Rheological characterization of carbonate sludge slurries (Part II): evidence of Herschel-Bulkley behavior

Abstract

The rheological characterization of carbonated sludge pulps is essential for the design and optimization of pipeline transport systems in the Cuban mining-metallurgical industry. Previous studies have classified these suspensions as Bingham plastics based on limited shear rate ranges (16 s⁻¹ – 300 s⁻¹). This research presents an updated rheological characterization using the Herschel–Bulkley model, which accounts  for nonlinear post-yield behavior over a broader shear rate spectrum (10 s⁻¹ –650 s⁻¹). Through an experimental analysis of 63 samples with solid concentrations (C) between 17 and 50 %, pH values ranging from 7,71 to 8,52, and polydispersity indices (s) from 0,713 to 0,985; it is demonstrated that the Herschel–Bulkley model provides a superior fit (R² > 0,99) compared to the Bingham model (R² ≤ 0,9823). The yield stress (τ₀) exhibits an exponential dependence on solid concentration with a critical transition around 30 %, while pH shows an asymptotic influence approaching the point of zero charge. From a practical standpoint, using the Bingham model overestimates the head loss by 13 % to 41 % (at 30 % and 50 % solids) relative to the Herschel–Bulkley model, which implies pump oversizing and higher-than-actual energy consumption. The developed empirical correlations [τ₀, K, n, μₐ = f (C, pH, s)] allow estimation of rheological parameters under typical operating conditions of the Comandante Pedro Sotto Alba Nickel Company with an error of < 4,4%.