Modeling of isothermal processes in porous materials on the basis of the concept of an ensemble of pores

A class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometric parameters (for example, the pore size) is considered. The cases of pores saturated with single-and two-phase multicomponent liquid mixtures are investigated. The properties of equilibrium states of the mixture are derived from the minimum free energy condition and the transfer laws from the decreasing free energy condition. The hydrodynamic connectivity of the pores is described by two types of kernels: one describes the spatial connectivity and the other the connectivity in an elementary macrovolume. Analytically and numerically, the one-dimensional problems of establishment of a steady-state regime, propagation of a passive admixture, and two-phase flow (an analog of the Buckley-Leverett problem) are investigated. A relationship between the models in question and relaxational filtration models is demonstrated. A simple model of capillary hysteresis related with the non-monotonicity of the pore area to volume ratio function is proposed.     

Dynamics of a Quantum Damped Oscillator with Relaxation

The quantum problem of a nonlinear oscillator interacting with the field of harmonic oscillators with continuously distributed frequencies is examined. The Heisenberg representation is used. It is demonstrated that after elimination of field variables from the equation, the oscillator dynamics is described by an integro-differential operator equation. It is proved that in the general nonlinear case, an exact solution for the quantum oscillator demonstrates dissipative behavior under certain limitations on the relaxation kernel.     

Filtration through a porous barrier between two communicating vessels

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 149–153, January–February, 1989.     

Dynamic theory of thermal fluctuations with allowance for the spatiotemporal nonlocality

Previously the author showed that classical statistical mechanics for a certain class of external forces is equivalent to nonlocal hydrodynamics [1]. In the present work, formulas are derived that describe a one-to-one interrelationship between hydrodynamic nonlocality kernels and the correlation function for the thermal fluctuations of hydrodynamic quantities. This allows the spatiotemporal hydrodynamic nonlocality to be investigated in principle, for example, from spectra of molecular scattering. Analytical forms of model nonlocality kernels are discussed. Institute of Earth Physics of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebhykh Zavedenii, Fizika, No. 4, pp. 30–33, April, 2000.     

On some thermodynamic effects in small molecular systems

The behavior of a gas-liquid system in a small volume has been studied. In the absence of the thermodynamic limit, the problem has been examined by methods of statistical physics. This allows the use of new mathematical methods previously applied in nuclear physics. Within the modified droplet model of a real gas sandwiched between two extended plates, an additional component of the pressure, which was previously discussed and exhibits characteristic oscillations at change in the volume, has been found. Qualitative coincidence with the previously reported molecular dynamics simulations has been found.