### Abstract

Steady, two-dimensional, viscous, fully developed, laminar flows are studied by the methods of isoperimetric estimations, complex analysis, and asymptotic approximations. The Carman-Kozeny averaging of velocity over the cross-sectional area of a tube is shown to become meaningless for some fractures deviating from "normal" convex shapes. Permeability of constituting tubes is estimated from above and below using a novel characteristic, the momentum of the flow domain about its boundary. Poiseuille-type flows in double-connected and misconnected domains are discussed. Longitudinal and transversal flows through a nonplanar zigzag fracture composed of annular segments are studied by an asymptotic solution of the Poisson equation and an exact solution of the Navier-Stokes equation, correspondingly. The lubrication theory approximation is compared with the case of a nonparabolic velocity profile within the fracture. The influence of tortuosity on permeability is established by calculation of the flux ratio through curved and planar fractures. For the Stokes approximation, a double-periodic combination of plane fractures and circular enlargements is studied using the Rayleigh solution and its generalization. A two-dimensional Darcian flow through a system with regular square occlusions is studied and kinematic channeling is quantified by the travel time along the fastest streamline.

Original language | English |
---|---|

Pages (from-to) | 125-148 |

Number of pages | 24 |

Journal | Journal of Porous Media |

Volume | 8 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Materials Science(all)
- Physical and Theoretical Chemistry
- Fluid Flow and Transfer Processes
- Catalysis

### Cite this

*Journal of Porous Media*,

*8*(2), 125-148. https://doi.org/10.1615/JPorMedia.v8.i2.30

**Analytical solutions and estimates for microlevel flows.** / Avkhadiev, F. G.; Kacimov, A. R.

Research output: Contribution to journal › Article

*Journal of Porous Media*, vol. 8, no. 2, pp. 125-148. https://doi.org/10.1615/JPorMedia.v8.i2.30

}

TY - JOUR

T1 - Analytical solutions and estimates for microlevel flows

AU - Avkhadiev, F. G.

AU - Kacimov, A. R.

PY - 2005

Y1 - 2005

N2 - Steady, two-dimensional, viscous, fully developed, laminar flows are studied by the methods of isoperimetric estimations, complex analysis, and asymptotic approximations. The Carman-Kozeny averaging of velocity over the cross-sectional area of a tube is shown to become meaningless for some fractures deviating from "normal" convex shapes. Permeability of constituting tubes is estimated from above and below using a novel characteristic, the momentum of the flow domain about its boundary. Poiseuille-type flows in double-connected and misconnected domains are discussed. Longitudinal and transversal flows through a nonplanar zigzag fracture composed of annular segments are studied by an asymptotic solution of the Poisson equation and an exact solution of the Navier-Stokes equation, correspondingly. The lubrication theory approximation is compared with the case of a nonparabolic velocity profile within the fracture. The influence of tortuosity on permeability is established by calculation of the flux ratio through curved and planar fractures. For the Stokes approximation, a double-periodic combination of plane fractures and circular enlargements is studied using the Rayleigh solution and its generalization. A two-dimensional Darcian flow through a system with regular square occlusions is studied and kinematic channeling is quantified by the travel time along the fastest streamline.

AB - Steady, two-dimensional, viscous, fully developed, laminar flows are studied by the methods of isoperimetric estimations, complex analysis, and asymptotic approximations. The Carman-Kozeny averaging of velocity over the cross-sectional area of a tube is shown to become meaningless for some fractures deviating from "normal" convex shapes. Permeability of constituting tubes is estimated from above and below using a novel characteristic, the momentum of the flow domain about its boundary. Poiseuille-type flows in double-connected and misconnected domains are discussed. Longitudinal and transversal flows through a nonplanar zigzag fracture composed of annular segments are studied by an asymptotic solution of the Poisson equation and an exact solution of the Navier-Stokes equation, correspondingly. The lubrication theory approximation is compared with the case of a nonparabolic velocity profile within the fracture. The influence of tortuosity on permeability is established by calculation of the flux ratio through curved and planar fractures. For the Stokes approximation, a double-periodic combination of plane fractures and circular enlargements is studied using the Rayleigh solution and its generalization. A two-dimensional Darcian flow through a system with regular square occlusions is studied and kinematic channeling is quantified by the travel time along the fastest streamline.

UR - http://www.scopus.com/inward/record.url?scp=19544385432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19544385432&partnerID=8YFLogxK

U2 - 10.1615/JPorMedia.v8.i2.30

DO - 10.1615/JPorMedia.v8.i2.30

M3 - Article

VL - 8

SP - 125

EP - 148

JO - Journal of Porous Media

JF - Journal of Porous Media

SN - 1091-028X

IS - 2

ER -