Porous nickel samples are considered as simple thermodynamically equilibrium mixtures of condensed and gaseous phases, assuming mechanical, thermal, and kinematic equilibrium, i.e., Pᵢ = P, Tᵢ = T, and uᵢ = u are the pressure, temperature, and mass velocity of component i, respectively, while P, T, and u denote the corresponding mixture quantities. Under these assumptions, the motion of the multicomponent medium can be described as that of a single continuum governed by a special equation of state that accounts for the properties and concentrations of the mixture components, thereby significantly reducing the number of governing equations. The applicability of the equation of state is extended to the low-pressure regime by introducing a logarithmic dependence of the Grüneisen coefficient on density. The shock adiabats calculated for nickel specimens with different initial porosities are in good agreement with the available experimental data. It is shown that the parameters of the mixture equation of state exhibit only a weak dependence on pressure. The thermodynamic consistency of the mixture equation of state in the Mie-Grüneisen form is established by demonstrating that the pressure and specific internal energy, expressed as functions of specific volume and temperature, satisfy the required thermodynamic relations even when the equation-of-state parameters depend on the current pressure. The results indicate that the proposed equation of state is applicable to shock compression over the pressure range from 0.5 to 1000 GPa.
The kinetic substantiation of the equations of classical hydrodynamics asserts that the use of Boltzmann's molecular chaos hypothesis makes it possible to build classical hydrodynamics on the basis of three hydrodynamic values, namely, density, velocity and pressure. The distributions of these variables, known as the principal hydrodynamic values, depend only on the initial and boundary conditions of the problem, whereas binary particle collisions do not affect the formation of distributions. The equations of multimoment hydrodynamics, previously derived by one of the authors, are based on six principal hydrodynamic values, one of which is responsible for the stresses arising in the medium. In this paper, the classical kinetic theory is used to substantiate the existence of the principal stress tensor. It is shown that the principal stress tensor plays a crucial role in the interpretation of unstable processes occurring when the state of the medium is far from statistical equilibrium. Solutions to the multimoment hydrodynamic equations provide the system with several possible evolution scenarios. Pair entropy, or more precisely its time derivatives, indicates the unique direction in which the system evolves. The principal stress tensor makes the dominant contribution to the entropy of the system. Thus, it is precisely the principal stress tensor that determines the temporal behavior of entropy, making it possible to predict the direction of evolution of a strongly nonequilibrium medium after stability loss.
This paper examines direct and inverse problems of unsteady filtration to a fracture in a cylindrical reservoir based on the diffusivity equation. To facilitate the interpretation of well-test data from low-permeability reservoirs, an approach introducing new dimensionless coordinates is proposed. In these coordinates, the numerical solutions for bottomhole pressure as a function of time describe all flow regimes and are universal with respect to reservoir properties, differing only in shape according to the well completion type. A complex filtration parameter is introduced to characterize the evolution of the dimensionless hydraulic resistance of the reservoir. Additionally, a complex storage parameter is defined to quantify the ratio of the fluid inflow volume to the current volume of fluid compression within the effective reservoir investigation region during the flowing period, i.e., before well shut-in. The proposed dimensionless parameters are applied to the solution of the inverse unsteady flow problem for interpreting bottomhole pressure data obtained after well shut-in. The approach is validated using field data, and the calculated results are compared with the dimensionless data obtained from the comprehensive well testing. The comparison demonstrates excellent agreement, with discrepancies not exceeding 0.5%.
In this paper, we give a presentation of the fundamental group of the complement of links in the Poincare homology sphere in terms of generators and relations.
Fluorine is widely used in various branches of modern industry. Fluorine production is an energy- and capital-intensive process. This paper develops a unified mathematical model of electrolytic fluorine production based on four interrelated physical processes: electrochemistry, hydrodynamics, heat transfer, and chemical kinetics. Using the developed model, numerical simulations of the electrolytic fluorine production process in a medium-temperature electrolyzer were performed. In the calculations, three main parameters affecting the amount of fluorine produced were considered: the HF content in the electrolyte (%), the electrolyte temperature (°C), and the anode current density (A/cm²). The obtained results were compared with the analytical solution based on Faraday's law of electrolysis. Good agreement between the data confirms the validity of the developed mathematical model of electrolytic fluorine production. The proposed mathematical model of the electrolysis process for gaseous fluorine production allows parametric studies aimed at optimizing operating conditions and improving process efficiency. The model can be used in the development of new electrolyzer designs and in the modernization of existing devices. The relationships derived from this model provide deeper insight into the physical processes underlying electrolysis.
