Spreading Front Research Articles

Flowerlike Spreading of Micellar Films during Emulsion Drop Evaporation

We investigated the film spreading during the evaporation of submillimeter oil-in-water emulsion droplets on a solid surface, and observed a novel phenomenon where the film follows a two-layer spreading. In combination with the instability at the film front, the spreading front acquires a flowerlike pattern. The emergence of the two-layer structure is attributed to micelles within the oil film that yield an oscillating disjoining pressure. By considering both the slipping condition and the disjoining pressure, a scaling analysis is carried out that agrees well with the observed film spreading dynamics. The film spreading follows Tanner’s law initially, while it becomes faster at a later stage, where the film radius follows r∼t1/2 for weak slip and r∼t3/8 for strong slip conditions. Published by the American Physical Society 2024

A blow-up result of a free boundary problem with nonlinear advection term

We study a free boundary problem for the reaction-diffusion equation with nonlinear advection term u t = u xx − u u x + u p ( p > 1 ) on [ 0 , h ( t ) ] . This model describes species that live in an uninhabitable area and tries to spread into a new area, the free boundary h ( t ) represents such a spreading front. By considering the initial data σϕ , we have two sharp results. There is some σ ∗ > 0 , blow up happens when σ > σ ∗ , vanishing happens when σ < σ ∗ and the transition case happens when σ = σ ∗ . Additionally, we also have another trichotomy result: the solution is either blow up or converging to a small stationary state or converging to a big stationary state.

Nonlinear impacts of climate change on dengue transmission in mainland China: Underlying mechanisms and future projection

Dengue fever is a climate-sensitive health concern caused by mosquito-borne virus. Both temperature- and precipitation-related factors are important for dengue transmission. Previous studies mainly focused on the effects of individual factors on the spread of dengue. However, given the potential synergistic effects of temperature and precipitation on virus transmission, it is vital to provide a holistic view of their interplay in shaping the transmission patterns. In this study, utilizing a vectorial capacity (VC)-based mathematical model, we investigated the mechanisms by which the daily mean temperature (DMT), diurnal temperature range (DTR) and daily mean precipitation (DMP) jointly influence the dengue spread. We further forecast future dengue patterns in mainland China under different climate scenarios (Shared Socioeconomic Pathways (SSP)) by 2050 and 2080. Results show that these three climate factors trigger complex nonlinear effects on dengue transmission. Interactions between DMT and DTR plays a decisive role in determining the spreading fronts of dengue epidemics, while DMP considerably impacts its transmission intensity. Although future climate changes would facilitate northward expansion of areas at risk of dengue under SSP245 and SSP585, significant contraction would happen under SSP126. These findings illuminate the interacting mechanisms of temperature and precipitation on dengue transmission, call for the comprehensive considerations of DMT, DMP and DTR in formulating effective dengue control policies, and warrant achieving a sustainable future in line with the SSP126 scenario to effectively mitigate dengue transmission risks and ensure a resilient future.

Bifurcation delay and front propagation in the real Ginzburg-Landau equation on a time-dependent domain.

This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equationwith periodic boundary conditions on isotropically growing or shrinking domains. First, we obtain closed-form expressions for the delay of primary bifurcations on a growing domain and show that the additional domain growth before the appearance of a pattern is independent of the growth time scale. We also quantify primary bifurcation delay on a shrinking domain; in contrast with a growing domain, the time scale of domain compression is reflected in the additional compression before the pattern decays. For secondary bifurcations such as the Eckhaus instability, we obtain a lower bound on the delay of phase slips due to a time-dependent domain. We also construct a heuristic model to classify regimes with arrested phase slips, i.e., phase slips that fail to develop. Then, we study how propagating fronts are influenced by a time-dependent domain. We identify three types of pulled fronts: homogeneous, pattern spreading, and Eckhaus fronts. By following the linear dynamics, we derive expressions for the velocity and profile of homogeneous fronts on a time-dependent domain. We also derive the natural "asymptotic" velocity and front profile and show that these deviate from predictions based on the marginal stability criterion familiar from fixed domain theory. This difference arises because the time dependence of the domain lifts the degeneracy of the spatial eigenvalues associated with speed selection and represents a fundamental distinction from the fixed domain theory that we verify using direct numerical simulations. The effect of a growing domain on pattern spreading and Eckhaus front velocities is inspected qualitatively and found to be similar to that of homogeneous fronts. These more complex fronts can also experience delayed onset. Lastly, we show that dilution-an effect present when the order parameter is conserved-increases bifurcation delay and amplifies changes in the homogeneous front velocity on time-dependent domains. The study provides general insight into the effects of domain growth on pattern onset, pattern transitions, and front propagation in systems across different scientific fields.

