Phase Transition Front Research Articles

A Multifront Problem of Freezing-Thawing Moist Soil

Construction activities in the North of Western Siberia is carried out in specific conditions of the cryolithozone. The study of heat transfer processes in freezing soils near buildings is necessary to ensure their successful operation. Heat exchange with phase transition is traditionally described by Stefan problem, which is a system of differential equations of parabolic type with standard boundary conditions and a subsidiary condition on the phase transition boundary. It is possible to formally pass on to one equation of the conductivity type, but in that case the delta function appears in one of the coefficients. The delta function reflects the Joule heat release at the phase transition temperature. A widespread “pass-through counting” method reduces the Stefan problem to a boundary problem for a nonlinear heat conductivity equation. With this approach, the calculation results in a temperature field. But it is difficult to identify the position of the phase transition boundary on the temperature field. A large number of methods for solving the Stefan problem are developed, in which the required value is the phase transition front coordinate. The common disadvantage of these methods is their unsuitability for situations with several fronts, when these fronts appear and disappear, change the movement direction, merge with each other. The article presents a method for solving the Stefan problem, which allows to obtain the front coordinate as a zero isotherm. As an example this method is used to solve the problem of freezing-thawing of moist soil under the influence of seasonal surface temperature fluctuations. The method eliminates the need to control the evolution of each front. The Stefan problem is considered as a limiting case of the general phase transition problem in a certain temperature range. Standard transformations and application of Green’s function allow to write down a problem in the form of an integral equation. The approximate solution is obtained in the form of a recurrent formula.

A Multifront Problem of Freezing-Thawing Moist Soil

Construction activities in the North of Western Siberia is carried out in specific conditions of the cryolithozone. The study of heat transfer processes in freezing soils near buildings is necessary to ensure their successful operation. Heat exchange with phase transition is traditionally described by Stefan problem, which is a system of differential equations of parabolic type with standard boundary conditions and a subsidiary condition on the phase transition boundary. It is possible to formally pass on to one equation of the conductivity type, but in that case the delta function appears in one of the coefficients. The delta function reflects the Joule heat release at the phase transition temperature. A widespread “pass-through counting” method reduces the Stefan problem to a boundary problem for a nonlinear heat conductivity equation. With this approach, the calculation results in a temperature field. But it is difficult to identify the position of the phase transition boundary on the temperature field. A large number of methods for solving the Stefan problem are developed, in which the required value is the phase transition front coordinate. The common disadvantage of these methods is their unsuitability for situations with several fronts, when these fronts appear and disappear, change the movement direction, merge with each other. The article presents a method for solving the Stefan problem, which allows to obtain the front coordinate as a zero isotherm. As an example this method is used to solve the problem of freezing-thawing of moist soil under the influence of seasonal surface temperature fluctuations. The method eliminates the need to control the evolution of each front. The Stefan problem is considered as a limiting case of the general phase transition problem in a certain temperature range. Standard transformations and application of Green’s function allow to write down a problem in the form of an integral equation. The approximate solution is obtained in the form of a recurrent formula.

Two-phase disintegration of high-pressure retrograde fluid jets at near-critical injection temperature discharged into a subcritical pressure atmosphere

