Solution of two dimensional Stokes flow with elliptical coordinates and its application to permeability of porous media

2021 ◽  
pp. 1-18
Author(s):  
Mustapha Hellou ◽  
Franck Lominé ◽  
Mohamed Khaled Bourbatache ◽  
Mohamed Hajjam
Keyword(s):  
Porous Media ◽  
Stokes Flow ◽  
Biharmonic Equation ◽  
Fluid Flows ◽  
Gegenbauer Polynomials ◽  
Series Expansions ◽  
Two Dimensional ◽  
Elliptic Coordinates ◽  
Elliptical Coordinates

Abstract Analytical developments of the biharmonic equation representing bi-dimensional Stokes flow are realized with elliptic coordinates. It's found that the streamfunction is expressed with series expansions based on Gegenbauer polynomials of first and second kinds with order one Cn1and Dn1. A term corresponding to order n=-1 is added in view to create drag on a body around which the fluid flows. Application to an array of elliptic cylinders is made and the permeability of this medium is determined as a function of porosity.

FLUID PERMEABILITY IN TWO-DIMENSIONAL PERCOLATION POROUS MEDIA

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2523-2528 ◽  
Author(s):  
ZHI-FENG LIU ◽  
XIAO-HONG WANG
Keyword(s):  
Porous Media ◽  
Viscous Fluid ◽  
Percolation Theory ◽  
Fluid Flows ◽  
Scaling Relations ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Fluid Permeability ◽  
Numerical Grid ◽  
Conductivity Problem

The scaling relations for the fluid permeability in percolation structures are numerically studied using both of the coarse numerical grid and the refined numerical grid. We suggest that the permeability for viscous fluid flows in two-dimensional lattice percolation porous media be equivalent to the conductivity problem in percolation theory, independent of the simulation refinements. The refined numerical grid does not lead to the new universality.

scholarly journals Structures and Instabilities in Reaction Fronts Separating Fluids of Different Densities

2019 ◽  
Vol 24 (2) ◽  
pp. 51
Author(s):  
Johan Llamoza ◽  
Desiderio A. Vasquez
Keyword(s):  
Porous Media ◽  
Density Gradient ◽  
Stokes Flow ◽  
Numerical Solutions ◽  
Mass Density ◽  
Fluid Velocity ◽  
Two Dimensional ◽  
Narrow Gap ◽  
Reaction Fronts ◽  
Brinkman’S Equation

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele–Shaw cells or porous media, with the hydrodynamics modeled by Brinkman’s equation. The time evolution of the front is described with a Kuramoto–Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman’s equation lead to the same results as Darcy’s laws for narrow gap Hele–Shaw cells. For large gaps, modeling the hydrodynamics using Stokes’ flow lead to the same results.

scholarly journals Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

2017 ◽  
Vol 473 (2202) ◽  
pp. 20170134 ◽  
Author(s):  
Darren G. Crowdy ◽  
Samuel J. Brzezicki
Keyword(s):  
Stokes Flow ◽  
Biharmonic Equation ◽  
Elastic Solid ◽  
Two Dimensional ◽  
Slip Boundary Conditions ◽  
Arbitrary Angle ◽  
Full Account ◽  
Slip Boundary ◽  
Singularity Type ◽  
Strain Stress

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

Two-Dimensional Flow of Polymer Solutions Through Porous Media

1999 ◽  
Vol 2 (3) ◽  
pp. 251-262
Author(s):  
P. Gestoso ◽  
A. J. Muller ◽  
A. E. Saez
Keyword(s):  
Porous Media ◽  
Polymer Solutions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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