2011/08/31 by Taha Sochi
Physics and Astronomy · Mathematics · #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.1142/s1793962313500116
23 pages, 5 figures, 1 table. This is an extended and improved version. arXiv admin note: substantial text overlap with arXiv:1006.1515
arxiv created 2012/12/11 · arxiv updated 2013/04/23
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.