Problems in Non-Newtonian Fluid Mechanics

Abstract

In this thesis we are concerned with the rheological behaviour of industrial liquids such as polymer solutions in complex flow situations and the possibility of predicting this behaviour. Preliminary consideration is given to the rheometrical characterization of several elastico-viscous test solutions using an R16 Rheogoniometer. Results of simple shear flow and oscillatory shear flow measurements are shown in Appendix A. These data enable us to choose the most appropriate solutions for our experimental studies. Implicit models of the Oldroyd-Maxwell type are chosen as our constitutive equations to characterize the complex behaviour of the liquids considered. These models retain the simplicity necessary to solve complicated flow problems of the sort considered in this work. Chapter 2 explains the reasons behind this choice. Chapter 3 deals with the numerical method chosen to solve the very complex equations governing the flow of elastic liquids in complex flow situations. The method is of the generalized Conjugate Gradient type with incomplete LU-decomposition. This is used to solve the discretized equations using finite differences with central difference formulae. The first flow problem considered deals with two unsteady pipe flows. In the first situation, the flow is generated by a pulsatile pressure gradient in a stationary pipe. The second concerns axial vibrations of the pipe wall with constant pressure gradient. Since experimental data for both are available, in Chapter 4 we attempt to simulate the experimental results using a conventional perturbation