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 geom...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 nondimensional 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.展开更多
文摘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 nondimensional 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.