In this study, n-hexane was compressed beyond six times its critical pressure and discharged into argon at subcritical pressure (with respect to the injectant). The injection temperature systematically varied from sub- to supercritical values to investigate near-critical disintegration phenomena of retrograde jets. Here, the ratio of the pressure in the nozzle reservoir and chamber was always above 14 leading to highly-expanded injections. We analyzed the breakup process in terms of combined shadowgraphy and light scattering measurements. Close to the critical point, different physical mechanisms have been observed. Their occurrence is predominantly determined by the expansion process resulting from the thermodynamic conditions in nozzle reservoir and chamber in combination with thermodynamic properties of the injectant. The experimental images for near- but subcritical injection temperatures imply that a fluid in liquid state expands in the nozzle and atomizes downstream of it. For sufficiently low backpressures, high liquid superheats trigger rapid vapor formation across a thin transition layer inside the nozzle that leads to a choked two-phase flow. A thermodynamic model that assumes a discontinuous phase transition layer and uses metastable fluid properties provides a physical explanation of the resulting underexpanded two-phase disintegration downstream of the nozzle exit . An increase to supercritical injection temperatures increases the compressibility of the fluid within the nozzle. An isentropic flow analysis showed that this triggers choking at thermodynamic states in the supercritical pressure regime resulting in the discharge of a sonic single-phase fluid. The expansion within the Mach barrel can lead to a supersaturated fluid state at near-critical temperature. In this case, a sharp phase transition front established approximately half a nozzle diameter downstream of the exit. We defined a dimensionless parameter to characterize the two-phase extent in underexpanded jets with near-critical phase transition based on initial injection conditions and retrograde fluid properties. We deduced the axial extent of the two-phase region from light scattering signals for a wide parameter range and demonstrate that it features a clear dependency upon the proposed parameter, which demonstrates its feasibility.

Instability of the Phase Transition Front during Water Injection into High-Temperature Rock

Water injection into a high-temperature geothermal reservoir saturated with superheated vapor is investigated. A solution to the one-dimensional problem in the form of a traveling wave is found. It is shown that there exist two types of solutions which correspond to the boiling of water and the condensation of vapor. In the condensation regime with high initial pressure, vapor ahead of the phase transition front is shown to be in a supercooled state. For moderate or law initial pressure, solutions with condensation and boiling are thermodynamically consistent. Linear stability of the phase transition surface between the water and vapor regions is analyzed. It is shown that the phase transition front moving at constant velocity is always unstable.

Dynamics of discontinuities in elastic solids

The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.

Pick-up and impact of flexible bodies

Picking up, laying down, colliding, rolling, and peeling are partial-contact interactions involving moving discontinuities. We examine the balances of momentum and energy across a moving discontinuity in a string, with allowance for injection or dissipation by singular supplies. We split the energy dissipation according to its invariance properties, discuss analogies with systems of particles and connections with the literature on shocks and phase transition fronts in various bodies, and derive a compatibility relation between supplies of momentum and translation-invariant energy. For a moving contact discontinuity between a string and a smooth rigid plane in the presence of gravity, we find a surprising asymmetry between the processes of picking up and laying down, such that steady-state kinks in geometry and associated jumps in tension are not admissible during pick-up. This prediction is consistent with experimental observations. We briefly discuss related problems including the falling folded chain, peeling of an adhesive tape, and the “chain fountain”. Our approach is applicable to the study of impact and locomotion, and to systems such as moored floating structures and some musical instruments that feature vibrating string and cable elements interacting with a surface.

Bubble nucleation and growth in very strong cosmological phase transitions

Strongly first-order phase transitions, i.e., those with a large order parameter, are characterized by a considerable supercooling and high velocities of phase transition fronts. A very strong phase transition may have important cosmological consequences due to the departures from equilibrium caused in the plasma. In general, there is a limit to the strength, since the metastability of the old phase may prevent the transition to complete. Near this limit, the bubble nucleation rate achieves a maximum and thus departs from the widely assumed behavior in which it grows exponentially with time. We study the dynamics of this kind of phase transitions. We show that in some cases a gaussian approximation for the nucleation rate is more suitable, and in such a case we solve analytically the evolution of the phase transition. We compare the gaussian and exponential approximations with realistic cases and we determine their ranges of validity. We also discuss the implications for cosmic remnants such as gravitational waves.

Instability of a liquid–vapor phase transition front in inhomogeneous wettable porous media

The stability of vertical flows through a horizontally extended two-dimensional region of a porous medium is considered in the case of presence of a phase transition front. It is shown that the plane steady-state phase transition front may have several steady-state positions in the wettable porous medium and the necessary condition of their existence is obtained. The spectral stability of the plane phase transition interface is investigated. It is found that in the presence of capillary forces exerted on the phase transition front in the wettable medium the plane front can be destabilized on the mode with both infinite and zero wavenumbers (short- and long-wave instabilities); the short-wave instability can then exist even in the case of the sole steady-state position of the front.

