Front Dynamics Research Articles

Dynamics of front-like water evaporation phase transition interfaces

We study global dynamics of phase transition evaporation interfaces in the form of traveling fronts in horizontally extended domains of porous layers where a water located over a vapor. These interfaces appear, for example, as asymptotics of shapes of localized perturbations of the unstable plane water evaporation surface caused by long-wave instability of vertical flows in the non-wettable porous domains. Properties of traveling fronts are analyzed analytically and numerically. The asymptotic behavior of perturbations are described analytically using propagation features of traveling fronts obeying a model diffusion equation derived recently for a weakly nonlinear narrow waveband near the threshold of instability. In context of this problem the fronts are unstable though nonlinear interplay makes possible formation of stable wave configurations. The paper is devoted to comparison of the known results of front dynamics for the model diffusion equation, when two phase transition interfaces are close, and their dynamics in general situation when both interfaces are sufficiently far from each other.

Quenching by Falling Cryogenic Liquid Film of Extremely Overheated Plate with Structured Capillary-Porous Coating

The paper presents results of a computational experiment simulating rapid cooling by falling liquid nitrogen film of an overheated vertical copper plate with a structured capillary-porous coating. A dynamic pattern of the running quench front was obtained, and it correlates satisfactorily with that observed in the experiments. The features of the heat transfer and quench front dynamics in the transient process are studied. The maximum density of the heat flux carried away into the liquid turned out to exceed by far that in quasi-stationary conditions. The presence of capillaryporous coating significantly affects the dynamics of quenching and temperature fields and makes it possible to reduce the total quenching time more than threefold. Initialization of a quench front on a plate with a structured capillary-porous coating occurs at a temperature much higher than the thermodynamic limit of liquid superheat. The reliability of the numerical simulation results was confirmed via direct comparison with experimental data on the variation of the plate temperature, as well as on the velocity and geometry of the quench front.

The dogs that didn't bark in the Blitz: transpecies and transpersonal emotional geographies on the British home front

This paper uses a case study of animals in wartime to ask how historical animal geographers might approach the historical geography of emotions. Its substantive focus is the entangled emotional experiences of humans and companion animals during the Second World War on the British home front. Arguing against a focus on the practical and political difficulties of keeping pets, this paper moves away from the preemptive killing of pets during the phoney war of 1939–1940 to evidence for the value placed on pets by pet owners, civilians in general and the British state. Drawing principally on Mass-Observation surveys, this paper investigates the complexities of the emotional dynamics of the home front, where affect and emotion between people and individual companion animals were transmitted and amplified. Moreover, it is emphasised that transpecies emotions were portrayed as valuable to wartime morale, and thus became part of governmental calculation. Taking morale as a distinct form of collective affect targeted by the wartime state, we can thus add a more-than-human dimension to historical geographies of emotion. In sum, this paper argues that emotion should be considered as both a transpersonal and a transpecies phenomenon: transpersonal because collectively mediated, and transpecies because of the emotional interactions between people and nonhuman animals.

Flow of buoyant granular materials along a free surface

We study experimentally the flow of light granular material along the free surface of a liquid of greater density. Despite a rich set of related geophysical and environmental phenomena, such as the spreading of calved ice, volcanic ash, debris and industrial wastes, there are few previous studies on this topic. We conduct a series of lock-release experiments of buoyant spherical beads into a rectangular tank initially filled with either fresh or salt water, and record the time evolution of the interface shape and the front location of the current of beads. We find that following the release of the lock the front location obeys a power-law behaviour during an intermediate time period before the nose of beads reaches a maximum runout distance within a finite time. We investigate the dependence of the scaling exponent and runout distance on the total amount of beads, the initial lock length, and the properties of the liquid that fills the tank in the experiments. Scaling arguments are provided to collapse the experimental data into universal curves, which can be used to describe the front dynamics of buoyant granular flows with different size and buoyancy effects and initial lock aspect ratios.

Two-layer displacement flow of miscible fluids with viscosity ratio: Experiments

We investigate experimentally the density-unstable displacement flow of two miscible fluids along an inclined pipe. This means that the flow is from the top to bottom of the pipe (downwards), with the more dense fluid above the less dense. Whereas past studies have focused on iso-viscous displacements, here we consider viscosity ratios in the range 1/10–10. Our focus is on displacements where the degree of transverse mixing is low-moderate, and thus a two-layer, stratified flow is observed. A wide range of parameters is covered in order to observe the resulting flow regimes and to understand the effect of the viscosity contrast. The inclination of the pipe (β) is varied from near horizontal β = 85° to near vertical β = 10°. At each angle, the flow rate and viscosity ratio are varied at fixed density contrast. Flow regimes are mapped in the (Fr, Re cos β/Fr)-plane, delineated in terms of interfacial instability, front dynamics, and front velocity. Amongst the many observations, we find that viscosifying the less dense fluid tends to significantly destabilize the flow. Different instabilities develop at the interface and in the wall-layers.

