Multilayer flow of Giesekus fluids in pressure driven two-dimensional channel at small values of the mobility parameters

In this dissertation we investigate the velocity and stress fields in shear flow of multilayer immiscible Giesekus Fluids with equal densities. The shear flows of Non Newtonian multilayer fluids and their stability is of great interest in a variety of commercially important polymer processing operations, such as film blowing, extrusions, and various coating flows.;In the first part of this dissertation we solve the problem for one dimensional steady state flow between moving parallel plates with an associated pressure gradient. This nonlinear problem is solved by a computational method based on spectral techniques. The velocity profile and the associated stress profiles are obtained numerically. There are two parameters that govern the nonlinear character of such fluids: The Giesekus mobility parameter and the Weisenberg number, which is a measure of the relaxation time of the fluid. When either one of the parameters is zero, the fluid exhibits Newtonian behavior. Our computational scheme confirms this. Our calculations reveal that as the mobility parameters increase, the sensitivity of the velocity profile to the relaxation time is increased. In two layered flows larger Weisenberg numbers give rise to larger deviations of the velocity from the Newtonian parabolic profile. Our calculations also reveal that as the relaxation times are increased, the evaluation of the velocity and stress fields becomes more involved due to increased nonlinearity in the problem. We observe that the direction of the pressure gradient may have an influence on the sensitivity of the velocity profile to relaxation times. In the configuration of a nearly Newtonian thin layer on top of a thicker non Newtonian layer, our calculations indicate that a favorable pressure gradient increases the sensitivity of the velocity profile to variations of relaxation time. An adverse pressure gradient does not seem to have the same effect.;In the second part of this dissertation we follow a linearization approach by an expansion for a small mobility parameter to solve the two dimensional steady-state problem. The linear one-dimensional zeroth order approximation is obtained analytically, and the first order correction is calculated using finite difference methods in conjunction with Gauss-Siedel iteration. This correction produces circulatory cells oriented in the direction of the flow. The combination of the zero-order and first-order correction is an undulated rectilinear flow with the undulation depending on the character of the first order correction. This approach may be utilized as an alternative method for studying the stability of multilayer flows of polymers for a variety of thickness ratios and material parameters.