Capillary ascension in porous media: A scaling law

A relationship between the microstructure of a porous medium and the height of ascension of a fluid in the material is proposed. The porous medium is modelled by means of a square lattice randomly filled with matter. A scaling law is derived from a numerical simulation. An analytical solution is also obtained and compared with the numerical results.     

Regularity properties of H-graphs

It is proved that if H(u) is non-decreasing and if , then if u (x) describes a graph over a disk B _R (0), with (upward oriented) mean curvature H(u), there is a bound on the gradient that depends only on R, on u (0), and on the particular function H (u). As a consequence a form of Harnack's inequality is obtained, in which no positivity hypothesis appears. The results are qualitatively best possible, in the senses a) that they are false if H is constant, and b) the dependences indicated are essential.?The demonstrations are based on an existence theorem for a nonlinear boundary problem with singular data, which is of independent interest. Received: April 22, 1996     

关于“毛细现象的能量来源”的讨论

对《大学物理》１９９４年第１２期所刊登的“毛细现象的能量来源”的文作了补充讨论。     

Implications of the phase rule for capillary systems containing surfaces and three-phase contact lines with surface and linear constraint relations

The phase rule is generalized to heterogeneous systems with moderately curved surfaces and linear or line-phase boundaries. It will be shown that the number of degrees of freedom or variancef of a capillary sysem is, in general, larger than that predicted by the classical Gibbs' phase rule. Restrictions on the value off for capillary systems is intimately connected with the imposition of mechanical constraints like the Laplace and Young equations of capillarity. As a direct consequence, it may be shown that the variance for anr-component, three-phase solid-liquid-vapour system (i.e., a liquid drop on a solid surface) is different from that of anr-component, liquid-liquid-vapour system. This conclusion has important implications for the existence or possible existence of equation-of-state type relations.     

Simulation of capillary-dominated displacements in microtomographic images of reservoir rocks

Displacement simulation in realistic pore networks, such as those derived from X-ray microtomography, is presented for the regime where capillarity controls fluid motions and spatial distributions. Complex displacement sequences involving both imbibition and drainage are constructed to extract wettability indices. The percolation properties of predicted equilibrium phase distributions are analyzed. Equilibrium fluid distributions are used to model transport properties for each phase.     

Effect of fluids properties on non-equilibrium capillarity effects: Dynamic pore-network modeling

We have developed a Dynamic Pore-network model for Simulating Two-phase flow in porous media (DYPOSIT). The model is applicable to both drainage and imbibition processes. Employing improved numerical and geometrical features in the model facilitate a physically-based pore-scale simulator. This computational tool is employed to perform several numerical experiments (primary and main drainage, main imbibition) to investigate the current capillarity theory. Traditional two-phase flow formulations state that the pressure difference between the two phase is equal to the capillary pressure, which is assumed to be a function of saturation only. Many theoretical and experimental studies have shown that this assumption is invalid and the pressure difference between the two fluids is not only equal to the capillary pressure but is also related to the variation of saturation with time in the domain; this is referred to as the non-equilibrium capillarity effect. To date, non-equilibrium capillarity effect has been investigated mainly under drainage. In this study, we analyze the non-equilibrium capillarity theory under drainage and imbibition as a function of saturation, viscosity ratio, and effective viscosity. Other aspects of the dynamics of two-phase flow such as trapping and saturation profile are also studied.     

外压对饱和蒸气压的影响

讨论了外压对液体饱和蒸气压的影响,并利用毛细现象中力学平衡条件和等温气压公式对此作了推导.