Laser modification of heating surfaces: A new approach to reduce boiler slagging

Slagging and fouling of boilers are typical technological problems in the combustion of solid fuels (especially coal and biomass). This study proposes a novel approach based on laser texturing of the near-surface layer of steel used to make heating surfaces of coal-fired boilers. This approach is aimed at improving the resistance of metal surfaces to slagging. The formation of slag deposits on the surfaces of AISI 310 S steel modified by laser radiation has been experimentally studied. The formation of slag melt was analyzed on the surface of modified and polished steel plates during heating to 1400 °C. High-temperature heating and interaction with slag led to a change in the chemical composition of the steel. A significant increase in the chromium content (up to 47%) of the steel surface and the transformation of its texture with the formation of grains up to 2.5 µm in size were established. Laser surface treatment significantly increased the resistance of the steel to such changes and also reduced the grain size to 1.5 µm. As a result of laser modification of surfaces, the temperature of slag formation shifts to higher values (higher by 60–75 °C compared to the unmodified polished surface). The anisotropic texture (cauliflower type) contributed to a decrease in the size of the slag spreading front, and also had by self-cleaning properties from the mineral melt. The latter allows to increase the reliability and energy efficiency of boiler equipment.

Development of a standard for accelerated determination of frost resistance of autoclaved aerated concrete

AbstractIntroductionThe “Introduction” analyses the mechanisms of concrete frost damage and describes standard methods for determining the frost resistance of lightweight and cellular concrete.Research methodsThe frost resistance at different freezing temperatures was carried out on samples of autoclaved cellular concrete of D400 to D600 density. Specimens with dimensions of 100 × 100 × 100 mm were cut from prefabricated parts in accordance with EN 771‐4. During the experiment, frost resistance of ААС samples was determined at a standard temperature of −18 ± 2°C, as well as at temperatures from −5°C to −40°C4.Results and discussionIn the paper, frost resistance of concrete at various freezing temperatures was evaluated by the experimental‐analytical method, which is based on the assumption that frost resistance, expressed in the number of cycles (F) should be inversely proportional to the volume of frozen water at this temperature.The frost resistance of concrete was evaluated experimentally and analytically at different freezing temperatures, assuming that the frost resistance (F), expressed in the number of cycles, should be inversely proportional to the volume of frozen water at that temperature V(t).Determination of the rate of ice spreading front and moisture diffusion in building materials by conductometric method during one‐sided freezing allows a more detailed study of the mechanisms of frost failure of building materials.ConclusionsThe proposed experimental‐analytical method for evaluating AAC frost resistance at different freezing temperatures allows, with a small expenditure of time, to obtain more complete information on the material behavior in freezing temperatures than it is provided by the existing standard methods. The analysis of the dependence of freezing resistance on temperature also allows revealing the regions of temperature where it changes most strongly, and to shift, if necessary, these regions towards lower or higher temperatures by adjusting the composition and technology of AAC production.The developed combined method of independent measurements of moisture diffusion kinetics and ice content makes it possible to determine the speed of diffusion of ice formation front and moisture conductivity depending on the composition (capillary‐porous structure) of samples and their initial storage conditions. This information can give a more reliable picture of the behaviour of AAC under alternating temperature loading under varying initial moisture conditions.

Impact dynamics of compound drops of fluids with density contrast

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$ ) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$ . In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$ , volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$ .

The analytical solution to the migration of an epithelial monolayer with a circular spreading front and its implications in the gap closure process.

The coordinated behaviors of epithelial cells are widely observed in tissue development, such as re-epithelialization, tumor growth, and morphogenesis. In these processes, cells either migrate collectively or organize themselves into specific structures to serve certain purposes. In this work, we study a spreading epithelial monolayer whose migrating front encloses a circular gap in the monolayer center. Such tissue is usually used to mimic the wound healing process in vitro. We model the epithelial sheet as a layer of active viscous polar fluid. With an axisymmetric assumption, the model can be analytically solved under two special conditions, suggesting two possible spreading modes for the epithelial monolayer. Based on these two sets of analytical solutions, we assess the velocity of the spreading front affected by the gap size, the active intercellular contractility, and the purse-string contraction acting on the spreading edge. Several critical values exist in the model parameters for the initiation of the gap closure process, and the purse-string contraction plays a vital role in governing the gap closure kinetics. Finally, the instability of the morphology of the spreading front was studied. Numerical calculations show how the perturbated velocities and the growth rates vary with respect to different model parameters.