Hamiltonian Formalism for the Problem of Optimal Motion Control under Multiple Criteria

This paper describes methods for optimizing solutions to problems of controlled dynamics under multiple criteria. Such problems are usually solved by reduction to scalarized costs. However, preferable in realistic cases is the analysis of the whole Pareto front with description of its evolutionary dynamics. This is done via the introduction of vector-valued multiobjective dynamic programming similar to the classical approach described in [1]. It is shown that, under certain conditions, a multiobjective analogue of the classical principle of optimality holds for the introduced vector-valued cost function. As a result, a vector-valued version of the Hamilton–Jacobi–Bellman equation is introduced and the dynamics of the whole Pareto front is presented.

Filtration Gas Combustion in a Porous Ceramic Annular Burner for Thermoelectric Power Conversion

ABSTRACTA numerical study of the combustion of lean methane/air mixtures in a porous media burner is performed using novelty geometry, cylindrical annular space. The combustion process takes place in the porous space located between two pipes, which are filled with alumina beads of 5.6 mm diameter forming a porosity of 0.4. The outer tube diameter of 3.82 cm is isolated; meanwhile the inner tube of 2 cm in diameter is covered by a continuous set of thermoelectric elements (TE) for transforming heat energy into electricity. To achieve and maintain the proper temperature gradient on TE, convective heat losses are considered from the TE. Computer simulations focus on the two-dimensional (2D) temperature analysis and displacement dynamics of the combustion front inside the reactor, depending on the values of the filtration velocity (0.1 to 1.0 m/s), the heat loss coefficient from the internal cylinder (400–1500 W/m2/K), and the fuel equivalence ratio (0.06– 0.5). The conditions that maximized the overall performance of the process of energy conversion are: 0.7 m/s of the filtration velocity, 0.363 of the fuel equivalence ratio and 1500 W/(m2·K) of the heat transfer coefficient from the internal cylinder, to obtain 2.05 V electrical potential, 21 W of electrical power, and 5.64% of the overall process efficiency. The study shows that the cylindrical annular geometry can be used for converting the energy of combustion from lean gas mixtures into electricity, with a performance similar to the specified by manufacturers of thermoelectric elements (TE).

Retraction of the dissolution front in natural porous media

The dissolution of porous materials in a flow field controls the fluid pathways through rocks and soils and shapes the morphology of landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive volumes in a dissolving medium, is a prerequisite for describing dissolution-induced structure emergence and transformation. Despite its fundamental importance, the report on the dynamics of a dissolution front in an evolving natural microstructure is scarce. Here we show an unexpected, spontaneous migration of the dissolution front against the flow direction. This retraction stems from infiltration instability induced surface generation, which leads to an increase in reactive surface area when a porous medium dissolves in an imposing flow field. There is very good agreement between observations made with in situ, X-ray tomography and model predictions. Both show that the value of reactive surface area reflects a balance between flow-dependent surface generation and destruction, i.e. the “dry” geometric surface area of a porous material, measured without a flow field, is not necessarily the upper limit of its reactive surface area when in contact with reactive flow. This understanding also contributes to reconciling the discrepancies between field and laboratory derived solid-fluid reaction kinetics.

Regime shifts by front dynamics

Ecosystems are highly nonlinear dissipative systems that often admit multiple alternative stable states, but seldom have the time span to converge to these states as they are repeatedly interfered by environmental changes and disturbances. Multiplicity of stable states in variable and disturbed environments is of high concern because of the possible occurrence of regime shifts, i.e. state transitions that involve large, abrupt decline in ecosystem function. State transitions induced by disturbances, however, need not be abrupt as the disturbances are often limited in their spatial extent. In that case they induce local state transitions that result in spatially confined alternative-state domains. The subsequent dynamics crucially depend on the dynamics of the transition zones or fronts that bound these domains. In this paper we study three aspects of front dynamics that affect the nature of regime shifts and their outcomes: single-front motion, front interactions and front instabilities. Using models of dryland vegetation as a case study we show that fronts can change their speed and invert their direction of motion as parameters change across a threshold value – the Maxwell point, that fronts may slow down or stop entirely when interacting with other fronts, and that disturbances may change one front type to another, each with its distinct speed. We further study the implications of these three aspects of front dynamics to gradual regime shifts. We show that such shifts can occur due to the propagation of a perturbation beyond its original extent, that such a transition does not necessarily culminate in the alternative state, i.e. it may remain incomplete, and that the time it takes for a regime shift to occur can be changed by front manipulations. Since gradual regime shifts can take place far from the typical tipping point considered, early warning signals of an approaching tipping point would fail in predicting gradual regime shifts. A more relevant approach for these regime shifts may be the development of detection and prevention methods, which can be applied during an ongoing gradual regime shift due to its slow dynamics. We conclude with a discussion of the need to develop such methods and of other ecological contexts that may benefit from them.

