Experimental measurements of the normal stresses in sheared Stokesian suspensions

Abstract

We present experimental measurements of the normal stresses in sheared Stokesian suspensions. Though the suspending fluid is Newtonian, dispersing rigid non-Brownian particles in it yields a suspension that is non-Newtonian, as it exhibits normal stress differences and an excess isotropic pressure in viscometric flows. At small to moderate concentrations, the normal stresses are very small in magnitude, and hence difficult to measure. This difficulty is compounded by the presence of noise due to unavoidable experimental artifacts. Owing to these limitations, most measurements reported earlier were carried out at relatively high particle concentrations, and some at shear rates large enough that the effects of particle and fluid inertia may have been significant. In our study, we have used a novel technique to measure the small stress levels. This was achieved by applying a sinusoidally varying shear rate with a fixed (low) frequency superimposed on a constant shear rate, and using a lock-in amplifier to measure the Fourier component of the same frequency in the stress signal. We have measured normal stresses in cylindrical-Couette and parallel-plate geometries, and combined these measurements to determine the two normal stress differences for particle volume fractions in the range 0.3–0.45. While the normal stresses are very small at low concentrations, they rise rapidly with increasing concentration. The normal stresses vary linearly with the magnitude of the shear rate, and are independent of its sign. In contrast to polymeric solutions, both normal stress differences are negative, and the first normal stress difference is significantly smaller in magnitude. We compare our data with the results of earlier studies, and observe good agreement.