Non-Newtonian fluids in flow and deformation exhibit viscous or viscoelastic or viscoplastic behavior or any combination of them. These fluids are usually called viscoelastic ή viscoplastic. Examples of viscoelastic fluids are commercial plastics (in solution or melt form) and rubber. Examples of viscoplastic materials are paints, ceramics, pastes, blood and several foodstuffs, such as margarine, mayonnaise, and ketchup. Their processing, under steady-state (e.g. extrusion) or transient conditions (e.g. injection molding), is the prime occupation in the plastics, rubber, food, and ceramics industries, etc. Their modeling and numerical simulation are considered a difficult research task and a relatively modern undertaking in scientific computations.
In the current course several models of non-Newtonian behavior are studied. Specifically, there are the simple viscous models of power law, Carreau, Cross, Bingham, Herschel-Bulkley, Casson, etc. Then there are the simple linear viscoelastic models of Maxwell, Oldroyd-B, etc, and the more advanced non-linear integral viscoelastic models, incorporating a spectrum of relaxation modes for a better description of the complex rheological behaviour of polymers. Using such rheological constitutive equations and the finite element method (FEM), it is possible ? and relatively easy ? to solve various problems in the processing of viscoelastic and viscoplastic materials.
Examples are given from extrusion processing, and in particular flow through extrusion dies of polymer melts and coating flows of polymer solutions. Several viscoelastic flow phenomena are simulated, such as vortex growth, extrudate swell from dies, and reduced coating thickness, which are of special interest to the practioners in the plastics and coating industries.