A novel rheometer plate was used to measure radial pressure profiles during cone-and-plate and parallel-plate shearing flows of a concentrated colloidal dispersion of polymethyl methacryalate spheres suspended in dioctyl phthalate. There is a long history of using suspensions of this type as a model rheological system. The measured pressure profile can be used to calculate N1 and N2, and also provides a check on the flow field in the rheometer. At shear rates just below onset of shear thickening, our measurements show that N1 is positive as predicted by Stokesian dynamics simulations of model Brownian hard spheres, but we are unable to determine the sign of N2. After the onset of thickening, we find that in both flow geometries the pressure increases sharply with radial position. This is in striking contrast to the pressure profiles ordinarily observed for viscoelastic liquids with the exception of certain liquid crystal polymers, for which the pressure decreases with radial position. Under these conditions, the apparent values of N1 and N2 are both negative with N2 N1, as predicted by the Stokesian dynamics simulations. However, the flow in the cone-and-plate rheometer may not be viscometric after the onset of shear thickening.
Lee, M.; Alcoutlabi, Mataz; Magda, J. J.; Dibble, C.; Solomon, M. J.; Shi, X.; and McKenna, G. B., "The effect of the shear-thickening transition of model colloidal spheres on the sign of N1 and on the radial pressure profile in torsional shear flows" (2006). Mechanical Engineering Faculty Publications and Presentations. 10.
Journal of Rheology