A semi-empirical approach to evaluating rise time of power-law fluids in a capillary rheometer

摘要

This paper reports an explicit semi-empirical approach to evaluating the rise time of power-law fluids in a capillary rheometer. The semi-empirical evaluation is accomplished from the combination of a linear frequency model and experimental data (Hatzikiriakos and Dealy [3]). The linear frequency model is transformed from a unidimensional transient model we develop. The transient model, which is calculated using the method of characteristics and the finite difference method, and the semi-empirical approach, are validated against the experimental data. The results show that the consistency found between numerical transient calculations and experimental results justifies the application of the proposed transient model. The semi-empirical approach predicts the rise time comprehensively and accurately in the range of ((1/n + 3)/4)(n)gamma(n-1)(0), from 0.03 to 0.35, where gamma (0) is the apparent shear rate. We also found a curve f(n) that divides a rise time variation with power-law index n into two zones at a low shear rate on the gamma (0) - n plane. The rise time monotonically increases with an increasing n when the shear rate is above the curve (gamma (0) f (n)); when the shear rate is below the curve, it monotonically decreases with an increasing n. These equations are also suitable for Newtonian fluids. The semi empirical approach can be used for estimation of the rise time in rheometer-like structures, while the transient model can be used for detailed analysis of power-law fluids in circular pipes. The evaluation of other non Newtonian fluids and the influence of transitional and turbulent flows, slip walls, and ultra-high shear rates on the rise time and pressure transient remain to be investigated in future work.