Falling ball method for determining zero shear and shear-dependent viscosity of polymeric systems: Solutions,melts, and composites

The falling ball method (FBM) is one of the well-established techniques for measuring the viscosity of Newtonian liquids at the room as well as at elevated temperatures and pressures. Owing to its simplicity and low cost, the possibility of extending its range of application to non-Newtonian systems including virgin and filled polymer melts, composites, polymer-solutions, and so forth, is explored here, In this work, theoretical results for the flow of power-law fluids past a sphere have been used to extract the values of the zero-shear viscosity and shear-dependent viscosity in the low-shear rate limit. The theoretical scheme outlined here has been validated by presenting comparisons with experimental results for scores of polymer solutions for which both falling sphere and rheological data are available in the literature. Indeed, the good correspondence obtained between these two independent data is encouraging and it is thus possible to use the FBM for shear-thinning systems when the resulting Reynolds numbers are such that the flow is viscosity-dominated, and the inertial effects are negligible. This implies that the Reynolds number should be ≤ ~1 for shear-thinning fluids and ≤ ~10⁻⁵ for shear-thickening fluids.