An Eulerian description of fluids containing visco-elastic particles

Equations governing the flow of fluid containing visco-hyperelastic particl es are developed in an Eulerian framework. The novel feature introduced her e is to write an evolution equation for the strain. It is envisioned that t his will simplify numerical codes which typically compute the strain on Lag rangian meshes moving through Eulerian meshes. Existence results for the fl ow of linear visco-hyperelastic particles in a Newtonian fluid are establis hed using a Galerkin scheme.