Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices

Abstract

We present the results of measuring the three viscometric functions [the relative viscosity ηr, and the first (N1) and second (N2) normal stress differences] for nominally monosize sphere suspensions in a silicone fluid, which is nominally Newtonian. The measurements of ηr and N1−N2 were made with a parallel-plate rheometer, while we used the open semicircular trough method to give N2 directly. With the trough method measurements of N2 could be made down to a 10% concentration (φ=0.1); measurements were continued up to 45% concentration. The trough surface shows visually that N2 is directly proportional to the shear stress τ, and the measurements of N2 agree quite well with the results of Zarraga et al. [J. Rheol. 44, 185–220 (2000)] in the range where concentrations overlap (0.3–0.45) and with those of later investigators. The results for N1 show greater scatter. In the range 0.1≤φ≤0.45, our best estimate of N2/τ is −4.4φ3 and that of N1/τ is −0.8φ3. Hence, the magnitude of N2 is much greater than that o...