A rheological law to describe powder agitation in a lab-scale paddle mixer: Shear band observation and dimensional analysis

This work adopts an in-system rheological approach to analyse powder flow behaviour in dense flows under mechanical agitation. For this purpose, an empirical law has been developed to assess powder rheology within a laboratory mixing setup, focusing on interactions between the paddles and the powder bed in dense flow. This model, is an empirical law, based on the μ(I)-rheology-like framework derived from dimensional analysis and shear band visualization. It reveals good predictive capabilities for powders of similar particle shapes but different sizes across various filling ratios. This approach addresses challenges in measuring complex powder parameters, such as the effective friction coefficient ${\mu }_{\mathrm{eff}}$, establishing a practical and easily applicable model that facilitates the scaling up of mixing processes and allows for better anticipation of forces exerted on the paddles. Comparisons with Hatano's equation showed a good fit with the rheological framework, particularly for deep powder beds. Better evaluation of the shear band width and reconsideration of normal stress assumptions may be the way forward to improve the accuracy of this μ(I)-rheology.