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Register a new userTracer Dispersion in Porous Media with Spatial Correlations
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We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolation-like porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We show that the resulting statistical properties of the tracer can be approximated by a Levy walk model, which is a consequence of the broad distribution of velocities plus the existence of spatial correlations in the porous medium.
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Selective excitation of a diffusive systems transmission eigenchannels enables manipulation of its internal energy distribution. The fluctuations and correlations of the eigenchannels spatial profiles, however, remain unexplored so far. Here we show that the depth profiles of high-transmission eigenchannels exhibit low realization-to-realization fluctuations. Furthermore, our experimental and numerical studies reveal the existence of inter-channel correlations, which are significant for low-transmission eigenchannels. Because high-transmission eigenchannels are robust and independent from other eigenchannels, they can reliably deliver energy deep inside turbid media.
We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results are valid under very general conditions and should be helpful in the analysis of measurements of wave transport through complex systems and in the design of randomly or periodically structured materials with specific transport properties.
Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.
We study by extensive numerical simulations the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder - frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour $sim t^{4/3}$, $t$ being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position $X$ along the $x$-axis. Our analysis evidences that in absence of the lattice gas particles the latter has a Gaussian central part $sim exp(- u^2)$, where $u = X/t^{2/3}$, and exhibits slower-than-Gaussian tails $sim exp(-|u|^{4/3})$ for sufficiently large $t$ and $u$. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.
We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex dynamics and feedbacks involved in local fracturing and the production of crackling noise. Under strain-controlled loading micro-cracks initially nucleate in an uncorrelated way all over the sample. As loading proceeds the damage localizes into a narrow damage band inclined at 30-45 degrees to the load direction. Inside the damage band the material is crushed into a poorly-sorted mixture of mainly fine powder hosting some larger fragments. The mass probability density distribution of particles in the damage zone is a power law of exponent 2.1, similar to a value of 1.87 inferred from observations of the length distribution of wear products (gouge) in natural and laboratory faults. Dynamic bursts of radiated energy, analogous to acoustic emissions observed in laboratory experiments on porous sedimentary rocks, are identified as correlated trails or cascades of local ruptures that emerge from the stress redistribution process. As the system approaches macroscopic failure consecutive bursts become progressively more correlated. Their size distribution is also a power law, with an equivalent Gutenberg-Richter b-value of 1.22 averaged over the whole test, ranging from 3 down to 0.5 at the time of failure, all similar to those observed in laboratory tests on granular sandstone samples. The formation of the damage band itself is marked by a decrease in the average distance between consecutive bursts and an emergent power law correlation integral of event locations with a correlation dimension of 2.55, also similar to those observed in the laboratory (between 2.75 and 2.25).
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