Analytical solutions and estimates for microlevel flows

F. G. Avkhadiev, A. R. Kacimov

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 languageEnglish
Pages (from-to)125-148
Number of pages24
JournalJournal of Porous Media
Volume8
Issue number2
DOIs
Publication statusPublished - 2005

Fingerprint

Analytical Solution
estimates
Estimate
Permeability
Tube
permeability
approximation
tubes
Lubrication Theory
Approximation theory
two dimensional flow
Isoperimetric
Zigzag
Complex Analysis
occlusion
Enlargement
Asymptotics of Solutions
Poisson equation
Asymptotic Approximation
Travel Time

ASJC Scopus subject areas

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

Cite this

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

In: Journal of Porous Media, Vol. 8, No. 2, 2005, p. 125-148.

Research output: Contribution to journalArticle

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