorable for volcanogenic massive sulfide (VMS) deposits in modern and ancient greenstone belts, and therefore the particular geochemical signatures of the mafic volcanic rocks are potentially important for area selection in base metal exploration.

Surface wettability-induced modulations of droplet breakup in a bifurcated microchannel

We explore the dynamics of droplet propagation and subsequent disintegration in a symmetric bifurcating Y-microchannel by varying the wettability characteristics of one of the daughter channels while maintaining the wettability of the other constant. The temporal evolution of the droplet is numerically investigated using the phase-field method. Based on the neck-width evolution, the droplet bifurcation phenomenon has been divided into three separate stages, namely, squeezing, transition, and pinch-off. During the squeezing stage, the rate of change of neck width increases as the wettability angle decreases, while an opposite trend is observed at the pinch-off stage, leading to almost identical breakup time for the droplet regardless of the wettability angle. We identify pertinent regimes of droplet breakup, such as symmetric breakup, asymmetric breakup, no-breakup upper channel, no-breakup lower channel, and spreading regime, over wide ranges of capillary numbers (Ca) and viscosity ratio (μr). Our study indicates that an increase in the relative influence of viscous force (high Ca) reduces the droplet's wettability effect. The same pattern is obtained when the viscosity of the droplet is increased in relation to the viscosity of the carrier fluid. In contrast, for low Ca flows, the relatively strong interfacial tension favors the wettability characteristics of the surface, resulting in a dominance of non-breakup regimes. The regime plots proposed in this paper depict the roles of Ca and μr on various breakup regimes in detail. Such regime diagrams may emerge as fundamental design basis of microfluidic devices in diverse applications, such as biopharmaceuticals, microreactors, and food processing.

The role of viscoplastic drop shape in impact

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

Modeling parameters for predicting the fire-induced progressive collapse in steel framed buildings

Fire is one of the extreme loading events that a building may experience during its service life and can have severe consequences on the safety of its occupants, first responders, and the structure. Steel framed buildings under severe fires can experience high levels of instability at a local or global level, which in turn can lead to the partial or progressive collapse of the structure. However, in current practice, fire resistance of structures is obtained without due consideration to a number of critical factors, and this is mainly due to the high level of complexity in undertaking advanced analysis of structures under fire exposure. This paper presents a parametric study on a ten-story braced steel framed building subjected to fire exposure wherein six different parameters are evaluated: fire severity, fire spread, load paths, temperature-induced creep, local instability, and analysis regime. Results from validated finite element models are utilized to evaluate the influence of the different parameters and recommend critical parameters to be incorporated in the analysis. Results show that the susceptibility of fire-induced progressive collapse significantly depends on the severity of the fire exposure scenario, including fire intensity, fire spread, and extent of burning. Also, accounting for the full effects of transient creep in fire-induced progressive collapse analysis is needed to obtain conservative failure times under severe to very intense fire exposure. Additionally, results from the parametric study infer that the sectional classification of a steel section based on local instability can alter under fire exposure and this effect is more critical in steel columns located in the higher stories of the building; a nonslender column at ambient conditions can transform to a slender section at elevated temperatures. This can induce temperature-induced local instability in the column and lead to an early onset of instability at member and structural levels.

Universality of Scaling Laws Governing Contact and Spreading Time Spans of Bouncing Liquid Marbles and its Physical Origin.

The impact of liquid marbles coated with a diversity of hydrophobic powders with various solid substrates, including hydrophobic, hydrophilic, and superhydrophobic ones, was investigated. The contact time of the bouncing marbles was studied. Universal scaling behavior of the contact time tc as a function of the Weber number (We) was established; the scaling law tc = tc(We) was independent of the kind of powder and the type of solid substrate. The total contact time consists of spreading time and retraction time. It is weakly dependent on We and this is true for all kinds of studied powders and substrates. This observation hints to the surface tension/inertia spring model governing the impact. By contrast, the spreading time ts scales as [Formula: see text], n = 0.28 - 0.30 ± 0.002. We relate the origin of this scaling law to the viscous dissipation occurring within the spreading marbles. The retraction time tr grows weakly with the Weber number. The scaling law was changed at threshold values of We ≅ 15-20. It is reasonable to explain this change with the breaking of the Leidenfrost regime of spreading under high values of We.

