The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids

The total stress of a concentrated suspension of noncolloidal spheres in a Newtonian fluid was characterized by independent measurements in viscometric flows. Using a suspension balance formulation, the normal stress in the vorticity direction (Sigma(33)) for a suspension undergoing simple shear was extracted from Acrivos et al.'s [Int. J. Multiphase Flow 19, 797 (1993)] resuspension data in a Couette device. Employing a new correlation for the relative viscosity mu(r) which obeys the Einstein relation in the dilute limit while diverging at random close packing, it was found that Sigma(33)/tau (where tau is the magnitude of the shear stress) was a strong function of the solid volume fraction phi, scaling as phi(3)e(2.34 phi). The relative viscosity, measured in a parallel plate viscometer, was in good agreement with the proposed correlation, while the normal stress differences N-1 and N-2 for concentrated suspensions (phi = 0.30-0.55) were characterized using parallel plate and cone-and-plate geometries, as well as laser profilometry measurements of the suspension surface deflection in a rotating rod geometry. The normal stresses were proportional to the shear stress tau, and with beta = N-1/tau and delta = N-2/tau, the parameter combinations resulting from the three experimental geometries, beta- delta, beta, and delta+1/2 beta, were all seen to increase with phi according to the derived scaling phi(3)e(2.34 phi). Furthermore, the best-fit N-1 and N-2 values consistent with the set of experiments were both negative, with \N-2\ > \N-1\ at any given concentration and shear rate. Taken together, the results obtained allow a complete determination of the total stress of a sheared suspension and in particular enabled us to compute the shear-induced particle-phase pressure Pi, as defined in jeffrey et al. (C) 2000 The Society of Rheology. [S0148-6055(00)00402-8].