Average energy flow of optical pulses in dispersive media

The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.     

Hydrodynamics in two-phase flow within porous media

Ultra-fast magnetic resonance imaging techniques are used to image liquid distribution in two and three dimensions during air-water co-current down flow through a fixed bed of cylindrical porous pellets of length and diameter 3 mm, packed within a 43 mm internal diameter column in both the trickle- and pulsing-flow regimes. The data acquisition times used were 20 and 280 ms, giving 2-D and 3-D spatial resolutions of 1.4 mm x 2.8 mm and 3.75 mm x 3.75 mm x 1.87 mm, respectively. This work reports images of local pulsing events within the bed occurring during the trickle-to-pulse flow transition. The evolution of the local instabilities is studied as a function of increasing liquid velocity at constant gas velocity.     

Inertial capture in flow through porous media

We investigate through numerical calculation of non-Brownian particles transported by a fluid in a porous medium, the influence of geometry and inertial effects on the capture efficiency of the solid matrix. In the case of a periodic array of cylinders and under the action of gravity, our results reveal that δ ～ St, where δ is the particle capture efficiency, and St is the Stokes number. In the absence of gravity, we observe a typical second order transition between non-trapping and trapping of particles that can be expressed as δ ～ (St ? St _c ) ^α , with an exponent α ≈ 0.5, where St _c is the critical Stokes number. We also perform simulations for flow through a random porous structure and confirm that its capture behavior is consistent with the simple periodic model.     

Stochastic effects on single phase fluid flow in porous media.

The flow encoded PEPI technique has been used to measure the fluid velocity distribution and fluid flow of water passing through a phantom comprising randomly distributed 10 mm glass beads. The object of these experiments is to determine the degree of causality between one steady-state flow condition and another. That is to say, knowing the mean fluid velocity and velocity distribution, can one predict what happens at a higher mean fluid velocity? In a second related experiment flow is established at a given mean fluid velocity. The velocity distribution is measured. The flow is then turned off and later re-established. In both kinds of experiment we conclude that the errors in predicting the flow velocity distribution and the errors in re-establishing a given velocity distribution lie well outside the intrinsic thermal noise associated with velocity measurement. It follows, therefore, that the causal approach to prediction of flow velocity distributions in porous media using the Navier-Stokes approach is invalid.     

Two—phase flow in correlated pore—throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and ε. The E～ L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.     

Electric field driven flow in natural porous media

Electric fields were applied to fluid-saturated packed sand beds (0.23+/-0.03 mm average pore diameter), and the effects on the mobility of the water molecules were monitored using stimulated echo (STE) and pulsed field gradient (PFG) experiments. The mean flow velocity, averaged over the entire sample, is expected to vanish in closed systems, but the PFG and time dependent signal decay was enhanced beyond the effects of thermal diffusion, due to velocity dispersion. The internal flow generated by the electric field was shown to be fully time-reversible upon inverting the electric field polarity (for total flow times of up to 0.4s), a strong indication that the NMR detected displacements were mainly due to electro-osmotic flow (EOF). However, a comparison of the velocity dispersion for different electrolyte concentrations showed that the measured effect scaled with the applied power VI (V = voltage, I = electric current), rather than with the voltage alone, contrary to the prediction of the basic model for EOF in a single capillary channel.     

Singularities of the Hele-Shaw flow and shock waves in dispersive media

We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg-de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.     

Fluid flow through three-dimensional fibrous porous media

A system of self-consistent equations for determining the hydrodynamic resistance of dilute fibrous porous media in the case of arbitrary low Reynolds numbers and arbitrary random packing of the fibers in the media is derived on the basis of a multiple-scattering hydrodynamic theory. The equations obtained are applied to the case of isotropic packing of the fibers and to the anisotropic case when all the fibers are orthogonal to the direction of fluid flow. Equations are derived and analyzed for the velocity correlation function in a random fibrous medium. The longitudinal and transverse diffusion coefficients of a passive impurity embedded in the fluid are calculated. Zh. éksp. Teor. Fiz. 113, 2109–2128 (June 1998)     

Magnetic resonance visualisation of single- and two-phase flow in porous media.

Three-dimensional MRI and flow visualisation data are presented for single and two-phase flow occurring within packed beds of glass spheres. The initial motivation for this work has been to understand the operation of fixed-bed reactors used in many chemical processing operations; these systems also serve as model porous media in which to investigate the effect of the structure of a pore space on the flow phenomena occurring within it. For the case of single-phase flow, maps of the liquid shear rate components are calculated from which forces on individual spheres within the bed are obtained. The velocity histogram for flow transverse to the direction of superficial flow is exponential in both negative and positive directions. This form of the velocity histogram implies an exponential form for the displacement propagator, in contrast to the Gaussian distribution obtained by pulsed gradient spin echo measurements. This difference arises because the spatially resolved velocity imaging sequence measures only the average velocity within each voxel and is insensitive to the effects of incoherent (diffusive) motion. Visualisations of air-water flow through a sphere pack are also reported and the capability of MRI to yield information on rivulet formation and surface wetting characteristics is illustrated.     

Using NMR displacement imaging to characterize electroosmotic flow in porous media.

Pulsed field gradient nuclear magnetic resonance (PFG-NMR) and NMR imaging were used to study temporal and spatial domains of an electrokinetically-driven mobile phase through open and packed segments of capillaries. Characteristics like velocity distribution and an asymptotic dispersion are contrasted to viscous flow behavior. We show that electroosmotic flow in microchannel geometries can offer a significant performance advantage over the pressure-driven flows at comparable Peclét numbers, indicating that velocity extremes in the pore space of open tubes and packed beds are drastically reduced. An inherent problem of capillary electrochromatography that we finally address is the existence of wall effects when in the general case the surface zeta-potentials of the capillary inner wall and the adsorbent particles are different. Using dynamic NMR microscopy we were able resolve this systematic velocity inequality of the flow pattern which strongly influences axial dispersion and may be responsible for long time-tails of velocity distribution in the mobile phase.     

Two-phase flow in porous media: dynamical phase transition

We study numerically the behavior of two-phase flow in porous media via the parameters capillary number and viscosity ratio, under steady-state conditions and various levels of saturation. We construct a phase diagram, where the phases are defined according to whether one or both fluids move. We establish a semi-empirical theory for the location of the phase boundaries. The steady-state conditions are obtained by implementing biperiodic boundary conditions.     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

Geometrical optics in dispersive media

We present a systematic derivation of Geometrical Optics in dispersive media from Maxwell's equation for the presence of charges and currents, by using the two-timing approximation technique. A propagation equation for the polarisation plane is also derived.     

Saturation overshoot and hysteresis for twophase flow in porous media

Saturation overshoot and hysteresis for two phase flow in porous media are briefly reviewed. Old and new challenges are discussed. It is widely accepted that the traditional Richards model for twophase flow in porous media does not support non-monotone travelling wave solutions for the saturation profile. As a concequence various extensions and generalizations have been recently discussed. The review highlights different limits within the traditional theory. It emphasizes the relevance of hysteresis in the Buckley–Leverett limit with jump-type hysteresis in the relative permeabilities. Reviewing the situation it emerges that the traditional theory may have been abandoned prematurely because of its inability to predict saturation overshoot in the Richards limit.     

Stochastic langevin model for flow and transport in porous media

We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.