Energy approach to the description of the dynamics of hydrocarbon spills

An energy approach to the problem of theoretical description of axisymmetric and quasi-one-dimensional oil product spills is presented. Within the framework of these models, approximate equations describing the evolution of the size of oil spots over time were derived. Solution of these equations describing the characteristics of spills of both a limited area (for machine oil stains) and unlimited spills of crude oil is obtained. A number of laboratory experiments have been carried out to study the dynamics of spreading of a spot of reference engine oil and crude oil for axisymmetric and quasi-one-dimensional flows. The presented theoretical and experimental results are in good agreement for both spreading regimes.

A Study on the Dynamic Collision Behaviors of a Hydrous Ethanol Droplet on a Heated Surface

This study uses high-speed imaging to investigate the dynamic collision behavior of a single hydrous ethanol droplet in different water/ethanol ratios on a heated horizontal glass surface. The initial droplet diameter varied from 3.3 to 4.1 mm, and the impact velocity was 0.57 m/s. The study covers a range of surface temperatures (373 K to 553 K) and ethanol mass fractions (0% to 100%) to reveal four regimes of droplet-impinging behaviors, including quiescent surface evaporation, puffing or partial boiling, explosive nuclear boiling, and the Leidenfrost effect. The addition of volatile ethanol to less volatile water shifts the droplet collision behavior toward explosive boiling and the Leidenfrost phenomenon. As the ethanol mass fraction increased from 0% to 100%, the superheat limit temperature decreased by approximately 80 K, while the Leidenfrost temperature decreased by at least 100 K. The dimensionless droplet diameter in the regime of droplet spreading with quiescent surface evaporation is influenced by surface temperature, surface tension, and viscosity. Meanwhile, the dimensionless diameter and height of a droplet in the regime of the Leidenfrost phenomenon are mainly influenced by its surface tension. The study concludes that a single parameter, such as the superheat level, Weber number, or Reynolds number, is difficult to describe droplet collision behavior, and multiple factors would be required to best describe droplet collision behavior and establish empirical correlations. However, it is feasible to predict partial collision behaviors by using one of the single parameters under certain conditions.

Droplet orthogonal impact on nonuniform wettability surfaces

AbstractThe vast majority of prior studies on droplet impact have focused on collisions of liquid droplets with spatially homogeneous (i.e., uniform‐wettability) surfaces. But in recent years, there has been growing interest on droplet impact on nonuniform wettability surfaces, which are more relevant in practice. This paper presents first an experimental study of axisymmetric droplet impact on wettability‐patterned surfaces. The experiments feature millimeter‐sized water droplets impacting centrally with on a flat surface that has a circular region of wettability (Area 1) surrounded by a region of wettability (Area 2), where (i.e., outer domain is less wettable than the inner one). Depending upon the droplet momentum at impact, the experiments reveal the existence of three possible regimes of axisymmetric spreading, namely (I) interior (only within Area 1) spreading, (II) contact‐line entrapment at the periphery of Area 1, and (III) exterior (extending into Area 2) spreading. We present an analysis based on energetic principles for , and further extend it for cases where (i.e., the outer domain is more wettable than the inner one). The experimental observations are consistent with the scaling and predictions of the analytical model, thus outlining a strategy for predicting droplet impact behavior for more complex wettability patterns.

Recessions and flattening of the yield curve (1960–2021): A two-way road under a regime switching approach

The one-way relationship that goes from the term spread to recessions has been widely studied. However, the relationship between term spread and the business cycle, in addition to being bidirectional, is conditioned by the cyclical phase itself. To demonstrate this, we have modelled the bidirectional relationship between term spread and the business cycle by extracting two interrelated latent Markov variables: the first, drawn from four activity indicators, replicates the phases of the US business cycle; the second, from the term spread of the yield curve, identifies two regimes: an ordinary regime (positive slope) and a flattening regime. By analyzing both the transition between these regimes and forecasted probabilities, we find that this bidirectional relationship is not symmetrical. That is, the term spread signals a change in the business cycle regime while the cyclical factor only signals the beginning of the ordinary regime of the term spread, not its ending. To illustrate the model, we confirm the beginning of the COVID-19 recession in March of 2020, and the corresponding start of the ordinary regime in the term spread.

