L. V. Matveev

Anomalous diffusion in generalized Dykhne model

Contaminant transport is investigated in the generalized Dykhne model differing from the original Dykhne model by the presence of advection in the high-permeability medium. An analysis is presented of transport regimes and concentration tail behavior in the high-permeability medium. It is found that the transport regimes include anomalous ones: subdiffusion and quasi-diffusion. A difference is revealed between longitudinal and transverse transport. Regime change over time leads to multiple-regime long-distance asymptotic behavior of concentration distributions. An analogy is drawn between the problems examined here and transport through comb structures.

Impurity Transport in Percolation Media

An equation describing the impurity transport in a percolation medium is obtained and the inferences drawn from this equation are analyzed based on the scale invariance concept. A determining part in this analysis is allowance for the sinks inherent in such media. At distances shorter than the correlation length, the particles are transferred in the regime of subdiffusion; at large distances, the concentration asymptotics exhibits a characteristic “tail” shape. In the medium occurring in the state above the percolation threshold, the impurity transport over time periods longer than the characteristic time related to the correlation length is well described by the classical equation with a renormalized diffusion coefficient. In this case, the concentration tail has a Gaussian shape at moderate distances and tends to subdiffusion asymptotics at very long distances. A relation is established between the factor determining renormalization of the diffusion coefficient and the factor determining a decrease in the number of active impurity particles at large times.

Anomalous transport regimes in a stochastic advection-diffusion model

A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium.

Advection of an Impurity in Percolation Media with a Finite Correlation Length

The impurity transport regimes in percolation media with a finite correlation length, which are caused by advection and diffusion mechanisms, have been analyzed. It has been shown that the change in the transport characteristics of a medium from the self-similar type to the statistically homogeneous type occurs through two stages because of the structural features of percolation clusters (presence of a backbone and dead ends). As a result, new anomalous transport regimes appear in the system. The quasi-isotropic and moderately and strongly anisotropic media have been considered.

High-temperature transition of uranium dioxide to the super-ion state

A microscopic model of the high-temperature (T≈2670 K) phase transition of uranium dioxide to the super-ion state is developed. It is shown that accounting for the interaction of the point defect subsystem with the electron subsystem in the mean-field approximation (where this interaction leads to significant additional screening of the charge of some of the defects) and then calculating the configurational entropy of the point defects with allowance for the actual symmetry of the UO2 crystalline lattice affords satisfactory agreement with the available experimental data on the degree of disorder of the anion sublattice and the behavior of the specific heat of uranium dioxide in the given temperature range.

Impurity transport in a dual-porosity medium with sorption

A nonstationary model of impurity transport in a dual-porosity (fractured porous) medium with sorption is proposed. It is shown that the equilibrium between dissolved and adsorbed phases is absent for a prolonged time, which leads to the development of nonclassical impurity transport regimes. Parameter values are found for which the behavior of the system cannot be described using the conventional model of equilibrium sorption even at large times for which the equilibrium between dissolved and adsorbed components should be established.

Impurity transport in the model of a dual-porosity regularly heterogeneous medium with colloids

The problem of impurity advection in a channel surrounded by a weakly permeable medium with drifting colloidal particles present in the channel is solved. A regime in which the front of the impurity cloud moves with a constant velocity and the concentration behind the front decreases as a power law is established due to the impurity adsorption on colloids and its diffusive exchange with the matrix on moderate time scales. On long time scales, the transport in the channel is quasi-diffusive as a result of the impurity desorption and its eventual escape into the matrix.

Asymptotic regimes and structure of concentration tails in the Dykhne model

A transport problem is solved for a high-contrast regularly inhomogeneous medium. Transport regimes and structure of the concentration tails in high-permeability regions are analyzed for two geometries of such regions: a plane layer and a right cylinder. It is shown that changes with time of transport regimes lead to complex asymptotic particle distributions at long distances (concentration “tails”). The time dependence of the total number of active particles and depth of particle penetration into the low-permeability region are calculated.

Colloid-Facilitated Impurity Leaching in Statistically Homogeneous Dual-Porosity Media

A model for the leaching of an impurity from a statistically homogeneous dual-porosity medium is proposed. The region of partial leaching grows according to a diffusion law on moderate time scales. A region completely cleaned of the impurity whose boundary moves with a constant velocity arises on long time scales. A transition region is formed at the leaching front. Its size increases proportionally to the square root of time. The possibility of a significant acceleration of the leaching process by the introduction of colloidal particles capable of adsorbing the impurity into the fluid is shown.

A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

AbstractThe properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x≪x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nux∝x3/4. In the second regime, at x≫ x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is