Fingering Instability of Binary Droplets on Oil Pool

The interfacial instability of a complex fluid in a multiphase flow system is ubiquitous in both nature and industry. We experimentally investigated the spreading and interfacial instability dynamics of a binary droplet (a water and 2-propanol (IPA) mixture) on an immiscible (sunflower oil) pool. For droplets of 40 wt% IPA solution on sunflower oil, fingering instability occurred at the spreading liquid front. To reveal the interfacial characteristics of the spreading and fingering processes, we analyzed the interplay among the speed, diameter, and number of fingers on the spreading front. Based on our observations, the finger length, wavelength between the fingers, head length, and neck length were quantified. Our experimental results clearly demonstrate that fingering instability can be driven by the capillary effect for a liquid–liquid system as well as the Plateau–Rayleigh instability. We hope that our results will inspire further experimental and numerical investigations to provide deeper insights into the interfacial dynamics of multicomponent droplets in a liquid pool.

Two-species nonlocal cross-diffusion models with free boundaries

A class of two-species nonlocal cross-diffusion models with free boundaries in one space dimension is investigated. In the models, the two species exist initially in (−∞,s10] and (−∞,s20], respectively, and then spread into the right space. The spreading fronts and nonlocal cross-diffusion of the species are described by the free boundaries and integral diffusion operators, respectively. By introducing some parameterized ODE problems and by applying the contraction mapping theorem and deriving some estimates, we give the global existence and uniqueness of solutions for the models. These results are applied to the nonlocal cross-diffusion prey-predator and competition models.

A free boundary problem for a ratio-dependent predator–prey system

In this paper, we study a free boundary problem for a ratio-dependent predator–prey system in one space dimension, in which the free boundary is only caused by prey, representing the spreading fronts of prey. We discuss the long time behaviors of solution as $$t\rightarrow \infty $$ and establish a spreading–vanishing dichotomy; namely, either the two species successfully spread to infinity as $$t\rightarrow \infty $$ and survive in the new environment, or they cannot spread to the whole space and the prey will vanish eventually. Then, the criteria for spreading and vanishing are obtained. Furthermore, when spreading occurs, some estimates of the asymptotic speed of h(t) as $$t\rightarrow \infty $$ are provided. Finally, some realistic and meaningful phenomena are discovered.

A West Nile virus nonlocal model with free boundaries and seasonal succession.

The paper deals with a West Nile virus (WNv) model, in which the nonlocal diffusion characterizes the long-range movement of birds and mosquitoes, the free boundaries describe their spreading fronts, and the seasonal succession accounts for the effect of the warm and cold seasons. The well-posedness of the mathematical model is established, and its long-term dynamical behaviours, which depend upon the generalized eigenvalues of the corresponding linearized differential operator, are investigated. For both spatially independent and nonlocal WNv models with seasonal successions, the generalized eigenvalues are studied and applied to determine whether the spreading or vanishing occurs. Our results extend those for the case with nonlocal diffusion but no free boundary and those for the case with free boundary but local diffusion, respectively. The generalized eigenvalues reveal that there exists positive correlation between the duration of the warm season and the risk of infection. Moreover, the initial infection length, the initial infection scale and the spreading ability to new areas all play important roles for the long time behaviors of the time dependent solutions.

Long-time dynamics of an epidemic model with nonlocal diffusion and free boundaries: Spreading speed

&lt;p style='text-indent:20px;'&gt;This paper is a sequel to Wang and Du [&lt;xref ref-type="bibr" rid="b15"&gt;15&lt;/xref&gt;], on the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the spreading front is represented by the free boundaries in the model. In [&lt;xref ref-type="bibr" rid="b15"&gt;15&lt;/xref&gt;], it was shown that the model is well-posed, and its long-time dynamical behaviour is governed by a spreading-vanishing dichotomy; however, the spreading speed was not determined. In this paper, we completely determine the spreading speed of the model when spreading happens. We find a threshold condition for the diffusion kernels &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ J_1 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; and &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ J_2 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; such that the asymptotic spreading speed is finite precisely when this condition is satisfied. Moreover, this speed is determined by a unique semi-wave solution which exists exactly when this threshold condition holds. When this condition is not satisfied, and spreading is successful, we prove that the asymptotic spreading speed is infinite, namely accelerated spreading happens.&lt;/p&gt;