Beef price spread relationship with processing capacity utilization

We investigate the relationships of the often-publicized live cattle to box beef price spread and weekly and Saturday slaughter capacity utilization (CU). We find that an increase in the price spread in the previous period does positively impact national Saturday slaughter CU under a low price spread regime, but not in the identified middle and high regimes. Also, changes in weekly or Saturday slaughter CU does not impact the price spread except for the high regime. Our results do not support the notion that weekly, or Saturday slaughter CU is used by the beef packers to control the price spread.

Scalloped pattern deposition during the spreading and drying of polymer droplets.

Droplets containing polyvinylpyrrolidone (PVP) dissolved in ethanol display a distinctive scalloped pattern at the rim while spreading and drying on a high-energy surface. Two distinct spreading regimes are observed, leading to the formation of a thin film with a uniform height that extends from the original droplet. An experimental study indicates polymer accumulation at the edge containing trace water, resulting in a surface tension gradient across the droplet, enhancing the droplet's spreading. This fast-spreading film develops a ridge at the contact line and becomes unstable. The influence of evaporation within the droplet shows no significant effect on the wavelength of the instability. Instead, the magnitude of the surface tension gradient and the surface energy of the substrate emerge as the dominant factors influencing the instability. This observation is validated by saturating the environment surrounding the droplet with ethanol vapour to reduce evaporation or employing solvents with low vapour pressure. Additionally, PVP in ethanol droplets deposited on hydrophobic substrates demonstrate a stable and pinned contact line, contrasting the behaviour observed on high-energy surfaces. By identifying the critical overlap concentration of the polymer, the transitional threshold between the scalloped instability and ringlike morphology is determined. The scalloped instability can be suppressed by removing residual water from the solution, eliminating the surface tension gradient, indicating that Marangoni forces are the underlying cause of the observed instability. The long-wave evolution equation, assuming a constant Marangoni shear flow, accurately predicts the most unstable wavelength, demonstrating good agreement with experimental observations.

Modelling of flame spread over biomass fuel arrays with various inclined angles and spacings

Flame spread of combustible materials with discontinuous distribution is a typical heat and mass transfer process that contributes a lot to the thermal disaster of building fires and wildland fires. However, application models of flame spread over discrete fuels have not been well addressed. In this study, 54 groups of line arrays of birch rods, 5 mm in diameter and 55 mm long, were designed by varying nine spacings (S, 1–9 mm) and six slopes (θ, 15°−90°). Under the combined effect of fuel spacing and slope, flame spread behaviors are categorized into continuous flame spread regime (regime I) and discrete flame spread regime (regime II). Under the two regimes, calculation models of incident heat flux are respectively determined, which can predict flame spread rate well. Moreover, flame spread rate and mass loss rate per unit area present a growing tendency with increasing spacing in regime I, but have a limited dependency in regime II. The prediction models of mass loss rate and flame spread rate are developed, which match the experimental results well. Furthermore, a correlation between dimensionless flame length and modified dimensionless heat release rate is proposed in the inclined configuration. In the vertical configuration, flame length presents a power-law dependency on the heat release rate per unit width with the exponent range of 1.202–1.838.

