Viscous fingering of a thixotropic fluid in a porous medium or a narrow fracture

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Abstract

We consider the flow of a fluid with a modified Bautista–Manero rheology injected radially into a porous medium or unidirectionally into a widening fracture. Linear stability analysis of the flows demonstrates that viscous fingering instabilities are possible, supported essentially by the thixotropic nature of the fluid: the growth rate of unstable perturbations scales approximately with the relaxation rate of the fluid, while their spatial scale is set in the radial case by where is the areal injection rate, and in the fracture case by a ‘relaxation lengthscale’ which cannot be deduced by purely dimensional reasoning. It appears likely that the same instability mechanism can occur in other shear-thinning thixotropic fluids.
Original languageEnglish
Pages (from-to)117-127
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Volume135
DOIs
Publication statusPublished - 2006

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Porous Media
Porous materials
Fluid
Fluids
fluids
Linear stability analysis
Shear Thinning
shear thinning
Shear thinning
Rheology
Linear Stability Analysis
rheology
Length Scale
Injection
Reasoning
Unstable
Likely
injection
Perturbation
perturbation

Keywords

  • thixotropic fluid
  • viscous fingering
  • fluid mechanics

Cite this

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abstract = "We consider the flow of a fluid with a modified Bautista–Manero rheology injected radially into a porous medium or unidirectionally into a widening fracture. Linear stability analysis of the flows demonstrates that viscous fingering instabilities are possible, supported essentially by the thixotropic nature of the fluid: the growth rate of unstable perturbations scales approximately with the relaxation rate of the fluid, while their spatial scale is set in the radial case by where is the areal injection rate, and in the fracture case by a ‘relaxation lengthscale’ which cannot be deduced by purely dimensional reasoning. It appears likely that the same instability mechanism can occur in other shear-thinning thixotropic fluids.",
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T1 - Viscous fingering of a thixotropic fluid in a porous medium or a narrow fracture

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AB - We consider the flow of a fluid with a modified Bautista–Manero rheology injected radially into a porous medium or unidirectionally into a widening fracture. Linear stability analysis of the flows demonstrates that viscous fingering instabilities are possible, supported essentially by the thixotropic nature of the fluid: the growth rate of unstable perturbations scales approximately with the relaxation rate of the fluid, while their spatial scale is set in the radial case by where is the areal injection rate, and in the fracture case by a ‘relaxation lengthscale’ which cannot be deduced by purely dimensional reasoning. It appears likely that the same instability mechanism can occur in other shear-thinning thixotropic fluids.

KW - thixotropic fluid

KW - viscous fingering

KW - fluid mechanics

U2 - 10.1016/j.jnnfm.2006.02.004

DO - 10.1016/j.jnnfm.2006.02.004

M3 - Article

VL - 135

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EP - 127

JO - Journal of Non-Newtonian Fluid Mechanics

JF - Journal of Non-Newtonian Fluid Mechanics

SN - 0377-0257

ER -