An expression has been derived to describe both saturated and unsaturated permeability of porous media in terms of the pore size distribution as obtained from mercury-injection data or water-desorption isotherms. An interaction model has been adopted wherein both pore radius and effective area available for flow have been considered. The permeability values obtained using this expression have been compared with water and gas permeabilities of a variety of porous media. Satisfactory agreement is found between experimental and calculated values over a wide range of permeability.The flow of fluids through porous materials is of great significance in the fields of industrial chemistry, oil technology and agriculture. In general, it may be stated that the principal interest is in the transport through reactive materials. However, interpretation of transport data is complicated by the fact that at the present time no entirely adequate description of flow through inert granular materials exists. Two main types of approach are at present being used in this problem ; the first results in the Kozeny-Carman equation 1 which is derived using the hydraulic radius and tortuosity concepts. It has been assumed that tortuosity may be obtained from electrical resistivity measurements. This approach has been discussed by Wyllie and Spangler 2 and Faris et al. 3 The other treatment of this problem is a statistical one developed by Childs and Collis-George 4 and is based on the probability of the continuity of pores in adjacent places within the poious medium. Both these approaches to the problem depend on the pore size distribution of the medium but that of Childs and Collis-George is related only to the pore size distribution, and requires no additional data such as the electrical resistivity of the porous medium filled with a conducting fluid. More recently, Marshall 5 has developed an equation which is essentially similar to that of Childs and Collis-George.Recently, Fatt 6 has put forward flow concepts wherein the porous medium is likened to a network of capillaries. In this treatment, and the electrical analogue of Probine,7 the assumed nature of the porous solid is somewhat similar to that used here.The theory presented here is a further development of the pore interaction model proposed by Childs and Collis-George.4 The equations presented closely describe saturated and unsaturated permeability as a function of bed porosity, fluid content and pore size distribution. THEORYIn a porous solid there is point-to-point variation in the volume, area and linear proportions of solid to non-solid. A porous material is envisaged as consisting of solid spheres which interpenetrate each other, separated by spherical pores which also interpenetrate; the solid and pore systems are therefore symmetrical. By using this model, it is possible to arrive at a generalized relationship between the porosity and the cross-sectional area controlling flow in a porous material. When the porosity of an isotropic porous medium is given by ~r n l per ml of...
The aims of this paper are threefold: to increase the level of awareness within the shock‐capturing community of the fact that many Godunov‐type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very‐high‐resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.
We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas & Sturtevant: a Mach 1.22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These flows are modelled using the two-dimensional compressible Euler equations for a two-component fluid (air-helium or air–Refrigerant 22). Utilizing a novel shock-capturing scheme in conjunction with a sophisticated mesh refinement algorithm, we have been able to reproduce numerically the intricate mechanisms that were observed experimentally, e.g. transition from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, and jet formation. The level of agreement lends credibility to a number of observations that can be made using information from the simulations for which there is no experimental counterpart. Thus we can now present an updated description for the dynamics of a shock-bubble interaction which goes beyond that provided by the original experiments.
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