Newtonian Flow in Converging-Diverging Capillaries

Abstract

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

23 pages, 5 figures, 1 table. This is an extended and improved version. arXiv admin note: substantial text overlap with arXiv:1006.1515

References in corpus (1)

• The Flow of Newtonian Fluids in Axisymmetric Corrugated Tubes

Cited by in corpus (8)

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• Flow of Navier-Stokes Fluids in Converging-Diverging Distensible Tubes
• Flow of Navier-Stokes Fluids in Cylindrical Elastic Tubes
• The Yield Condition in the Mobilization of Yield-Stress Materials in Distensible Tubes
• Compositional Pore-Network Modeling of Gas-Condensate Flow
• Methods for Calculating the Pressure Field in the Tube Flow