Rheology dictated spreading regimes of a non-isothermal sessile drop

In the present work, within the framework of thin film theory, we delineate the interaction between the interfacial dynamics of thermal Marangoni flow and non-Newtonian rheology by considering a spreading droplet over a non-isothermal substrate. The numerical simulations, performed at different equilibrium contact angles $(\theta _e)$ , dimensionless thermocapillary strengths $(\beta )$ and shear-dependent viscosities $(n)$ , reveal that the fluid rheology nonlinearly influences the mechanisms of disjoining pressure and Marangoni stress. Accordingly, three distinct spreading regimes for non-Newtonian drops arise. Results indicate that the Marangoni film regime, having an approximate linear drop shape, sustains at lower $\theta _e$ , higher $\beta$ and $n$ ranges. Also, shear-thickening drops display an early onset of thermocapillary time scale and a steeper advancing front, while their shear-thinning counterparts retain a significant curvature for a much longer time. Contrastingly, the droplet regime is identified by fixed shape and uniform speed $(U)$ at higher $\theta _e$ and lower $(\beta$ , $n)$ combinations. Here, an intricate interplay between $\beta$ and $n$ realizes a sharp increase in $U$ for shear thinning compared with its invariance for shear-thickening droplets. The transition regime appears as an intermediate regime between the other two and involves multiple ruptured droplets. In all the regimes, we observe slower (faster) spreading of shear-thinning (thickening) droplets than the Newtonian droplets. In addition, the variations in $n$ cause intense characteristic modulations to spreading attributes like droplet morphology and transient spreading behaviour, and also act as a switching mechanism between different spreading regimes. These unique results may be utilized for superior control of non-isothermal biofluid droplets in microfluidics.

Numerical study of drop spread and rebound on heated surfaces with consideration of high pressure

The impact of a drop on a solid surface has been studied for many years. However, most of the previous numerical simulations were focused on the drop impact on a surface at room temperature and standard atmospheric pressure. This paper presents a numerical study of n-heptane and n-decane drops impacting solid surfaces with the consideration of high temperature and high pressure using smoothed particle hydrodynamics (SPH). The SPH method is validated against experiments from our work and literature. This work is focused on two typical drop-impact regimes, namely, spread and rebound. Different drop impact sequences were simulated at the wall temperature in the range of 27–400 °C and the ambient pressure between 1–20 bars. The difference between the inception of film boiling and liquid saturation temperature was found to decrease with elevating ambient pressure. The spread factor and apex height are investigated for the regime of spread. The results indicate that the lower viscosity fluid has a smaller spread factor as compared to the fluid with higher viscosity. The variation of Leidenfrost temperature with ambient pressure for both n-heptane and n-decane droplets is established numerically and compared with the trend observed in the experiment. The simulation outcomes of drop rebound for high boiling point liquid (n-decane) in the film boiling regime at atmospheric pressure show that with the increasing wall temperature, the drop rebound height and vapor layer height increase. Finally, the effect of ambient pressure on drop rebound height and velocity is investigated. The numerical results indicate that the increase in ambient pressure reduces the droplet rebound velocity and rebound height.

Isothermal and non-isothermal spreading of a viscous droplet on a solid surface in total wetting condition

We study the isothermal and non-isothermal spreading of viscous silicone oil droplets on a glass surface in total wetting condition. In particular, the effects of viscosity, impact velocity, and substrate temperature on the spreading dynamics are reported. We employ high-speed photography to record time-varying droplet shapes from the side. An infrared camera maps the temperature distribution on the liquid–gas interface. In the isothermal inertial-capillary or early regime, the initial spreading is driven by inertial forces, and kinetic energy converts into surface energy and gets dissipated by bulk viscosity. The later stage is governed by the balance of surface energy and viscosity dissipation, i.e., capillary–viscous or late regime. The characteristics timescales of the two regimes are obtained using scaling arguments. The measured crossover time from early to late spreading regimes for different cases of impact velocity and viscosity corroborates with a scaling analysis developed in the present work. Measurements confirm the value of exponents of established power-law spreading with time in early and late regimes r∼tn. At a larger substrate temperature, the spreading magnitude is larger for droplets with larger viscosity and is explained by the reduction of viscous dissipation by heating the droplet. However, in the case of non-isothermal spreading of a low viscosity droplet, recoiling after the early spreading reduces the spreading magnitude compared to the isothermal case. We explain the recoiling and spreading rates obtained in different cases. We analyze unsteady heat transfer between the droplet and substrate by combining measurements and a numerical model.

Quantifying the dynamic spreading of a molten sand droplet using multiphase mesoscopic simulations

Molten sand droplets deposited on gas turbine engine components cause severe damage. To better understand the deposition process, we study the wetting dynamics of a highly viscous molten sand droplet on a smooth substrate. A universal contact line spreading, independent of the droplet size, is observed with the characteristic inertial and viscous spreading regimes. It is also shown that the dynamic contact angle is in excellent agreement with Cox's theory.