Defining an operational selectivity window for rare-earth flotation using a Box–Behnken design

Rare-earth flotation in naturally occurring complex ores is governed by mineralogical heterogeneity, incomplete liberation, dissolved species, and dynamically evolving surface conditions, making single-point optimization of limited process relevance. In this study, an operational selectivity window was defined for a complex bastnaesite ore (Dong Pao deposit, Vietnam) using a design-of-experiments framework. A Box–Behnken design quantified the interactive effects of pH, hydroxamic acid collector dosage, and temperature on total rare earth oxide (TREO) grade and recovery. Response surface models revealed nonlinear interactions and identified a favorable operational selectivity window at neutral pH (pH 7–8) and moderate collector dosage. To complement the identified operational selectivity window with an independent system-level indicator, zeta potential measurements were performed for the bulk feed across the investigated pH range and for froth concentrate and tailings obtained under the selected operating conditions, revealing distinct surface-state differentiation between floated and non-floated fractions. Validation flotation tests within the operational selectivity window produced a concentrate containing 49.7% TREO at 87.8% overall recovery. These results demonstrate that integrating response-surface modeling, circuit-level validation, product mineralogical confirmation, and system-level electrokinetic differentiation provides a reproducible and process-relevant route for defining an operational selectivity window in naturally occurring complex rare-earth ores, rather than relying solely on single-point optimization.