Метод решения обратной задачи Стефана для контроля состояния ледопородного ограждения при проходке шахтных стволов

Mathematical statement of direct and inverse problem of Stefan for horizontal layer of rock massif with homogenous and isotropic thermophysical properties is presented. It is assumed as a hypothesis that heat transfer in vertical direction is negligible compared to heat exchange in horizontal plane. At the initial moment, the rock massif has a uniform temperature and the temperature on surfaces of freezing columns was the same for all columns and constant in time. A method proposed allows getting an approximate solution of the direct Stefan problem for a single freezing column with a small consumption of computational resources. Based on a proposed method, a high-speed algorithm for solving inverse Stefan problem for the case of a single freezing column is built. An algorithm is based on the gradient descent method. The effect on the solution of different types of functions used is analyzed. Functions approximate the temperature field in a cooling zone. It is established that time dependence of the radius of a phase transition front essentially depends on the type of an approximation function. The most preferable is an integral exponential function that is a solution to the one-dimensional heat equation in cylindrical coordinates. Then, proposed technique and algorithm are considered for the case of variety of freezing columns that form circle counter and random number of control wells. Results of the calculation of inverse Stefan problem for conditions of the shaft No. 1 of the mine being under construction at the Petrikovsky ore mining and processing enterprise are presented. The calculation included well inclinometry based on geological data. It was studied how measurements of the temperature made at different wells can affect obtaining solution. Options of interpretation of inconsistency of temperatures measured in control wells are offered. Probabilistic analysis of ice wall thickness is carried out.

Effect of the mass-transfer intensity on the dynamic relations on a phase interface

The dynamic relations on the phase interface are derived in the isothermal approximation for liquids in which the dependence of the surface energy on the mass flux across the phase interface must be taken into account. The criterion of stability of subsonic phase-transition fronts with plane waves with respect to small perturbations is determined. The dependence of the surface tension on the mass flux is calculated for the well-known exact solution to the problem of the structure of isothermal phase transition within the framework of the generalized van der Waals model.

Morphological instability of an evaporation front moving in a geothermal reservoir

The evaporation front moving with a constant velocity through a high-temperature geothermal reservoir is investigated. The solution in the form of a traveling wave is represented. The existence of a thermodynamically consistent solution and the solution with superheating of water ahead of the phase transition front is demonstrated. A boundary separating two types of the solutions is found in the domain of constitutive parameters. Stability of the solutions obtained is investigated by means of the normal mode method. It is shown that the criterion of superheating of water ahead of the boiling front and the criterion of linear stability of the front do not coincide.

The role of conduction electrons in the formation of thermal boundary resistance of the metal-dielectric interface and resistivity of metal films, at low temperatures (Review Article)

This review article is a discussion of the role played by conduction electrons in the formation of an effective acoustic transparency at the interface between narrow metal films and dielectric substrates with high thermal conductivity, within the framework of the acoustic mismatch between solids. We consider both steady and transient regimes of phonon radiation from metal films heated by electric current or short laser pulses, at low temperatures. We discuss in detail how the electron-phonon energy relaxation τe and the average exit time of the phonons from the films τes can be found using the experiment. A theoretical analysis of these problems is carried out using kinetic equations for the phonon and electron distribution functions. We examine the steady modes of relaxation and diffusion heat removal from the moving plane phase transition front in the film geometry. In most cases, we discuss the relationship between the theoretical results of the review authors and the existing experimental situation.

