On the calculation of the viscosity function through flows with non-uniform shear rate

CLAUDIO L. A. BERLI, JULIO A. DEIBER

Costa Verde, Rio de Janeiro, Brasil

Congreso; EMPROMER 2005; 2005

The determination of the viscosity function in conventional rheometry requires the knowledge of both the shear stress and the shear rate at one place in the rheometric cell. The calculation of these rheometric variables from experimental data is readily carried out in flows where the shear rate is uniform, such as in small-gap rotational rheometry, where the shear stress and the shear rate are directly obtained from the torque and the angular speed in the instrument, respectively. In contrast, mathematical difficulties arise when the shear rate is non-uniform in the cell, as in the cases of capillary and wide-gap rotational rheometries. The problem involves the inversion of an integral equation, the solution of which is not unique due to the scattering present in experimental data. Different proposals to handle this ill-posed problem can be found in the recent literature, apart from the classical Weissemberg-Rabinowitsch-Mooney procedure. In this work, we revise briefly the subject and discuss a method to process experimental data from non-uniform shear flows. The mathematical procedure involves the solution of the fluid dynamics in the rheometric cell, by using a suitable viscosity model for the fluid under study. In addition, a numerical algorithm was designed to identify the best set of model parameters representing the fluid. Results for typical non-Newtonian liquids studied in different cells are discussed. The procedure is also expected to be useful to evaluate the viscosity function in non-conventional rheometric cells that involve additional complexities in data treatment.