Transport processes in fractals. VI. Stokes flow through Sierpinski carpets

1986 ◽  
Vol 29 (1) ◽  
pp. 15 ◽  
Author(s):  
P. M. Adler
Keyword(s):  
Stokes Flow ◽  
Transport Processes ◽  
Flow Through ◽  
Sierpinski Carpets

Transport processes in periodic porous media

1995 ◽  
Vol 299 ◽  
pp. 1-15 ◽  
Author(s):  
R. B. Saeger ◽  
L. E. Scriven ◽  
H. T. Davis
Keyword(s):  
Porous Media ◽  
Stokes Equation ◽  
Stokes Flow ◽  
Scaling Law ◽  
Equation System ◽  
Transport Processes ◽  
Formation Factor ◽  
Flow Through ◽  
Elliptic Grid Generation ◽  
The Stokes Equation

The Stokes equation system and Ohm's law were solved numerically for fluid in periodic bicontinuous porous media of simple cubic (SC), body-centred cubic (BCC) and face-centred cubic (FCC) symmetry. The Stokes equation system was also solved for fluid in porous media of SC arrays of disjoint spheres. The equations were solved by Galerkin's method with finite element basis functions and with elliptic grid generation. The Darcy permeability k computed for flow through SC arrays of spheres is in excellent agreement with predictions made by other authors. Prominent recirculation patterns are found for Stokes flow in bicontinuous porous media. The results of the analysis of Stokes flow and Ohmic conduction through bicontinuous porous media were used to test the permeability scaling law proposed by Johnson, Koplik & Schwartz (1986), which introduces a length parameter Λ to relate Darcy permeability k and the formation factor F. As reported in our earlier work on the SC bicontinuous porous media, the scaling law holds approximately for the BCC and FCC families except when the porespace becomes nearly spherical pores connected by small orifice-like passages. We also found that, except when the porespace was connected by the small orifice-like passages, the permeability versus porosity curve of the bicontinuous media agrees very well with that of arrays of disjoint and fused spheres of the same crystallographic symmetry.

scholarly journals Stokes flow through a slit with periodic reabsorption: An application to renal tubule

2016 ◽  
Vol 55 (2) ◽  
pp. 1799-1810 ◽  
Author(s):  
T. Haroon ◽  
A.M. Siddiqui ◽  
A. Shahzad
Keyword(s):  
Stokes Flow ◽  
Renal Tubule ◽  
Flow Through

Stokes Flow Through a Row of Cylinders Between Parallel Walls: Model for the Glomerular Slit Diaphragm

1994 ◽  
Vol 116 (2) ◽  
pp. 184-189 ◽  
Author(s):  
M. Claudia Drumond ◽  
William M. Deen
Keyword(s):  
Stokes Flow ◽  
Stokes Equations ◽  
Slit Diaphragm ◽  
Hydraulic Permeability ◽  
Shear Stresses ◽  
Two Factors ◽  
Additional Resistance ◽  
Flow Through ◽  
Experimental Values ◽  
Glomerular Capillaries

As a model for flow through the slit diaphragms which connect the epithelial foot processes of renal glomerular capillaries, finite element solutions of Stokes equations were obtained for flow perpendicular to a row of cylinders confined between parallel walls. A dimensionless “additional resistance” (f), defined as the increment in resistance above the Poiseuille flow value, was computed for L/W≤4 and 0.1≤ R/L≤0.9, where L is half the distance between cylinder centers, W is half the distance between walls and R is the cylinder radius. Two factors contributed to f: the drag on the cylinders, and the incremental shear stresses on the walls of the channel. Of these two factors, the drag on the cylinders tended to be dominant. A more complex representation of the slit diaphragm, suggested in the literature, was also considered. The predicted hydraulic permeability of the slit diaphragm was compared with experimental values of the overall hydraulic permeability of the glomerular capillary wall.

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