Effective static and high-frequency viscosities of concentrated suspensions of soft particles

We obtain an analytic expression that allows to determine the static η and high-frequency η(∞) viscosities as function of the volume fraction φ of a concentrated suspension of soft spherical particles in a liquid of viscosity η(0). The particles consist of a hard core of radius a covered by a porous layer of thickness d. Suspensions of hard spheres and homogeneous porous particles are limiting cases of the model. The proposed expression incorporates the results for the intrinsic viscosity obtained on the basis of a cell model [H. Ohshima, Langmuir 26, 6287 (2010)] into a recently obtained relation for the effective viscosity of concentrated colloidal suspensions [C. I. Mendoza and I. Santamaría-Holek, J. Chem. Phys. 130, 044904 (2009); J. Colloid. Interface Sci. 346, 118 (2010)]. In this model, the correlations between the particles due to crowding effects are introduced through an effective volume fraction φ(eff) which is then used as integration variable in a differential effective medium procedure. The final expression is simple, accurate, and allows to collapse all the data in a universal master curve that is independent of the parameters characterizing the system. The only difference between the static and high-frequency cases is that in the later case φ(eff) also incorporates hydrodynamic interactions arising from the so-called relaxation term. We have tested the accuracy of our model comparing with experimental results for spherical polymeric brushes and simulations for the high-frequency viscosity of homogeneous porous particles. In all cases the agreement with the data is extremely good.