Peter Kondratenko

Anomalous transport regimes and asymptotic concentration distributions in the presence of advection and diffusion on a comb structure

We study the transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion, and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean-square displacement. However, quasidiffusion is an anomalous transport regime. We established that a change in transport regimes in time leads to a change in regimes in space. Concentration tails have a cascade structure, namely, consisting of several parts.

Limiting angular dependencies of heat transfer and stratification in a heat-generating fluid

Abstract A theoretical study is carried out for the distribution of heat flux to the boundary, as well as of the temperature and flow velocity in the lower part of the volume taken up by a one-component heat-generating fluid. The treatment is based on the analysis of the converging boundary layer in view of the conditions of joining its characteristics with those of the fluid in the stably stratified region of the volume. It is found that the dependence of the heat flux at the boundary, q, on the polar angle θ at θ ∗ ≪θ≪1 (where θ ∗ is some boundary angle), and the dependence of the temperature in the volume on the ratio of the height z to the characteristic size of the volume R, are power dependences, q∼θa, T b ∼ z/R b . The exponents for the cases of laminar and turbulent boundary layers are a=2, b=4/5 and a=24/13, b=9/13, respectively. The heat flux at θ ∗ weakly depends on θ and assumes the minimum value at θ=0. The ratio of the minimum heat flux qm to its average value 〈q〉, as well as the boundary angle θ ∗ as a function of the modified Rayleigh number, are given by the estimates qm/〈q〉∼RaI−1/6, θ ∗ ∼Ra I −1/12 . The results are in quite satisfactory agreement with experiment.

Anomalous Transport in Fractal Media with Randomly Inhomogeneous Diffusion Barrier

We investigate a contaminant transport in fractal media with randomly inhomogeneous diffusion barrier. The diffusion barrier is a low-permeable matrix with rare high-permeability pathways (punctures). At times, less than a characteristic matrix diffusion time, the problem is effectively barrier-free, where an effective source acts during the time

Random advection in a fractal medium with finite correlation length.

t_mathrm{eff} ll t

Transport Regimes and Concentration Tails for Classical Diffusion in Heterogeneous Media with Sharply Contrasting Properties

teff≪t. The punctures result in a precursor contaminant concentration at short times and additional stage of the asymptotic concentration distribution at long times. If the source surface area is large enough, then the barrier can be considered as statistical homogeneous medium; otherwise, strong fluctuations occur.