Society of Rheology through the American Institute of Physics
Journal of Rheology vol:57 issue:1 pages:197-221
In this paper we present an analytical solution of Reynolds’ equation for the hydrodynamic lubrication flow in a parallel plate-on-annulus configuration of a conventional rotational rheometer. In this triborheometrical configuration originally proposed by Kavehpour and McKinley (Tribology Letters 17, 327 (2004)) the shearing surfaces are pushed together by an externally applied normal force. Our solution predicts quantitatively how lubrication forces are enlarging the gap h between the surfaces with increasing angular velocity Ω, depending solely on the unavoidable misalignment α of the surfaces. The predicted gap evolution as well as the predicted scaling of the shear stresses σ21 ~ Ω2/3 for the hydrodynamic flow regime for Newtonian fluids are experimentally verified with PDMS melts of different viscosities. The analysis is extended to power-law fluids, and the consistency of theoretical predictions and experimental observation was shown for a strongly shear-thinning PIB in pristane solution. Finally, it is shown that for a known misalignment α of the triborheometrical configuration the setup can be used to determine the high shear viscosity of an unknown sample, in the current setup up to shear rates of 10^5 s-1.