Thermal Transients in District Heating Systems

Heat fluxes in a district heating pipeline systems need to be controlled on the scale from minutes to an hour to adjust to evolving demand. There are two principal ways to control the heat flux - keep temperature fixed but adjust velocity of the carrier (typically water) or keep the velocity flow steady but then adjust temperature at the heat producing source (heat plant). We study the latter scenario, commonly used for operations in Russia and Nordic countries, and analyze dynamics of the heat front as it propagates through the system. Steady velocity flows in the district heating pipelines are typically turbulent and incompressible. Changes in the heat, on either consumption or production sides, lead to slow transients which last from tens of minutes to hours. We classify relevant physical phenomena in a single pipe, e.g. turbulent spread of the turbulent front. We then explain how to describe dynamics of temperature and heat flux evolution over a network efficiently and illustrate the network solution on a simple example involving one producer and one consumer of heat connected by “hot” and “cold” pipes. We conclude the manuscript motivating future research directions.

Numerical research of solidification dynamics with anisotropy and thermal fluctuations

The influence of thermal fluctuations and anisotropy on the solidification process of a pure component is analyzed. It helps to understand the unstable freezing process where complicated structures such as dendrites could be formed due to a supercooling event reached during the cooling of the biological material. The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics. The analysis has been modeled in the framework of the Phase Field Method with Cahn-Hilliard formulation of a free energy functional [1]. The phase front is described by the Eulerian approach of fluid fields and formulated as a Phase Field scalar variable (order parameter) with a predefined, diffused boundary thickness. The results describe an influence scale onto directional phase front propagation dynamics, and how significant are stochastic thermal noises in micro-scale freezing.

Front dynamics of pH oscillators with initially separated reactants

The spatiotemporal dynamics of the Landolt-type pH oscillators are studied both numerically and experimentally with initially separated reagents in space. This configuration results in an A + B → oscillator front type system with localized patterns. The generic Rabai model of the pH-oscillators predicts the formation of an asymmetric acidic domain at the interface of the two zones loaded by different sets of chemicals. This asymmetry is caused by the initial conditions rather than the difference in the diffusivities of the components. As the influence of the negative feedback process increases, this acidic zone becomes to be localized around the interface. At some point, the acidic zone bifurcates, a less acidic zone separates and starts to move forward the oxidant rich zone. In a limited domain of parameters, spatiotemporal oscillations are found due to the instability of the main acidic zone. The appropriate conditions for the development of this periodic behavior is characterized by simulations. The numerically predicted phenomena are supported by experiments performed with the bromate–sulfite–ferrocyanide and with the hydrogen peroxide–sulfite–ferrocyanide systems, except the oscillatory phenomena.

Influence of a heat-absorbing surface on the propagation of a hemispherical flame

Gaseous explosions lead to severe damage. Elimination or mitigation of damage is a key problem in industrial safety. This paper presents an experimental study of hydrogen–air flame front dynamics and flame suppression by means of a surface coating. The experimental stand is a metal frame that confines the cylindrical envelope to a diameter of 1.5 m and 2.4 m in height of high-density 100 μm thick polyethylene. Experimental data on the hemispherical flame propagation in hydrogen–air mixtures with a hydrogen content of 15% were obtained at the initiation of combustion with an energy of 5 J. The flame propagates at atmospheric pressure over a solid aluminium wall or a layer of steel wool. To measure the flame propagation speed, an infrared InfraTec ImageIR 8320 camera with spectral range 2–5.7 μm was used. The flame acceleration dynamics were compared at flame radii up to 0.4 m. It was found that in a mixture with a hydrogen content of 15% the flame over the layer of steel wool propagates 2.5 times more slowly than that over the surface of an aluminium wall. The steel wool was investigated by scanning electron microscope using an energy dispersive analysis system before and after the passing of the flame front. The structure and chemical composition of the metal wool was studied. Calculation of heat absorption in the steel wool layer shows that the heat losses due to the absorption are the main phenomenon causing the flame front speed reduction, which was observed in the experiments. Additionally, the speed of the flame was affected by the absorption of oxygen and the release of heat during the oxidation of the steel wool, as well as by the roughness of the layer of steel wool.

