Flow of non-newtonian fluid through porous media

Pascal, H.; Pascal, F.

doi:10.1016/0020-7225(85)90066-7

Cited by 36 publications

(13 citation statements)

References 4 publications

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“…For yield stress fluids (mud, cement, concentrated emulsions, or foams), which flow like liquids only beyond a critical stress and behave as solids otherwise, various analytical or numerical approaches [4] have been developed but the validity of their physical assumptions could not be checked. Some in-depth physical studies suggested that two critical effects could occur: (i) at the pore scale the flowing volume increases with the pressure gradient [5] and (ii) at a macroscopic scale the flow starts as a percolation effect, i.e., at a critical pressure drop liquid regions exist only along a specific path throughout the porous medium [5,6], and as ∇p is increased more flowing paths progressively form within the porous medium.…”

Section: Introductionmentioning

confidence: 99%

Breaking of non-Newtonian character in flows through a porous medium

et al. 2014

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From NMR measurements we show that the velocity field of a yield stress fluid flowing through a disordered well-connected porous medium is very close to that for a Newtonian fluid. In particular, it is shown that no arrested regions exist even at very low velocities, for which the solid regime is expected to be dominant. This suggests that these results obtained for strongly nonlinear fluid can be extrapolated to any nonlinear fluid. We deduce a generalized form of Darcy's law for such materials and provide insight into the physical origin of the coefficients involved in this expression, which are shown to be moments of the second invariant of the strain rate tensor.

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Section: Introductionmentioning

confidence: 99%

Breaking of non-Newtonian character in flows through a porous medium

et al. 2014

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“…Equation (28) porous medium [31][32][33], as well as a balance between viscosity and inertia in Stokes' first [24,34] and second problems [25,26], where the operator is applied to the fluid velocity. We here rely on the previous mathematical analysis of the p-Laplacian equation to provide insight into our viscous-elastic problem, such as self-similarity and compact support of the solutions for pressure and deformation fields.…”

Section: P-laplacian Equation Governing the Pressure Field And Itsmentioning

confidence: 99%

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

2017

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In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a t n n+1 dependence on time (t), suggesting the ability to indirectly measure the power-law index (n) of shear-thinning liquids through measurements of elastic deformation.

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“…We consider a slightly compressible fluid, where the specific mass P is related to the pressure by the relation (2) Po is a reference pressure for which P = Po, and f3 is the compressibility coefficient.…”

Section: Governing Equationsmentioning

confidence: 99%

“…First let us recall from [2] some results concerning the equation (16). As shown in [2], the use of the similarity variable…”

Section: Governing Equationsmentioning

confidence: 99%

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On Some Self‐Similar Flows of Non‐Newtonian Fluids through a Porous Medium

Pascal

1990

Stud Appl Math

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This paper addresses the question of implications of the effects of fluid compressibility on the equations governing unsteady flows of power law fluids through a porous medium. A generalized Burgers equation is shown to arise in the flow description. Some self‐similar flows of practical interest are presented and discussed, from which the nonlinear effects associated with fluid compressibility are analyzed with regard to a better interpretation of transient pressure response in a well of non‐Newtonian displacing fluid tests.

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Flow of non-newtonian fluid through porous media

Cited by 36 publications

References 4 publications

Breaking of non-Newtonian character in flows through a porous medium

Breaking of non-Newtonian character in flows through a porous medium

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

On Some Self‐Similar Flows of Non‐Newtonian Fluids through a Porous Medium

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