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 of N1. Measurement uncertainties are given in the text—they depend on φ. We have also compared the new experiments with two sets of numerical simulations. There is considerable divergence, which remains to be explained, between some of the simulations and the experiments. However, agreement between experiment and some of the simulations of Bertevas et al. [Rheol. Acta 49, 53–73 (2010)] is reasonable.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...