The Modified Mixture Theory for Fluid-Filled Porous Materials: Applications

1987 ◽  
Vol 54 (1) ◽  
pp. 41-46 ◽  
Author(s):  
N. Katsube ◽  
M. M. Carroll
Keyword(s):  
Steady State ◽  
Porous Materials ◽  
Boundary Value Problems ◽  
Characteristic Length ◽  
Boundary Value ◽  
Fluid Velocity ◽  
Mixture Theory ◽  
Biot’S Theory ◽  
Biot's Theory ◽  
State Boundary

The recently established modified mixture theory for fluid-filled porous materials is applied to two steady state boundary value problems; also, how the newly developed theory provides more general solution than Biot’s theory is examined. The velocity profiles in steady state boundary value problems are found to depend on the ratio of a characteristic length of the microstructure to a characteristic length defined by the boundary conditions. As opposed to Biot’s theory, the zero fluid velocity condition on the boundary are satisfied and the existence of a non-Darcy flow closer to the boundary are shown.

The Modified Mixture Theory for Fluid-Filled Porous Materials: Theory

1987 ◽  
Vol 54 (1) ◽  
pp. 35-40 ◽  
Author(s):  
N. Katsube ◽  
M. M. Carroll
Keyword(s):  
Porous Materials ◽  
Velocity Gradient ◽  
Mechanical Response ◽  
Fluid Velocity ◽  
Mixture Theory ◽  
Biot’S Theory ◽  
Homogeneous Fluid ◽  
Biot's Theory ◽  
Flow Mechanisms ◽  
Flow Through

The mixture theory by Green and Naghdi is modified and applied to the problems of flow-through porous materials. By introducing porosity, we make clear that two constituents occupying the same point in the original mixture theory are an equivalent homogeneous solid and an equivalent homogeneous fluid which, respectively, represent a porous solid and a porous fluid in the actual sample. The micro-mechanical response studied by Carroll and Katsube is introduced and detailed deformation and flow mechanisms are provided at each point of the mixture. The resulting theory is compared with Biot’s theory and in fact reduces to Biot’s theory when the fluid velocity gradient terms are ignored.

Modification of Biot’s theory of porous materials

1997 ◽  
Vol 101 (5) ◽  
pp. 3145-3145
Author(s):  
H. Tavossi ◽  
B. R. Tittmann
Keyword(s):  
Porous Materials ◽  
Biot’S Theory ◽  
Biot's Theory

On Steady-State Filtration of Fluid in Strip-Like and Wedge-Shaped Porous Ground Bases

2014 ◽  
Vol 1020 ◽  
pp. 373-378
Author(s):  
Suren M. Mkhitaryan ◽  
H.V. Tokmajyan ◽  
S.A. Avetisyan ◽  
M.S. Grigoryan
Keyword(s):  
Steady State ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Vertical Velocity ◽  
Boundary Value ◽  
Integral Transforms ◽  
Plane Boundary ◽  
Filtration Theory

In statement of the steady-state filtration theory and within the framework of the Darcy`s law plane boundary value problems for the strip-like and wedge-shaped porous ground base are considered when through some system of segments on one face of the base the fluid with a certain vertical velocity or with a certain pressure is injected inside the base. These solutions are reduced to integral equations by means of integral transforms.

On One Class of Boundary Value Problems of the Steady-State Filtration Theory in Porous Grounds

2014 ◽  
Vol 1020 ◽  
pp. 367-372
Author(s):  
Suren M. Mkhitaryan ◽  
H.V. Tokmajyan
Keyword(s):  
Steady State ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Filtration Theory ◽  
Steady State Flow ◽  
Fluid Filtration ◽  
Flow Rates ◽  
Piecewise Constant ◽  
Coefficient Of Filtration ◽  
The Ideal

:In the framework of Darcy's law of filtration the investigation results of one class of boundary value problems of the steady-state filtration theory in porous ground base are presented. The plane mixed bounadry value problems on the structural analysis of hydrotechnical con­struction of dam type on filtrating ground base in the form of a layer of finite or infinite thickness are considered. The coefficient of filtration is assumed to be constant, piecewise constant, or changing by the depth of base according to the exponential law, the property of anisotropy of filtration is also taken into account. Axis-symmetric and three-dimentional boundary value problems of the theory of steady-state fluid filtration in a three-dimentional layer of a finite or infinite thickness are discussed. These problems are of the type of Lamb well-known hydrodynamic problems in the theory of steady-state flow of the ideal fluid, when through the circular or rectangular openeing of a rigid screen on the upper bound of the layer the liquid with a definite vertical velocity or with a definite pressure is injected into porous ground base. Here, the fields of velocities and pressures in the layer, as well as flow rates of liquid through the certain sections of the ground base are determined.

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