Vertical water distribution during the drying of polymer films cast from aqueous emulsions

We present a systematic study of the vertical uniformity of water distribution during the drying of waterborne colloidal films, testing the predictions of a Peclet number Pe defined for this system. Pe indicates the relative contributions of water evaporation and Brownian diffusion in determining the concentration profile in the vertical direction (i.e. normal to the substrate). When Pe < 1, the water concentration in films cast from an alkyd emulsion is found via magnetic-resonance profiling to be uniform with depth, which is consistent with expectations. When Pe > 1, a gradient in the water concentration develops, with less water near the interface with air. The water profiles reveal that the alkyd particles do not coalesce immediately upon contact in close-packing. At later times, a concentrated surface layer develops, but particles are not coalesced in this layer to form a continuous “skin”, but rather the structure is likely to be that of a biliquid foam. Received 20 March 2002 and Received in final form 12 June 2002     

Nondigital Implementation of the Arithmetic of Real Numbers

In the framework of a model for quantum computer media, a nondigital implementation of the arithmetic of the real numbers is described. For this model, an elementary storage cell is an ensemble of qubits (quantum bits). It is found that to store an arbitrary real number it is sufficient to use four of these ensembles and the arithmetical operations can be implemented by fixed quantum circuits.     

A Lattice Gas Automaton Simulation of the Nonlinear Diffusion Equation: A Model for Moisture Flow in Unsaturated Porous Media

We investigate a two-dimensional lattice gas automaton (LGA) for simulating the nonlinear diffusion equation in a random heterogeneous structure. The utilility of the LGA for computation of nonlinear diffusion arises from the fact that, the diffusion coefficient in the LGA depends on the local density of fluid particles which statistically determines the collision rate and thus, the mean free path of the particles at the microscopic scale. The LGA may therefore be used as a physical analogue to simulate moisture flow in unsaturated porous media. The capability of the LGA to account for unsaturated flow is tested through a set of numerical experiments simulating one-dimensional infiltration in a simplified semi-infinite homogenous isotropic porous material. Different mechanisms of interactions are used between the fluid and the solid phase to simulate various fluid–solid interfaces. The heterogeneous medium, initially at low density is submitted to a steep density gradient by continuously injecting fluid particles at high concentration and zero velocity along one face of the model. The propagation of the infiltration front is visualized at different time steps through concentration profiles parallel to the applied concentration gradient and the infiltration rate is measured continuously until steady-state flow is reached. The numerical results show close agreement with the classical theory of flow in unsaturated porous media. The cumulative absorption exhibits the expected t ^1/2 dependence. The evolution of the effective diffusion coefficient with the particle concentration is estimated from the measured density profiles for the various porous materials. Depending on the applied fluid–solid interactions, the macroscopic effective diffusivity may vary by more than two orders of magnitude with density.     

Interaction of evaporation fronts with a formation interface in a porous medium

The evolutionarity and structure of water-vapor phase discontinuities formed in a geothermal reservoir on the interface between permeable formations with different properties are considered. In the short-wave approximation a graphic method is proposed for solving the problem of breakdown of an arbitrary discontinuity in a geothermal reservoir consisting of two formations with different properties.     

Viscous Fingering Instability in Porous Media: Effect of Anisotropic Velocity-Dependent Dispersion Tensor

The viscous fingering of miscible flow displacements in a homogeneous porous media is examined to determine the effects of an anisotropic dispersion tensor on the development of the instability. In particular, the role of velocity-dependent transverse and longitudinal dispersions is investigated through linear stability analysis and nonlinear simulations. It is found that an isotropic velocity-dependent dispersion tensor does not affect substantially the development of the instability and effectively has the same effect as molecular diffusion. On the other hand, an anisotropic velocity-dependent dispersion tensor results in different instability characteristics and more intricate finger structures. It is shown that anisotropic dispersion has profound effects on the development of the fingers and on the mechanisms of interactions between neighboring fingers. The development of the new finger structures is explained by examining the velocity field and characterized qualitatively through a spectral analysis of the average concentration and an analysis of the variations of the sweep efficiency and relative contact area.     

Effect of Reactive Surface Areas Associated with Different Particle Shapes on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Rocks

In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.     

水下爆炸气泡与复杂弹塑性结构的相互作用研究

计及结构的弹塑性,将边界元法(BEM)与有限元法(FEM)耦合提出了气泡与弹塑性结构耦合动力学计算方法,并开发了全套的三维水下气泡分析程序（UBA）,计算值与实验值之间误差在10%以内．以水面舰船为例,将三维计算程序工程化．并分析了水下爆炸气泡载荷作用下船体的弹塑性响应,从船体结构典型单元上的应力时历曲线可以看出,在气泡坍塌时出现应力峰值,证实了气泡坍塌压力及射流引起的压力对舰船等结构造成严重毁伤．从气泡与舰船的相互作用中可以看出,舰船低阶垂向振型被激起,在气泡作用下呈鞭状运动,同时舰船随着气泡的膨胀和收缩作升沉运动,通过本文的分析得到了适合于工程应用的规律及结论．     

A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).     

Determination of Permeability Distributions Using NMR Velocity Imaging

This study develops a methodology for determining the absolute permeability distribution in a porous media sample using velocity data obtained from NMR imaging experiments. An objective function describing the discrepancy between observed and simulated data is reduced by iteratively updating the permeability. This parameter estimation scheme is based on an iterative method which uses optimal control theory to refine the estimates. Although this theory is developed for both isotropic and anisotropic porous media, the permeability reconstructions examined in this paper are restricted to the isotropic case. Synthetic data are used to investigate the impact of varying the noise in the experimental data, the degree of parameterization, the relative weighting of the regularization term in the objective function, and the amount and type of data required to obtain a satisfactory permeability reconstruction. These synthetic data are extracted from the solution of numerical experiments that have utilized an assumed permeability distribution. The methodology is also applied to data gathered in laboratory experiments for water flow in a sandstone sample.