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.

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.

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

Biot’s theory and granular media

Poromechanics ◽  
2020 ◽  
pp. 191-196
Author(s):  
Nicholas P. Chotiros
Keyword(s):  
Granular Media ◽  
Biot’S Theory ◽  
Biot's Theory

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

Turbulent Dispersion in Porous Materials as Modeled by a Mixing Cell with Stagnant Zone

1971 ◽  
Vol 11 (01) ◽  
pp. 57-62
Author(s):  
C.R. Kyle ◽  
R.L. Perrine
Keyword(s):  
Porous Material ◽  
Turbulent Flow ◽  
Porous Materials ◽  
Molecular Diffusion ◽  
Stagnant Zone ◽  
Skewed Distribution ◽  
Capillary Tubes ◽  
Fluid Movement ◽  
The Media ◽  
Flow Through

Abstract This paper reports on a simple theoretical analysis of dispersion in rapid flow through porous materials, giving a comparison of predicted results with experiments. The analytical model considers a pore structure which acts like a sequence of mixing cells, each coupled with a stagnant zone. Computed results compare very favorably with experimental observations on flow through a staggered matrix of cylinders. This, in turn, has been shown to behave the packed beds of spheres with corresponding properties. Agreement requires that values for certain theoretical parameters be fitted from the data The values required for these parameters are very reasonable. Development of parameters are very reasonable. Development of this approach could be useful for a number of related problems. Introduction The dispersion of two dynamically similar miscible liquids in laminar or turbulent flow through a porous material is a very complex process. However, it can be broken down into four process. However, it can be broken down into four basic mixing mechanisms:Molecular diffusion. Where the flow velocity is appreciable, or pore size is larger, diffusion is usually negligible. Molecular diffusion will not be discussed in this paper.Uneven fluid movement due to irregular pore geometry and inhomogeneities in the media. Both of these factors are difficult to treat, and are usually neglected in theoretical analysis.Uneven fluid movement due to velocity differences within the pores and passages. The zero-velocity boundary condition on each solid surface assures this type of mixing in both laminar and turbulent flow.Mixing by rotational flow, or by turbulent eddies within the pores or passages. The last two are both convective mixing processes and depend primarily upon the level of processes and depend primarily upon the level of energy dissipation in the media, as well as on the geometry of the system. In general as the velocity increases and the friction losses rise, so does the efficiency of the mixing process. Dispersion has been reviewed thoroughly by Perkins and Johnston and has been studied Perkins and Johnston and has been studied extensively by others. DIFFUSION MODEL OF DISPERSION The most commonly used mathematical model for dispersion in both laminar and turbulent flow is a diffusion-type equation (Refs. 1 or 5). The solution for a step function input with flow in the x-direction only, and with negligible lateral gradients, shows that an initial sharp interface degenerates into a broad mixing zone which grows approximately as the square root of the distance traveled. The solution also predicts a normal distribution for concentration as a function of distance. However, in most real systems "tailing" occurs, causing a skewed distribution. Usually the deviation is not serious and the diffusion equation may be used as a good approximation for the actual process. process. DISPERSION IN A TUBE Another simple model for laminar dispersion, neglecting molecular diffusion, is to consider a porous material as a bundle of capillary tubes. porous material as a bundle of capillary tubes. Sir Geoffrey Taylor showed that if one fluid in a capillary tube is displaced by another dynamically similar miscible fluid, the average concentration, C, at the tube exit is given by: 2C = (V /2V)p SPEJ P. 57

Sign in / Sign up

Export Citation Format

Share Document