Controllability of viscoelastic stresses for nonlinear Maxwell models

✍ Scribed by Michael Renardy

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 146 KB
• Volume: 156
• Category: Article
• ISSN: 0377-0257
• DOI: 10.1016/j.jnnfm.2008.06.010

✦ Synopsis

We investigate a class of models for viscoelastic fluids, in which the elastic stress is determined by a conformation tensor, and the conformation tensor is linked to the velocity field by a system of ordinary differential equations. We study the question which values of the conformation tensor can be reached in a homogeneous flow, subject to a given initial condition and arbitrary velocity fields. This problem is a special "easy" case for the question of controllability of viscoelastic flows. For a class of models, we show that constraints on the values of the conformation tensor are given by lower and/or upper bounds on its determinant. The behavior of seemingly similar models, e.g. the PTT, Giesekus and Peterlin dumbbell models, turns out to be surprisingly different.