Mesh filtration problems with a two-flow structure of phase velocities

This paper deals with the problem of filtration of a two-phase incompressible fluid within the Buckley-Leverett model. From a general point of view, a two-flow structure of conservation laws is investigated. In addition, since the solution in the Buckley-Leverett model is discontinuous, conservation laws are presented in the generalized integral form. A good illustration of the approach presented is the problem of gravitational segregation of oil and water in a porous medium. For this problem, a two-flow mesh structure of conservation laws is described.

Non-Equilibrium Crystallization of Monotectic Zn-25%Bi Alloy under 600 g

This study investigated the influence of supergravity on the segregation of components in the Zn–Bi monotectic system and consequently, the creation of an interface of the separation zone of both phases. The observation showed that near the separation boundary, in a very narrow area of the order of several hundred microns, all types of structures characteristic for the concentration range from 0 to 100% bismuth occurred. An additional effect of crystallization in high gravity is a high degree of structural order and an almost perfectly flat separation boundary. This is the case for both the zinc-rich zone and the bismuth-rich zone. Texture analysis revealed the existence of two privileged orientations in the zinc zone. Gravitational segregation also resulted in a strong rearrangement of the heavier bismuth to the outer end of the sample, leaving only very fine precipitates in the zinc region. For comparison, the results obtained for the crystallization under normal gravity are given. The effect of high orderliness of the structure was then absent. Despite segregation, a significant part of bismuth remained in the form of precipitates in the zinc matrix, and the separation border was shaped like a lens. The described method can be used for the production of massive bimaterials with a directed orientation of both components and a flat interface between them, such as thermo-generator elements or bimetallic electric cell parts, where the parameters (thickness) of the junction can be precisely defined at the manufacturing stage.

Three-Dimensional Interaction of Viscous Fingering and Gravitational Segregation in Porous Media

Viscous fingering is fluid dynamics instability induced on the displacement front when a less viscous fluid (LVF) displaces a more viscous fluid (MVF), thereby reducing the displacement efficiency. The displacement of a denser fluid by a less dense fluid produces a gravitational tongue. This gravitational segregation also reduces the displacement efficiency. In this study, the three-dimensional structure of the fingering pattern at the viscous fingering to gravitational segregation boundary was examined using X-ray microtomography on a packed bed of particles. At low gravity numbers, viscous fingering resembled that without gravity characterized by nonlinear interaction including tip-splitting, shielding, and coalescence. At intermediate gravity numbers, viscous fingering is associated with the gravitational tongue due to segregation. At high gravity numbers, a clear gravitational tongue penetrates from the inlet to the outlet. Consequently, the concentration near the injection point decreases and exhibits a flat profile in the flow direction. The displacement efficiency decreases with increasing gravity number, with the highest value achieved without gravity but depends on many factors, including the viscosity ratio and Péclet number.