Lubrication flows of generalized Newtonian fluids in slowly varying geometries with slip

Abstract

We investigate the isothermal, steady, creeping flow of generalized Newtonian fluids (GNFs) in symmetric tubes with slowly varying cross-sections, allowing for wall slip. Within the lubrication framework, a closed integro-algebraic equation governing the shear-rate distribution is derived. The formulation accommodates arbitrary shear-dependent viscosity functions and wall geometries. Exact analytical solutions are obtained for Newtonian and power-law fluids, while more complex viscosity laws are treated numerically through the development of an efficient algorithm. The formulation provides direct prediction of the shear-rate distribution, from which the remaining flow quantities follow. It is shown that slip modifies the streamline structure, while strongly nonlinear viscosity models lead to a more fundamental change in the flow kinematics, with streamlines no longer aligned with lines of constant transverse coordinates. The influence of configuration (axisymmetric or planar), geometry (linear or hyperbolic), rheology and slip on the pressure drop required to sustain a prescribed flow rate is quantified.