Flow of non‐Newtonian fluids in converging–diverging rigid tubes

Abstract

A residual‐based lubrication method is used to find the flow rate and pressure field in converging‐diverging rigid tubes for the flow of time‐independent category of non‐Newtonian fluids. Five converging‐diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel‐Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging‐diverging tubes, convergence to analytical solutions found earlier for the flow in converging‐diverging tubes of Newtonian fluids as special cases for non‐Newtonian, and convergence to analytical solutions found earlier for the flow of power‐law fluids in converging‐diverging tubes. A brief investigation was also conducted on a sample of diverging‐converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically‐symmetric converging‐diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.

Yield and Solidification of Yield-Stress Materials in Rigid Networks and Porous Structures

“…We therefore feel obliged to provide a general clarification about the computational framework which the current study relies upon. We have already fully explained this framework in some of our previous publications and hence for the purpose of saving space and avoiding repetition we refer the reader to the following papers: [14][15][16] where our computational framework is fully explained. More relevant details may also be found in [13,17] although these are mainly related to a onedimensional finite element Newtonian flow model.…”

Flow of Carreau Fluids Through Non-Uniform Pore throats

“…The geometry of pore-throats are approximated to have different cross sections [15]. Sochi [30] developed a residual-based lubrication method to calculate the flow rate in a converging-diverging pore throat. This method is based on discretizing the fluid conduit into ring-like elements.…”

“…Therefore, a different treatment is needed to solve the flow in non-uniform pore throats where the effects of the radial flow velocity component on the pressure distribution are considered. Also, Sochi [30] developed another semi-analytical model for Carreau fluid flows in uniform pore throats. This semi-analytical model require an iterative solver to determine the wall shear strain rate.…”