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We study theoretically and experimentally the thermal convection in long tilted fractures filled with a porous material (porous layer) embedded in an impermeable solid and saturated with a fluid. The solid is subjected to a constant, vertical temperature gradient and has thermal conductivity larger than that of the saturated porous layer. We discuss different cases of interest in terms of the fracture aspect ratio and the fracture-to-solid conductivity ratio. Analytical expressions for the temperature and velocity profiles of the flow in the porous layer are worked out for low-Rayleigh-number flows.

A numerical study of forced imbibition into capillary tubes under primary Bjerknes force is presented. A mathematical model is developed to predict the motion of a meniscus while an external force is applied. Remarkable enhancement in liquid flow attributed to the frequency and intensity of a waveform on primary Bjerknes force and to the viscosity of fluid was observed. It was found that imbibition optimal frequency for each equilibrium height depends on the time as ω(xeq)∼emt, where the recovery time is a viscosity function t(xeq)∼μH. The results are presented in a set of curves, which reveal the features of enhanced oil recovery of the system under consideration. Some physical implications are discussed.

In this work, we study the effects of geometric confinement on random walks and diffusion processes in systems of reduced dimensionality. Extensive Monte Carlo simulations of Gaussian random walks were performed on rectangular strips of infinite length. A special emphasis is made on the crossover from two- to one-dimensional diffusion in the Fickian regime. We found that the crossover behavior is controlled by the ratio of the strip width to the standard deviation of the walker step length distribution. Specifically, the characteristic time of crossover behavior scales quadratically with this ratio. Furthermore, the time dependence of the number of effective spatial degrees of freedom of the random walker on the strip is found to obey an ansatz characterized by the universal power-law exponent. This allows us to formulate the diffusion equation with the time dependent number of effective spatial degrees of freedom in the quasi-one-dimensional system.