Tracer Dispersion in Rough Open Cracks

Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface. This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained.     

Dispersion in annular climbing film flow

The dispersion of a tracer injected as a pulse into a climbing liquid film is investigated for a series of water and air flow rates, and for a number of different electrolyte tracers. It is found that at all flow rates the observed concentration distribution depends on the nature of the tracer. This observation is explained in terms of two effects: molecular diffusion in a viscous sub-layer and ion fractionation associated with droplet formation at the gas-liquid interface. The overall dispersive characteristics of the system are described in terms of a mathematical model assuming dispersed plug flow in both the film and entrained droplets with interchange between these phases. This model is fitted to experimental tracer concentration distributions using a non-linear least-squares regression procedure. The parameter values obtained from the fitting procedure are studied to determine trends with flow rates and tracer properties. Values for a film dispersion parameter, $\text{P}{}_{\mathrm{f}}$, are found to correlate significantly with the molecular diffusion coefficients of the tracers. Consistent values for an ion fractionation coefficient, $\text{k}{}_{\mathrm{if}}$, are also obtained.     

Dispersion in spatially periodic porous media

The method of volume averaging is applied to ordered and disordered spatially periodic porous media in two dimensions in order to compute the components of the dispersion tensor for low Peclet numbers ranging from 0.1 to 100. The effect of different parameters on the dispersion tensor is studied. The longitudinal dispersion coefficient decreases with an increase in disorder while the transverse dispersion coefficient increases. The location of discs in the unit cell influences the longitudinal dispersion coefficient significantly, compared to the transverse dispersion coefficient. Under a laminar flow regime, the dispersion coefficient is independent of Re_p. The predicted functional dependency of dispersion on the Peclet number agrees with experimental data. The predicted longitudinal dispersion coefficient in disordered porous media is smaller than that of the experimental data. However, the predicted transverse dispersion coefficient agrees with the experimental data.     

Particulate Dispersion in a Turbulent Serpentine Channel

Particulate dispersion in an S-shaped duct, with periodicity between inlet and exit, is studied by direct numerical simulation. Stokes numbers range from 0.125 to 6.0. In a straight, turbulent channel flow, eddies are responsible for particulate impact. Turbophoresis causes a mean drift toward the wall. In a curved channel, particle inertia can be the dominant cause of impact. Above the lowest Stokes number, particles form into a plume that leaves the inner bend and flows toward the outer wall. Turbulence then disperses the plume. Heavier particles cross the bend and reflect from the outer wall, forming a high concentration layer near the surface. The heaviest particles reflect again from the wall and are dispersed across the duct by turbulence. An empirical formula is used to analyze the propensity for particle impacts to erode the wall. The region of maximum erosion is not the region of maximum number of impacts, nor is it where the impact velocity is highest: the impact angle determines where erosion is largest.     

Dispersion and Chemical Reactions in Porous Media

The effect of chemical reactions on the process of admixture transport by a flow through a porous medium is considered. On the basis of a number of examples it is shown that the dispersion coefficient depends on the chemical reaction rate constant.     

Dispersion and localisation in structured Rayleigh beams

This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations appear to be similar, and hence mathematical models have a lot in common. In the present work, our main focus is on the analysis of dispersive waves, band-gaps and localised waveforms in structured Rayleigh beams. The Rayleigh beam theory includes the effects of rotational inertia which are neglected in the Euler–Bernoulli beam theory. This makes the approach applicable to higher frequency regimes. Special attention is given to waves in pre-stressed Rayleigh beams on elastic foundations.     

Dispersion in consolidated sandstone with radial flow

This paper presents some experimental and theoretical results for dispersion processes occurring in consolidated Berea sandstone with radial flow geometry. A comprehensive review of the derivation and application of several analytical solutions is also presented. The Galerkin finite element method is applied to solve the advection-dispersion equation for unidimensional radial flow.Individual and combined effects of mechanical dispersion and molecular diffusion are examined using velocity-dependent dispersion models. Comparison of simulated results with experimental data is made. The effect of flow rates is examined. The results suggest that a linear dispersion model,D=u, whereD is the dispersion coefficient,u the velocity and a constant, is not a good approximation despite its wide acceptance in the literature. The most suitable mathematical formulation is given by an empirical form of , whereD _ois the molecular diffusion coefficient. For the range of Péclet number (Pe=vd/D _m,wherev is the characteristic velocity,d the characteristic length andD _mthe molecular diffusion coefficient in porous media) examined (Pe=0.5 to 285), a power constant ofm=1.2 is obtained which agrees with the value reported by some other workers for the same regime.     

Automaton Simulations of Dispersion in Porous Media

A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.     

Problems of folding in the earth’s stratified crust

The problem of folding in the Earth’s stratified crust is addressed within the framework of solid mechanics. The history and formulation of the problem and approaches to its solution are briefly outlined. The initial stage of folding in strata with different mechanical properties is studied in detail using the piecewise-homogeneous medium model and the three-dimensional theory of stability. Conclusions of applied and fundamental importance are drawn from an analysis of solutions to a wide range of specific problems __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 3–44, February 2007.     