Dynamics of West Nile virus driven by seasonal fluctuations in a spatially variable habitat

&lt;p style='text-indent:20px;'&gt;Seasonality is the common phenomena in ecological evolution. Firstly, we formulate and explore a simplified West Nile virus model, which describes the transmission of West Nile virus driven by seasonal fluctuations in a spatially variable habitat where the spatial movement of the infectious mosquitoes and infectious birds are described by Laplace diffusion. The range of the infected area is assumed to be a moving interval &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ [0, h(t)] \subset \mathbb{R} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, with its right end point representing the spreading fronts of the disease. We will mainly investigate the impact of spatial heterogeneity of environment and temporal periodicity on the persistence and extinction of West Nile virus. The basic reproduction number &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ R_0^D $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; in a fixed region and the spatial-temporal risk index &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ R_0^F(t) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; for the free boundary problem, which depends on spatial heterogeneity, temporal periodicity and spatial diffusion, are defined by the associated linearized eigenvalue problems. Sufficient conditions for the spreading and vanishing of West Nile virus are presented for the spatial dynamics of the virus. At last, we explore the long time dynamical behavior of the solution to free boundary problem when the spreading occurs.&lt;/p&gt;

A Lagrangian approach to ex-vessel corium spreading over ceramic and concrete substrates using moving particle hydrodynamics

Understanding the spreading of molten core materials (corium) is vital for achieving post-accident heat removal and maintaining the integrity of the reactor containment during a severe nuclear accident. The spreading of highly viscous corium over sacrificial concrete and ablation-resistant ceramic substrates, consistent with recent VE-U9 experiments at the VULCANO facility, is investigated using a Lagrangian moving particle hydrodynamics (MPH) method. The spreading dynamics are coupled with a heat transfer model to account for the increase in melt viscosity due to solidification. Three alternative boundary conditions are considered at the melt-substrate interface to mimic the influence of low viscosity concrete ablation products on the spreading dynamics. Simulation of spreading under no-slip conditions closely resembled the spreading behavior observed over the inert ceramic substrate, advancing with a crawling motion with a steep profile in the proximity of the melt front. Spreading terminated due to a combination of thermal radiation from the free surface and the heat transfer to the substrate, leading to the formation of a continuous crust. Introduction of slip boundary models, to mimic lubrication of the interface by a film of low-viscosity concrete decomposition products, enabled the prediction of the gliding flow observed over the sacrificial concrete substrate, characterized by a shallow melt topology near the spreading front. The simulation results demonstrate excellent potential for Lagrangian models such as MPH to predict complex spreading dynamics in the presence of both melt solidification and lubrication at the substrate.

Gravity-driven coatings on curved substrates: a differential geometry approach

Drainage and spreading processes in thin liquid films have received considerable attention in the past decades. Yet, our understanding of three-dimensional cases remains sparse, with only a few studies focusing on flat and axisymmetric substrates. Here, we exploit differential geometry to understand the drainage and spreading of thin films on curved substrates, under the assumption of negligible surface tension and hydrostatic gravity effects. We develop a solution for the drainage on a local maximum of a generic substrate. We then investigate the role of geometry in defining the spatial thickness distribution via an asymptotic expansion in the vicinity of the maximum. Spheroids with a much larger (respectively smaller) height than the equatorial radius are characterized by an increasing (respectively decreasing) coating thickness when moving away from the pole. These thickness variations result from a competition between the variations of the substrate's slope and mean curvature. The coating of a torus presents larger thicknesses and a faster spreading on the inner region than on the outer region, owing to the different curvatures in these two regions. In the case of an ellipsoid with three different axes, spatial modulations in the drainage solution are observed as a consequence of a faster drainage along the short principal axis, faithfully reproduced by a three-dimensional asymptotic solution. Leveraging the conservation of mass, an analytical solution for the average spreading front is obtained. The solutions are in agreement with numerical simulations and experimental measurements obtained from the coating of a curing polymer on diverse substrates.

