Propagation Of Phase Transition Fronts Research Articles

Discontinuity-driven mesh alignment for evolving discontinuities in elastic solids

A special mesh adaptation technique and a precise discontinuity tracking are presented for an accurate, efficient, and robust adaptive-mesh computational procedure for one-dimensional hyperbolic systems of conservation laws, with particular reference to problems with evolving discontinuities in solids. The main advantage of the adaptive technique is its ability to preserve the modified mesh as close to the original fixed mesh as possible. The constructed method is applied to the martensitic phase-transition front propagation in solids.

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.

Hydrodynamics of phase transition fronts and the speed of sound in the plasma

The growth of bubbles in cosmological first-order phase transitions involves nontrivial hydrodynamics. For that reason, the study of the propagation of phase transition fronts often requires several approximations. A frequently used approximation consists in describing the two phases as being composed only of radiation and vacuum energy (the so-called bag equation of state). We show that, in realistic models, the speed of sound in the low-temperature phase is generally smaller than that of radiation, and we study the hydrodynamics in such a situation. We find in particular that a new kind of hydrodynamical solution may be possible, which does not arise in the bag model. We obtain analytic results for the efficiency of the transfer of latent heat to bulk motions of the plasma, as a function of the speed of sound in each phase.

Spherical and non-spherical bubbles in cosmological phase transitions

The cosmological remnants of a first-order phase transition generally depend on the perturbations that the walls of expanding bubbles originate in the plasma. Several of the formation mechanisms occur when bubbles collide and lose their spherical symmetry. However, spherical bubbles are often considered in the literature, in particular for the calculation of gravitational waves. We study the steady state motion of bubble walls for different bubble symmetries. Using the bag equation of state, we discuss the propagation of phase transition fronts as detonations and subsonic or supersonic deflagrations. We consider the cases of spherical, cylindrical and planar walls, and compare the energy transferred to bulk motions of the relativistic fluid. We find that the different wall geometries give similar perturbations of the plasma. For the case of planar walls, we obtain analytical expressions for the kinetic energy in the bulk motions. As an application, we discuss the generation of gravitational waves.

From the propagation of phase-transition fronts to the evolution of the growth plate in long bones

The various methodologies exploited in the study of the propagation of phase transition fronts in crystalline substances (inert matter) are examined and compared with a view to identifying mathematical tools useful in a scientific mechanobiological approach to the critical problem of the growth of long bones in mammals.

Stress-induced phase-transition front propagation in thermoelastic solids

A simplest possible mathematical model of martensitic phase transition front propagation is considered in the paper. Martensite and austenite phases are treated as isotropic linear thermoelastic materials. The phase transition front is viewed as an ideal mathematical discontinuity surface. Only one variant of martensite is involved. The problem remains nonlinear even in this simplified description that supposes a numerical solution. A non-equilibrium description of the process is provided by means of non-equilibrium jump relations at the moving phase boundary, which are formulated in terms of contact quantities. The same contact quantities are used in the construction of a finite-volume numerical scheme. The additional constitutive information is introduced by a certain assumption about the entropy production at the phase boundary. Results of numerical simulations show that the proposed approach allows us to capture experimental observations while corresponding to theoretical predictions in spite of the idealization of the process.

On the thermodynamic conditions at moving phase-transition fronts in thermoelastic solids

The main goal of the paper is to establish possible thermodynamic conditions at a phase boundary to describe a propagation of phase-transition fronts in crystalline solids. Classical equilibrium conditions are not valid in the case of fast propagation of sharp phase interfaces through the material during a stress-induced martensitic phase transformation. We propose to extend the equilibrium conditions to the non-equilibrium case in the framework of the thermodynamics of discrete systems. To provide the description of non-equilibrium states, the thermodynamic state space includes so-called contact quantities in addition to usual local equilibrium variables.

Dynamics of impact-induced phase transition fronts

Most experiments in martensitic phase transformations are performed under quasi-static loading of a specimen. The only well-documented experimental investigation concerning the impact-induced austenite-martensite phase transformations was given by Escobar and Clifton ([1], [2]). As Escobar and Clifton noted, measured velocity profiles provide a difference between the particle velocity and the transverse component of the projectile velocity. This velocity difference, in the absence of any evidence of plastic deformation, is indicative of a stress induced phase transformation that propagates into the crystals from the impact face. We develop a thermomechanical approach to the modeling of phase-transition front propagation based on the balance laws of continuum mechanics in the reference configuration [3] and the thermodynamics of discrete systems [4]. It is shown that the developed model captures the experimentally observed particle velocity difference.

THERMOMECHANICS OF HETEROGENEOUS MATERIALS WITH WEAKLY NONLOCAL MICROSTRUCTURE

A unified thermomechanical framework is presented for the theory of mechanically elastic materials the physical description of which requires the consideration of additional variables of state and of their gradients (weak nonlocality). This includes both the case of additional degrees of freedom carrying their own inertia and the case of diffusiw internal variables of state. In view of practical applications to fracture and propagation of phasetransition fronts. special attention is paid to the construction and immediate consequences of the equations of balance of canonical momentum (on the material manifold) and energy at regular points and at jump discontinuities. In particular. the general expression of the dissipation at, and of the driving force acting on. phase-transition fronts is formally obtained in such a broad framework. Brief applications include thermoelastic conductors (e.g. shape-memory alloys) and elastic ferromagnets in which both spin inertia and ferromagnetic exchange forces (magnetic ordering) are taken into account.

Driving Force on Phase Transition Fronts in Thermoelectroelastic Crystals

Starting from known physical balance laws and constitutive equations, this work develops in a rational number the canonical balance laws of momentum and energy at both regular and singular material points. This is achieved in the framework of the quasi-electrostatics of thermoelectroelastic crystals, with a view to providing a sound basis for the study of electroelastic fracture, and of the propagation of phase transition fronts. The latter receive special attention with the formulation of a true thermomechanics in which it is shown that a hot surface heat source develops at thermodynamically irreversible points of progress of such fronts. The expression of the driving force acting on such fronts in these conditions is obtained in terms of the relevant Hugoniot-Gibbs functional. This provides the basis for the formulation of simple criteria of progress of the front.

Material forces in thermoelastic ferromagnets

A systematic construction of the canonical balance of momentum (“pseudomomentum” on the material manifold) and energy is presented for materially inhomogeneous thermoelastic hard ferromagnets in which both exchange forces and magnetic-spin inertia are taken into account. The latter is of the gyroscopic type and endows the sources of quasi-inhomogeneities in the balance of pseudomomentum with special properties. The equations obtained will prove useful in further studies of the fracture of hard ferromagnets and of the propagation of phase-transition fronts in such materials.

Material Forces: Concepts and Applications

The unifying notion of material force which gathers under one vision all types of driving “forces” on defects and smooth or abrupt inhomogeneities in fracture, defect mechanics, elastodynamics (localized solutions) and allied theories such as in electroelasticity, magnetoelasticity, and the propagation of phase transition fronts, is reviewed together with its many faceted applications. The presentation clearly distinguishes between the role played by local physical balance laws in the solution of boundary-value problems and that played by global material balance laws in obtaining the expression of relevant material forces and devising criteria of progress for defects, in a general way. The advances made along this line, which may be referred to as Eshelbian mechanics, are assessed and perpectives are drawn.

Thermal interaction between water flow and frozen ground under hydroerosion

A model for one of the methods of thermal reclamation of frozen ground is proposed which allows for water flow temperature variations on the ground surface due to heat exchange between the water flow and a thawing solid. In a computation experiment, the specific features of phase transition front propagation and liquid temperature variation are studied.