Fractal porous media IV: Three-dimensional stokes flow through random media and regular fractals

1990 ◽  
Vol 5 (4) ◽  
pp. 325-340 ◽  
Author(s):  
R. Lemaitre ◽  
P. M. Adler
Keyword(s):  
Porous Media ◽  
Stokes Flow ◽  
Random Media ◽  
Three Dimensional ◽  
Flow Through

Computation of Flow Through a Three-Dimensional Periodic Array of Porous Structures by a Parallel Immersed-Boundary Method

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhenglun Alan Wei ◽  
Zhongquan Charlie Zheng ◽  
Xiaofan Yang
Keyword(s):  
Porous Media ◽  
Parallel Implementation ◽  
Flow Behavior ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Periodic Array ◽  
Immersed Boundary ◽  
Navier Stokes Equation ◽  
Flow Through ◽  
Ib Method

A parallel implementation of an immersed-boundary (IB) method is presented for low Reynolds number flow simulations in a representative elementary volume (REV) of porous media that are composed of a periodic array of regularly arranged structures. The material of the structure in the REV can be solid (impermeable) or microporous (permeable). Flows both outside and inside the microporous media are computed simultaneously by using an IB method to solve a combination of the Navier–Stokes equation (outside the microporous medium) and the Zwikker–Kosten equation (inside the microporous medium). The numerical simulation is firstly validated using flow through the REVs of impermeable structures, including square rods, circular rods, cubes, and spheres. The resultant pressure gradient over the REVs is compared with analytical solutions of the Ergun equation or Darcy–Forchheimer law. The good agreements demonstrate the validity of the numerical method to simulate the macroscopic flow behavior in porous media. In addition, with the assistance of a scientific parallel computational library, PETSc, good parallel performances are achieved. Finally, the IB method is extended to simulate species transport by coupling with the REV flow simulation. The species sorption behaviors in an REV with impermeable/solid and permeable/microporous materials are then studied.

Fabrication of a Microchannel Device With a Three-Dimensional Pore Network Using a Sacrificial Sugar Template

2020 ◽  
Author(s):  
Haipeng Zhang ◽  
Tomer Palmon ◽  
Seunghee Kim ◽  
Sangjin Ryu
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Pore Structure ◽  
Three Dimensional ◽  
Pore Network ◽  
Compressed Air ◽  
Microfluidic Channels ◽  
Two Phase ◽  
Flow Through ◽  
Phase Fluid

Abstract Porous media compressed air energy storage (PM-CAES) is an emerging technology that stores compressed air in an underground aquifer during the off-peak periods, to mitigate the mismatch between energy supplies and demands. Thus, PM-CAES involves repeated two-phase fluid flow in porous media, and ensuring the success of PM-CAES requires a better understanding of repetitive two-phase fluid flow through porous media. For this purpose, we previously developed microfluidic channels that retain a two-dimensional (2D) pore network. Because it was found that the geometry of the pore structure significantly affects the patterns and occupational efficiencies of a non-wetting fluid during the drainage-imbibition cycles, a more realistic microfluidic model is needed to reflect the three-dimensional (3D) nature of pore structures in the underground geologic formation. In this study, we developed an easy-to-adopt method to fabricate a microfluidic device with a 3D random pore network using a sacrificial sugar template. Instead of using a master mold made in photolithography, a sacrificial mold was made using sugar grains so that the mold could be washed away after PDMS curing. First, we made sugar templates with different levels of compaction load, and found that the thickness of the templates decreased as the compaction load increased, which suggests more packing of sugar grains and thus lower porosity in the template. Second, we fabricated PDMS porous media using the sugar template as a mold, and imaged their pore structure using micro computed tomography (micro-CT). Pores within PDSM samples appeared more tightly packed as the compacting force increased. Last, we fabricated a prototype PDMS channel device with a 3D pore network using a sugar template, and visualized flow through the pore network using colored water. The flow visualization result shows that the water was guided by the random pores and that the resultant flow pattern was three dimensional.

Stokes flow through periodic orifices in a channel

1994 ◽  
Vol 263 ◽  
pp. 207-226 ◽  
Author(s):  
Y. Zeng ◽  
S. Weinbaum
Keyword(s):  
Aspect Ratio ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Plane Wall ◽  
Channel Height ◽  
Infinite Plane ◽  
Electron Microscopic ◽  
Dimensional Solution ◽  
Aspect Ratios ◽  
Flow Through

This paper develops a three-dimensional infinite series solution for the Stokes flow through a parallel walled channel which is obstructed by a thin planar barrier with periodically spaced rectangular orifices of arbitrary aspect ratio B’/d’ and spacing D’. Here B’ is the half-height of the channel and d’ is the half-width of the orifice. The problem is motivated by recent electron microscopic studies of the intercellular channel between vascular endothelial cells which show a thin junction strand barrier with discontinuities or breaks whose spacing and width vary with the tissue. The solution for this flow is constructed as a superposition of Hasimoto's (1958) general solution for the two-dimensional flow through a periodic slit array in an infinite plane wall and a new three-dimensional solution which corrects for the top and bottom boundaries. In contrast to the well-known solutions of Sampson (1891) and Hasimoto (1958) for the flow through zero-thickness orifices of circular or elliptic cross-section or periodic slits in an infinite plane wall, which exhibit characteristic viscous velocity profiles, the present bounded solutions undergo a fascinating change in behaviour as the aspect ratio B’/d’ of the orifice opening is increased. For B’/d’ [Lt ] 1 and (D’ –- d’)/B’ of O(1) or greater, which represents a narrow channel, the velocity has a minimum at the orifice centreline, rises sharply near the orifice edges and then experiences a boundary-layer-like correction over a thickness of O(B’) to satisfy no-slip conditions. For B’/d’ of O(1) the profiles are similar to those in a rectangular duct with a maximum on the centreline, whereas for B’/d’ [Gt ] 1, which describes widely separated channel walls, the solution approaches Hasimoto's solution for the periodic infinite-slit array. In the limit (D’ –- d’)/B’ [Lt ] 1, where the width of the intervening barriers is small compared with the channel height, the solutions exhibit the same behaviour as Lee & Fung's (1969) solution for the flow past a single cylinder. The drag on the zero-thickness barriers in this case is nearly the same as for the cylinder for all aspect ratios.

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