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You are here : eLibrary : IAHR World Congress Proceedings : 35th IAHR Congress - Chengdu (2013) : THEME 3 - WATER ENGINEERING AND CIVILIZATION : Rheological Aspects of Filtration in Capillaries and Porous Bodies
Rheological Aspects of Filtration in Capillaries and Porous Bodies
Author : M.A. SATTAROV
The experimental law established as early as 1856 by the French engineer Darcy retains its priority as the basic linear law of motion of viscous homogeneous fluids through very narrow capillaries and homogeneous porous bodies. Darcy?s experiments were repeated by Dupuis (1863) under conditions of inhomogeneous filtration in sand soils, who found that the law becomes nonlinear and turns into a binomial law only near the well. However, calculating the well flow rate using the linear law, he obtained the well-known flow rate formula, named after him, whose accuracy was later proved by I. Charny. N.E. Zhukovskii (1889) used the Navier-Stokes system of equations to describe the motion of water in subsoil soils. Ignoring the convective part of acceleration, he linearized this equation, and assumed that the average velocity in unsteady conditions of filtration is proportional to the resistance of the porous body skeleton. Later this equation was used to solve some important questions associated with representation of the filtration laws. In (1899) King, using solid soil samples, observed a considerable deviation of filtration from its linear law. A.V. Nikolaev (1936) performed similar experiments with soil samples and established a power law of filtration. In the 1930s-1960s, there appeared some papers and books in which, on the basis of the results of some experiments, it was shown that water does not have Newtonian properties, that it is not a typical fluid but has a previously unnoticed property, namely, viscoplasticity, described in rheology by the Buckingham-Reiner formula. Thereby it was shown that Darcy?s law may not be valid even in sand soils. However, papers of E.C. Child, T. Tzimas (1969), A.I. Gorshkov (1972), and W. Novak (1972), differing by the experimental method, again confirmed the validity of Darcy?s law. It is in that period that, in addition to numerous experiments with capillaries and soils of different structures, a new mathematical model of filtration was suggested by the author. In this model, it was proposed to classify the process of filtration as flows of generalized Newtonian and generalized Bingham fluids. This solved the question of model representation of the laws of motion of ground waters at small filtration rates, which is the most widespread phenomenon in underground layers saturated with viscous fluids. This paper studies, for the first time, the questions of motion of various fluids at any pressure gradients in capillaries and porous media within the framework of A.N. Kolmogorov?s theory of small-scale turbulence where average statistical characteristics of the flow are considered to be the same as those of a turbulent flow with a transverse shear in a space consisting of a set of stable homogeneous lattices. The tortuosity of trajectories and small-scale pulsations of fluid particles in a fine-dispersed medium are compared with a homogeneous pseudo-turbulent flow having constant periodicity in time and space. The porous medium is represented as a set of capillaries with a flow and previously unknown characteristics: the coefficients of eddy viscosity and tortuosity of a pseudoturbulent flow with a transverse shear. The theory is illustrated by experimental data obtained by some scientists and the author. It is proved that the internal kinematic characteristics of the flow of various fluids (pure, inhomogeneous, and having mineral ions) greatly affect the flow rate, filtration coefficient, and other averaged parameters of filtration.
File Size : 399,308 bytes
File Type : Adobe Acrobat Document
Chapter : IAHR World Congress Proceedings
Category : 35th IAHR Congress - Chengdu (2013)
Date Published : 18/07/2016
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