The Linear Stability Analysis And Numerical Simulation Of Stratified Flows Of Shear-thinning Fluids

There is much theoretical and practical value in studying the stratified flow of twoimmiscible fluids inside a channel. With the extensive applications of interfacialsurfactant in multiphase flows, the investigation of stratified flow stability with thepresence of interfacial surfactant has become the focus of stability studies. A number offluids show non-Newtonian properties in the applications of stratified flows. Therefore,it is necessary to consider the influence of non-Newtonian properties on the stability ofstratified flows. However, the present researches mostly focus on the Newtonian fluidflow, probably due to the complication of non-Newtonian fluid models.In the present work, the power-law fluid model which is widely used in practicalapplications is adopted to investigate the influence of shear-thinning property on thelinear stability of stratified flows with interfacial surfactant present. The base flowsconsidered include stratified Couette flow between two parallel plates as well asstratified Poiseuille flow inside a straight cylindrical pipe (core-annular flow). Thecontrol equations are derived with the power-law fluid model and analytical solutions tothe base flows are presented, based on which linear disturbance equations are deduced.The Chebyshev collocation method is used to numerically calculate the disturbanceequations. A trouble appears in obtaining the numerical solution of shear-thinning fluidcore-annular flow, due to the singular point in cylindrical coordinate system, which issolved by introducing visual grids.The Couette flow results show that shear-thinning property enhances the influenceof viscosity stratification on the flow stability. Analyses indicate that shear-thinningproperty magnifies the discontinuity of the base flow velocity gradient across theinterface, which appears due to viscosity stratification. It is found in the core-annularflow results that shear-thinning property enhances the interfacial tension effect instability when the interface is close to the pipe wall, while weakens it when the interfaceis close to the pipe centerline. The reason is discovered by analyzing the stress balancecondition at the interface: the change of power-law index amounts to changing thecapillary number in certain conditions. When both viscosity stratification and interfacialtension exist, shear-thinning property influences the factor which decides the flowstability. The shear-thinning effect is complicated if the two factors are comparative, which may lead to an unstable "island" region in the neutral stability curve plot.Numerical simulation is also carried out both for stratified Couette flow andcore-annular flow. The simulation results agree with linear stability analysis, andconfirm the influence of shear-thinning property on viscosity stratification andinterfacial tension effects.