Viscoelastic properties of suspensions of noncolloidal hard spheres in a molten polymer

We report an experimental study on suspensions of solid particles in a viscoelastic polymer matrix. A commercial entangled poly(⁠$ε$-caprolactone) was used as the suspending fluid. Noncolloidal solid spheres (diameter = 15 μm) made of polymethylmethacrylate were dispersed in the polymer via a solvent casting method. The volume fraction of the spheres was varied from 5% to 30%, thus allowing to explore both dilute and concentrated regimes. Electron scanning microscopy demonstrated homogeneous dispersion of the spheres in the matrix. We measured the rheological properties of the suspensions both in linear and nonlinear regimes with both dynamic and transient tests. The experimental results demonstrate the reinforcement effect of the particles. Both viscous and elastic moduli increase as the concentration of the particles is increased. The results show good agreement with available theories, simulations, and previous experimental data. In particular, the second order parameter of the quadratic equation that describes the dependence of the shear viscosity of the suspension upon the volume fraction of particles is in agreement with the predicted value found by Batchelor [G. K. Batchelor and J. T. Green, “The hydrodynamic interaction of two small freely-moving spheres in a linear flow field,” J. Fluid Mech. 56, 375–400 (1972); G. K. Batchelor and J. T. Green, “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech. 56, 401–427 (1972); and G. K. Batchelor, “The effect of Brownian motion on the bulk stress in a suspension of spherical particles,” J. Fluid Mech. 83, 97–117 (1977)]. We probe experimentally that the linear rheological behavior of suspensions of particles in viscoelastic fluids is the same as for Newtonian fluids.