From Patterns to Function in Living Systems: Dryland Ecosystems as a Case Study

Spatial patterns are ubiquitous in animate matter. Besides their intricate structure and beauty they generally play functional roles. The capacity of living systems to remain functional in changing environments is a question of utmost importance, but its intimate relationship to pattern formation is largely unexplored. Here, we address this relationship using dryland vegetation as a case study. Following a brief introduction to pattern-formation theory, we describe a mathematical model that captures several mechanisms of vegetation pattern formation and discuss ecological contexts that showcase different mechanisms. Using this model, we unravel the different vegetation patterns that keep dryland ecosystems viable along the rainfall gradient, identify multistability ranges where fronts separating domains of alternative stable states exist, and highlight the roles of front dynamics in mitigating or reversing desertification. The utility of satellite images in testing model predictions is discussed. An outlook on outstanding open problems concludes this paper.

Control of evaporation by geometry in capillary structures. From confined pillar arrays in a gap radial gradient to phyllotaxy-inspired geometry

Evaporation is a key phenomenon in the natural environment and in many technological systems involving capillary structures. Understanding the evaporation front dynamics enables the evaporation rate from microfluidic devices and porous media to be finely controlled. Of particular interest is the ability to control the position of the front through suitable design of the capillary structure. Here, we show how to design model capillary structures in microfluidic devices so as to control the drying kinetics. This is achieved by acting on the spatial organization of the constrictions that influence the invasion of the structure by the gas phase. Two types of control are demonstrated. The first is intended to control the sequence of primary invasions through the pore space, while the second aims to control the secondary liquid structures: films, bridges, etc., that can form in the region of pore space invaded by the gas phase. It is shown how the latter can be obtained from phyllotaxy-inspired geometry. Our study thus opens up a route toward the control of the evaporation kinetics by means of tailored capillary structures.

Front dynamics and entanglement in the XXZ chain with a gradient

We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

Topological defects govern crack front motion and facet formation on broken surfaces.

Cracks develop intricate patterns on the surfaces that they create. As faceted fracture surfaces are commonly formed by slow tensile cracks in both crystalline and amorphous materials, facet formation and structure cannot reflect microscopic order. Although fracture mechanics predict that slow crack fronts should be straight and form mirror-like surfaces, facet-forming fronts propagate simultaneously within different planes separated by steps. Here we show that these steps are topological defects of crack fronts and that crack front separation into disconnected overlapping segments provides the condition for step stability. Real-time imaging of propagating crack fronts combined with surface measurements shows that crack dynamics are governed by localized steps that drift at a constant angle to the local front propagation direction while their increased dissipation couples to long-ranged elasticity to determine front shapes. We study how three-dimensional topology couples to two-dimensional fracture dynamics to provide a fundamental picture of how patterned surfaces are generated.

Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms

Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces.

Numerical study on the effect of temperature oscillations on the crystallization front shape during Czochralski growth of gadolinium gallium garnet crystal

Time-dependent, finite volume method calculations of momentum and heat transfer were carried out to investigate the correlation between oscillatory convection and the crystallization front dynamics during the Czochralski (Cz) growth of an oxide material. The present modeling allows us to illustrate the modification of the interface shape during the time period of oscillation of the flow manifesting as the formation of a cold plume beneath the phase boundary. It was shown that the instability mechanism is associated with an irreversible dramatic change in the interface shape, which occurs at a critical Reynolds number significantly lower than that is predicted by the quasi-stationary global model analysis of the Cz growth system. The baroclinic term which appears in the vorticity equation in a rotating stratified fluid is used to describe the numerical results of the model. The properties of the thermal waves were studied in the monitoring points located nearby the interface. The waves are regular but not in fact vertically correlated as observed in the case of baroclinic waves. The Rayleigh–Benard dynamics is suggested to be the predominant mechanism even though the instability is primarily baroclinic.

A mathematical model for adaptive vein formation during exploratory migration of Physarum polycephalum: routing while scouting

Exploring free space (scouting) efficiently is a non-trivial task for organisms of limited perception, such as the amoeboid Physarum polycephalum. However, the strategy behind its exploratory behaviour has not yet been characterised. In this organism, as the extension of the frontal part into free space is directly supported by the transport of body mass from behind, the formation of transport channels (routing) plays the main role in that strategy. Here, we study the organism’s exploration by letting it expand through a corridor of constant width. When turning at a corner of the corridor, the organism constructed a main transport vein tracing a centre-in-centre line. We argue that this is efficient for mass transport due to its short length, and check this intuition with a new algorithm that can predict the main vein’s position from the frontal tip’s progression. We then present a numerical model that incorporates reaction-diffusion dynamics for the behaviour of the organism’s growth front and current reinforcement dynamics for the formation of the vein network in its wake, as well as interactions between the two. The accuracy of the model is tested against the behaviour of the real organism and the importance of the interaction between growth tip dynamics and vein network development is analysed by studying variants of the model. We conclude by offering a biological interpretation of the well-known current reinforcement rule in the context of the natural exploratory behaviour of Physarum polycephalum.