The influence of heat transfer conditions on the parameters characterizing the ignition of coal-water fuel particles

The future of thermal power engineering both in Russia and abroad will depend in many respects on the use of coal as main fuel for generating heat and electricity. In this connection, matters concerned with development and introduction of new environmentally friendly and energy efficient coal firing technologies are becoming of much importance. Firing coal in the form of coal-water fuel is one of the most promising solutions. However, despite a rather long history of its development (more than 40 years), this technology has not found wide use as yet, which in all likelihood is due to lack of full mathematical and physicochemical models describing the processes that take place when a coal-water fuel particle undergoes thermal treatment and ignition. The article presents the results obtained from numerical solution of the coal-water fuel particle ignition problem taking into account simultaneously occurring main thermal treatment processes (thermal conductivity, water evaporation, filtration heat and mass transfer, thermal decomposition of the fuel organic part, and thermochemical interaction between water vapor and coke carbon). The ignition problem is solved using the finite difference method. For calculating the evaporation process taking into account nonequilibrium nature of the parameters at the interface boundary of the initial “coal-water fuel—dry coal” system, the method of capturing the phase transition front at the difference mesh node was used. The results obtained from numerical modeling were used for determining the conditions and parameters characterizing the ignition of coal-water fuel particles under the conditions typically existing in the furnace space of boiler units. The extent to which radiant heat transfer influences the ignition delay time is determined. It is shown that radiant heat transfer plays a determining role in the thermal preparation of fuel for ignition.

Transition Mechanism and Phase Transition Front of Li x Ni0.5Mn1.5O4

1. Introduction Nickel substituted manganese spinel LiNi0.5Mn1.5O4 (LNMO) shows high rate capability even it consist of micron-sized particles.[1] This is in contrast to LiFePO4 where only nano-sized particles show high rate performance. For the designing of high performance batteries, it is important to understand the phase transition mechanism of the micron-sized LNMO that is inseparably connected with the rate capability.[2] As the micron-sized LNMO particles is expected that the existence of possible intermediate states between the phases (namely Li1, Li1/2 and Li0) are captured by operando XRD while TEM analysis shows the existence of the phase transition front. In this study, we revealed the factor of reaction kinetics from phase transition behavior of the LNMO by operando (1 C and 5 C) synchrotron X-ray diffraction (XRD) measurement, and transmission electron microscopy (TEM) analysis. 2. Experimental procedure LNMO powder used as an active material has primary and secondary particle sizes of around 1 and 5-10 µm, respectively. The working electrode consisted of LNMO (80 wt.%), acetylene black (10 wt.%) and polyvinylidene difluoride (PVdF) binder (10 wt.%), coated on aluminum current foil. The electrochemical measurements of the electrode were employed using aluminum pouch type cells, metallic lithium as counter and reference electrodes, 1 mol dm-3 LiPF6 in a 3:7 mixture of EC/DMC, and a polyolefin film as a separator. The electrochemical charge and discharge tests were performed at room temperature and the potential range was between 3.5 and 5.0 V. The time-resolved XRD (TR-XRD) measurements were conducted at the BL28XU and BL46XU of SPring-8, Hyogo, Japan. The incident X-ray of 12.4 keV (0.100 nm wavelength) was used. We measured the diffractions in the region around the 115 peak of LNMO. The data acquisition time was 0.5 s and discharge tests were employed at rate of 1 or 5 C. The TEM was employed to analyze the particle morphology of initial LiNi0.5Mn1.5O4 powder and Li0.25Ni0.5Mn1.5O4 obtained by 1 C charging. Electron diffraction (ED) analysis and electron energy-loss spectroscopy (EELS) were also performed to analyze crystal structure and intraparticle distribution of the reacting material. 3. Results and Discussion Fig. 1 shows the XRD patterns obtained during the transition between Li1 and Li1/2, and Li1/2 and Li0 at charging process. When two symmetric peak profiles using the Gaussian functions are assumed for these phases at a region of two phases existence, the experimentally obtained intensity in between the two peaks is larger than the calculated intensity. It’s suggesting that there are minor diffractions with intermediate d values in addition to major ones of the phases. A good fit is obtained assuming two additional diffraction components, implying the existence of intermediates in between the phases. Compared to the homogeneous morphology of the pristine LNMO particle, cracks, stripes, lattice defects and regions of different contrast are observed in the charged sample as shown in Fig. 2. With ex-situ TEM analysis the coexistence of the two phases in primary particles is shown, suggesting that the phase front movement is slow and that the minor diffractions observed in operando XRD are originated from solid-solution domains at the phase transition front of Li x Ni0.5Mn1.5O4. At 5 C rate single phase transition behavior is observed for both Li1 and Li0 phases.

