A method for determining the rheological properties of viscoplastic fluids using a rectangular die

This study introduces a method for determining the rheological parameters of viscoplastic fluids with the use of rectangular dies. The relationship between the wall shear rate and the wall shear stress is investigated for the Casson, Herschel-Bulkley, and Robertson-Stiff rheological models, using two geometric constants for non-circular dies with a regular cross-section. Then, the rheological behavior and parameters of a collagen material were examined by an analytical method and by the proposed approximate method, using experimental data obtained by a slit viscometer and a rectangular die. The yield stress value of the collagen was determined employing the pressure relaxation method. The values were 2940 (+/- 209) Pa from the slit viscometer and 3100 Pa (+/- 200) Pa from the rectangular die. The rheological parameters of collagen were then obtained using the analytical method and the proposed approximate methods for Casson, Herschel-Bulkley, and Robertson-Stiff rheological models. It was shown that the wall shear rate and the wall shear stress values of the analytical method and the proposed method are in good agreement. It was found that the Herschel-Bulkley and Robertson-Stiff models successfully fitted the wall shear rate-wall shear stress curves with a coefficient of determination equal to or greater than 0.97, and the evaluated consistency values were 165 (+/- 71) Pa.sn for the Herschel-Bulkley model and 947 (+/- 225) Pa.sn for the Robertson-Stiff model, and the flow index values were found to be 0.50 (+/- 0.06) for the HerschelBulkley model and 0.32 (+/- 0.03) for the Robertson-Stiff model. However, it was shown that the Casson model is not suitable for describing the rheological characteristic of collagen material. Experimentally obtained parameters for the Herschel-Bulkley model were validated with the use of simulations, and it was found that the numerically and experimentally evaluated results showed good agreement. The maximum deviation was found to be less than 12%.