On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅰ)

The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered.It is assumed that the depth of the ocean is a positive constant.Firstly,if the initial data are square integrable,then by Fadeo-Galerkin method,the existence of the global weak solutions for the problem is obtained.Secondly, if the initial data and their vertical derivatives axe all square integrable,then by Faedo-Galerkin method and anisotropic inequalities,the existerce and uniqueness of the giobal weakly strong solution for the above initial boundary problem axe obtained.     

On two-dimensional large-scale primitive equations in oceanic dynamics （Ⅱ）

The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially. Here the depth of the ocean is positive but not always a constant. By Faedo-Galerkin method and anisotropic inequalities, the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained. Moreover, by studying the asymptotic behavior of solutions for the above problem, the energy is exponential decay with time is proved.     

On two-dimensional large-scale primitive equations in oceanic dynamics （Ⅰ）

The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered. It is assumed that the depth of the ocean is a positive constant. Firstly, if the initial data are square integrable, then by Fadeo-Galerkin method, the existence of the global weak solutions for the problem is obtained. Secondly, if the initial data and their vertical derivatives are all square integrable, then by Faedo-Galerkin method and anisotropic inequalities, the existerce and uniqueness of the global weakly strong solution for the above initial boundary problem are obtained.     

Paradigms and falsification in earthquake engineering

Particular reference is made to the works by E. Torroja and by A. M. Freudenthal, that can be seen as the father-works of a new paradigm in the study of structural engineering: the probabilistic approach to structural safety. The key idea of this approach is, according to Freudenthal, the selection of an acceptable risk of failure. The criteria that have been proposed for this selection in the case of constructions in earthquake-prone areas are discussed.Attention is then paid to the scientific reliability of seismic hazard analysis at a particular site, following the teachings of modern philosophy of science. The problem is discussed in the frame of the theory of falsification, due to K. Popper and I. Lakatos: it is recognised that the results of a seismic hazard analysis are not falsifiable; hence, they would not have a scientific status. In order to overcome this problem, it is proposed to shift the attention from the final results of the hazard analysis, which are not directly falsifiable, to the procedures which lead to that result. A method for falsifying these procedures is proposed.Invited lecture presented (in Italian) at the 4th Specialist Meeting of the Stochastic Mechanics Group of AIMETA, Rome, April 1990.     

On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅱ)

The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially.Here the depth of the ocean is positive but not always a constant.By Faedo-Galerkin method and anisotropic inequalities,the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained.Moreover,by studying the asymptotic behavior of solutions for the above problem,the energy is exponential decay with time is proved.     

Background current concept and chaotic advection in an oceanic vortex flow

The concept of background currents is offered in the examples of barotropic and baroclinic quasigeostrophic models. The background currents are characterized by constant value of potential vorticity, which minimize the energy of a system. Hamiltonian character of motion equations of fluid particles allows to apply such models to study chaotic advection.     

Dispersion and attenuation in thermoelastic multisize particulate composites

This paper deals with the problem of multiple scattering by a random distribution of spherical solid particles in a solid. The material properties of both media are taken as thermoelastic. The radii of the inclusions may be different. The self-consistent method in its variant of the effective medium is used to find the dispersion and attenuation of quasi-elastic, quasi-thermal and shear waves. The single scattering problem required by this technique is solved approximately by means of the Galerkin method applied to an integral equation using the Green function. Numerical results display a characteristic resonance phenomena which appears in the interval where the results are approximately valid, that is, for very long waves down to wavelengths about twice the largest diameter of the spheres. Examples are shown, for composites with two sets of inclusions, which have either a very similar or dissimilar size. Comparisons are made with the elastic counterpart. Among the material properties, the mass density ratio, inclusion to matrix, seems to play an important and simple role. Frequency intervals are distinguished and shown to depend on that ratio, where the attenuation and dispersion of quasi-elastic and P-waves are either very close to each other or not at all. The same applies to shear waves in either composite. The mass density ratio also displays a simple monotonic decreasing behaviour as a function of the frequency at the first attenuation maximum and velocity minimum. These results may be of interest for the nondestructive testing characterization of particulate composites.     

Topography and Dispersion Effects in Bottom Layer Dynamics

A hyperbolic model of a shallow water flow is considered with allowance for nonlinear and dispersion effects. The structure of traveling waves above a flat bottom is studied. Stability of small disturbances of a homogeneous flow and development of instability of a nonstationary flow above an inclined bottom are analyzed.     

Anomalous Dispersion in Pore-Scale Simulations of Two-Phase Flow

Transport in Porous Media - We investigate anomalous dispersion in steady-state two-phase flow though a random, artificial porous domain. A natural distribution of trapped wetting-phase fluid was...     

Hydrodynamic Dispersion and Lamb Surfaces in Darcy Flow

Transport in Porous Media - Transport processes such as the dispersion and mixing of solutes are governed by the interplay of advection and diffusion, where advection acts to organise fluid...