Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation. An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition boundary change. Calculation relationships are established for determining the phase transition temperature taking into account transport gradients and time for which the relative saturation reaches the boundaries of the phase transition.

Topological Equivalence of the Phase Diagrams of Molybdenum and Tungsten

We demonstrate the topological equivalence of the phase diagrams of molybdenum (Mo) and tungsten (W), Group 6B partners in the periodic table. The phase digram of Mo to 800 GPa from our earlier work is now extended to 2000 GPa. The phase diagram of W to 2500 GPa is obtained using a comprehensive ab initio approach that includes (i) the calculation of the T = 0 free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid–solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid–solid phase transition boundary in order to confirm the corresponding analytic form. For both Mo and W, there are two solid structures confirmed to be present on their phase diagrams, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp), such that at T = 0 the bcc–dhcp transition occurs at 660 GPa in Mo and 1060 GPa in W. In either case, the transition boundary has a positive slope d T / d P .

A parameters selection criterion of the numerical realisation of the continuous method for the Stefan problems

This paper suggests a selection criterion of the continuous method version for a numerical solution of the Stefan problem which would allow to calculate the phase transition boundary position with a required accuracy for a long period of time and would enable generalization to multidimensional problems. Despite a large number of works deal with the solution to the generalized Stefan problem by the continuous method, the choice of the smoothing interval value for numerical feasibility is not fully clear. A comparison of the calculation accuracy of the phase transition boundary position using different versions of the continuous method was carried out on an example of the well-known 1-D plane two-phase Stefan problem which possesses an analytical solution. The dependence of the total error of the numerical calculation of the phase transition boundary position on the value of the smearing interval is determined from the comparison of numerical and analytical solutions. An analysis of the reason for increase of this error with time at any choice of a constant smoothing interval is given. A version of the continuous method with a variable interval of the delta function smoothing, in which the proposed criterion is carried out, is discussed. The position of the phase transition boundary calculated proposed version matches the analytical solution with a required accuracy over a long period of time.

Stability, composition, and crystal structure of Fe-bearing Phase E in the transition zone

Fe-bearing phase E coexisting with ringwoodite and wadsleyite has been synthesized at near-geotherm temperatures in hydrous KLB-1 peridotite compositions held at 18 and 19 GPa, and 1400 °C for 27 h. The long heating duration time of syntheses implies that phase E can be a stable component of the mantle under hydrous conditions. Single-crystal X-ray diffraction analyses show that the M1 octahedral site is 72.1–75.2 at% occupied, whereas the M2 and tetrahedral Si sites are 2.4–2.9 at% and 18.9–19.8 at% occupied, respectively. The M1 site occupancies show a positive correlation with Fe/Mg molar ratios, indicating that Fe mainly occupies the M1 site in the phase E structure. High-pressure Raman spectroscopy shows that the framework Raman frequencies of Fe-bearing phase E increase continuously with increasing pressures up to 19 GPa at room temperature, and there is no indication for a major change in the crystal structure. If transition-zone regions adjacent to subducting slabs are hydrated by fluids generated at the top of the lower mantle, Fe-bearing phase E is expected to occur at wadsleyite-ringwoodite phase transition boundary (about 520 km) as an important phase for incorporating water.

Self-Similar Heat Transfer Processes in a Radiation-Transparent Solid Body Containing an Absorptive Inclusion with the System Featuring Phase Transitions

The paper considers the problem of determining temperature field parameters in a radiation-trans-parent isotropic solid body containing an absorptive inclusion, when the system features phase transitions. We identify sufficient conditions, meeting which ensures the possibility of self-similar heat transfer process taking place in the system under con-sideration. We qualitatively investigated physical properties of the self-similar process under study and determined its specifics. We provide a theoretical validation of implementing a thermostating mode of the moving phase transition boundary in the heat transfer process investigated

Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z 1 ( t )= βt 7/2 and Z 1 ( t )= βt 2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α , β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.