Characteristics of droplet exudation on slippery liquid-infused porous surfaces considering thermal effect

The self-healing property of slippery liquid-infused porous surfaces ensures the continuity and stability of the liquid film on the surfaces. Therefore, how to promote the exudation and spreading of the lubricant is the key to realize the self-healing. In this study, a numerical model of lubricant exudation and spreading in micropores was established under the stimulation of the external temperature field. The morphological evolution of the meniscus and the distribution characteristics of the internal pressure during the exudation process were investigated. The influence mechanism of the thermal effect on the exudation and film formation on the porous surface was revealed. Results show that the formation process of lubricating film includes the lubricant exudation in the pores, the growth and spreading of microdroplets on the porous surface. In the lubricant exudation stage, the internal pressure of the fluid is negative. When the lubricant exudes to the edge of the pore, the internal pressure of the liquid changes from negative to positive. The three-phase contact wire is pinned at the edge of the pore and droplets are formed on the porous surface. When the droplet begins to spread, the internal pressure of the droplet decreases for the increasing of the meniscus curvature radius. The spreading velocity decreases gradually in the form of fluctuation under the combined action of the time-varying resistance and driving force. At higher wall temperature, the droplet surface tension and viscous resistance decrease, whereas the thermal-capillary force and driving force increase. Therefore, the higher the wall temperature, the greater the average velocity of the droplet spreading front, and the better the droplet spreading performance. Therefore, higher wall temperature can promote the droplet exudation and spreading on the surface, which is conducive to the self-healing of the lubricating film.

A free boundary problem with nonlocal diffusion and unbounded initial range

We consider a free boundary problem with nonlocal diffusion and unbounded initial range, which can be used to model the propagation phenomenon of an invasion species whose habitat is the interval $$(-\infty ,h(t))$$ with h(t) representing the spreading front. Since the spatial scale is unbounded, a different method from the existing works about nonlocal diffusion problem with free boundary is employed to obtain the well-posedness. Then we prove that the species always spreads successfully, which is very different from the free boundary problem with bounded range. We also show that there is a finite spreading speed if and only if a threshold condition is satisfied by the kernel function. Moreover, the rate of accelerated spreading and accurate estimates on longtime behaviors of solution are derived.

A free boundary problem with nonlinear advection and Dirichlet boundary condition

We study a free boundary problem for Fisher–KPP equation with nonlinear advection ut=uxx−uux+f(u) on [0,h(t)], which can model the spreading of chemical substances or biological species in the moving region. In this model, the free boundary h(t) indicates the spreading front of the species. Due to some factors (such as the migration of species), the advection is affected by population density. This paper mainly studies the asymptotic behavior of solutions. We prove that, the solution is either spreading (the survival area [0,h(t)] tends to [0,+∞), the solution converges to a stationary solution defined on the half-line), or converging to small steady state ([0,h(t)] goes to a finite interval and the solution converges to a small stationary solution with compacted support), or converging to big steady state ([0,h(t)] tends to a bigger finite interval, the solution converges to a large stationary solution with compacted support). Besides this, we also prove that, when the input of the species is a critical value, the solution is either spreading or in converging to medium steady state. Additionally, we also have two different spreading results. Finally, using traveling semi-wave, we give the spreading speed when spreading happens.

A toy model of misfolded protein aggregation and neural damage propagation in neurodegenerative diseases

Neurodegenerative diseases (NDs) result from the transformation and accumulation of misfolded proteins within the nervous system. Several mathematical models have been proposed to investigate the biological processes underlying NDs, focusing on the kinetics of polymerization and fragmentation at the microscale and on the spread of neural damage at a macroscopic level. The aim of this work is to bridge the gap between microscopic and macroscopic approaches proposing a toy partial differential model able to take into account both the short-time dynamics of the misfolded proteins aggregating in plaques and the long-term evolution of tissue damage. Using mixtures theory, we consider the brain as a biphasic material made of misfolded protein aggregates and of healthy tissue. The resulting Cahn–Hilliard type equation for the misfolded proteins contains a growth term depending on the local availability of precursor proteins, that follow a reaction–diffusion equation. The misfolded proteins also possess a chemotactic mass flux driven by gradients of neural damage, that is caused by local accumulation of misfolded protein and that evolves slowly according to an Allen-Cahn equation. The diffuse interface approach is new for NDs and allows both to consider five different time-scales, from phase separation to neural damage propagation, and to reduce the computational costs compared to existing multi-scale models, allowing a time-step adaptivity. We present here numerical simulations in a simple two-dimensional domain, considering both isotropic and anisotropic mobility coefficients of the misfolded protein and the diffusion of the neural damage, finding that the spreading front of the neural damage follows the direction of the largest eigenvalue of the mobility tensor. In both cases, we computed two biomarkers for quantifying the aggregation in plaques and the evolution of neural damage, that are in qualitative agreement with the characteristic Jack curves for many NDs.