Solid Solution Domains at Phase Transition Front of LixNi0.5Mn1.5O4

Nickel‐substituted manganese spinel LiNi0.5Mn1.5O4 (LNMO) is a promising 5 V class positive electrode material for lithium‐ion batteries. As micron‐sized LNMO particles show high rate capability in its two‐phase coexistence regions, the phase transition mechanism is of great interest in understanding the electrode behavior at high rates. Here, the phase transition dynamics of LixNi0.5Mn1.5O4 is elucidated on high rate charging–discharging using operando time‐resolved X‐ray diffraction (TR‐XRD). The TR‐XRD results indicate the existence of intermediate states, in addition to the thermodynamically stable phases, and it is shown that the origin of such intermediate states is ascribed to the solid‐solution domains at the phase transition front, as supported by the analysis using transmission electron microscopy coupled with electron energy‐loss spectroscopy. The phase transition pathways dependent on the reaction rate are shown, together with possible explanation for this unique transition behavior.

Mathematical modelling of heat transfer process in layered materials accounting for phase transitions in individual layers

A mathematical model has been constructed for determining the temperature fields and motion of the phase transition boundaries without using the classical Stefan condition and the concentrated heat capacity. The model makes it possible to determine more accurately the location of the phase transition front and may be used at the computations for layered materials in the cases when there are several fronts, and they can merge. The modeling of the problem on determining the melting boundary in a three-layer material has been carried out for the one-dimensional case.

Numerical simulation of precipitate formation during the boiling of salt solution in a geothermal reservoir

The process of precipitate formation during vapor outflow from a high-temperature geothermal reservoir saturated with a salt solution is investigated numerically. The evaporation regimes characterized by the formation of a phase transition front are considered. Comparison with the asymptotic solution obtained previously is performed. In the region of parameters where the self-similar solution exists the numerical solution approaches the asymptotic one in a short time. In the region where the asymptotic solution does not exist the numerical solution shows that the solid salt saturation monotonically increases with catastrophic growth in the last stage, which leads to the filling of the pores with solid salt and the total blocking of the flow.

Numerical simulation of a phase transition problem with natural convection using hybrid FEM/EFGM technique

Purpose – The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection. Design/methodology/approach – The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM. Findings – A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases. Originality/value – The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.

Lower bound on the electroweak wall velocity from hydrodynamic instability

The subsonic expansion of bubbles in a strongly first-order electroweak phase transition is a convenient scenario for electroweak baryogenesis. For most extensions of the Standard Model, stationary subsonic solutions (i.e., deflagrations) exist for the propagation of phase transition fronts. However, deflagrations are known to be hydrodynamically unstable for wall velocities below a certain critical value. We calculate this critical velocity for several extensions of the Standard Model and compare with an estimation of the wall velocity. In general, we find a region in parameter space which gives stable deflagrations as well as favorable conditions for electroweak baryogenesis.

Dynamics and stability of moving fronts of water evaporation in a porous medium

We study stability of non-steady plane water evaporation fronts, arising in vertical flows with phase transition in horizontally extended domains of a porous medium. Isothermal motions in the non-wettable horizontal porous medium when a water layer is located over a vapor one is considered and homogeneous capillary forces on the phase transition front are taken into consideration. It is shown that motion of the mobile phase transition fronts depend on their initial position relative to bifurcation curves of the stationary fronts. The four domains in the parameter space are picked out where behavior of linear perturbations of the mobile fronts are different: in the first domain all perturbations decrease, in the second one only long-wave perturbations grow, in the third domain only short-wave perturbations grow and in the fourth one all perturbations grow. Dynamics of localized finite amplitude perturbations of the moving phase transition front are also studied numerically. It is established that their evolution is mainly influenced by the initial position of the perturbed front relative to the mentioned stability/instability domains.