Numerical simulation of planar elongational flow of concentrated rigid particle suspensions in a viscoelastic fluid

In this paper we study, by means of numerical simulation, planar elongational flow of concentrated, inertialess, non-Brownian rigid particle suspensions in a viscoelastic fluid. The simulation is 2D and follows the approach presented in our previous work \cite{DMHP06}. A small computational domain is obtained by considering a three-layer domain. The innermost part is used to calculate the suspension response, the outermost is used to set the elongational flow boundary conditions far from the particles, and an intermediate region is mandatory to allow the developing of viscoelastic stress fields around the particle before entering the innermost layer. This scheme allows to achieve steady state (in a statistical sense). A time-independent fixed grid is used to avoid difficulties due to deforming meshes and remeshing of the domain. A fictitious domain has been implemented in order to easily manage the rigid-body motion. The particles are described by their boundaries only (rigid-ring description) and the rigid-body motion is imposed through Lagrange multipliers. A DEVSS-G/SUPG finite element formulation is implemented, and the log-conformation representation of the constitutive equation is used in order to improve the numerical stability of the method.The suspending liquid is treated as a Giesekus fluid. The bulk properties are determined by using an averaging procedure. Bulk calculations show that the extensional viscosity increases, with respect to the unfilled fluid, with the particle area fraction as well as with the Weissenberg number. The strain hardening parameter is predicted to decrease with increasing particle area fraction. The relative increase of the strain hardening parameter with increasing Weissenberg numbers is greatly reduced for larger particle area fraction. The predicted reduction of strain hardening agrees with experimental evidence.