This project started on April 2005 with Dr Oliver Harlen and sponsored by the Microscale Polymer Processing project (mupp). For this project we consider a large number of inertialess solid particles suspended in viscoelastic fluids. The challenge of the project is to determine the rheological proprieties of the particulate suspension from the knowledge of the rheological proprieties of the ambient fluid and the proprieties of the particles. In order to solve the problem at reasonable computational cost, we solve the flow in a unit cell containing a small number of particles with doubly periodic boundary conditions to replicate a suspension on an unbounded domain with an infinite number of particles. The method combines the Lagrangian-Eulerian technique, where the constitutive equation is solved in a Lagrangian frame, with a quotient space representation to impose doubly periodic boundary conditions. The boundary conditions on the force and torque free particles are imposed treating the surface density force as a Lagrange multiplier to force the fluid inside the particles to behave as a rigid solid. In this formulation, the connectivity of the mesh preserves the sliding biperiodic frames, so that we do not needs to consider the biperiodicity as an additional constraint. This method has been applied to several different differential constitutive models, including the Oldroyd B, FENE-CR and FENE-P models, as well as more advanced molecularly based constitutive models such as the multimode pom-pom and Roliepoly models.
Preliminary results can be found here.