Effects of friction on the efficiency of open gradient magnetic separation in dry granular materials

Introduction. Magnetic separation is one of the most effective and widely used techniques for the purification and enrichment of materials. It plays a crucial role in mineral processing, recycling, and environmental applications, where the separation efficiency depends on both the magnetic field characteristics and the physical properties of the treated materials. Problem. A major limitation of existing studies is that the frictional drag force is often neglected in magnetic separation, although it can sometimes completely prevent the separation process. Goal. To estimate and experimentally verify the effect of frictional drag force on the performance and operational limits of open gradient magnetic separation (OGMS) under dry conditions. Methodology. An integrated analytical, numerical, and experimental approach was used. The granular medium was modeled as a complex fluid where friction acted as a drag force. The coupled magnetic and dynamic equations were solved using Finite Element (FE) – Runge–Kutta (RK4) methods, and results were validated experimentally with a permanent magnet drum separator. Results. To verify the obtained results experiments were carried out on samples of a mixture of sand and iron particles with different components sizes (iron particles and sand grains) in a permanent magnet drum separator. Limited to fine granulometries, the experiments carried out confirmed the results obtained theoretically. Scientific novelty. The study introduces a coupled FE–RK4 model that explicitly integrates the frictional drag force into the particle dynamic equations, enabling accurate prediction of trajectories and operational thresholds. This provides a realistic description of dry magnetic separation behavior, which has been largely overlooked in previous models of dry magnetic separation. Practical value. The findings provide engineers with a framework for optimizing dry OGMS performance. The developed model defines the threshold separating efficient from inhibited particle capture and clarifies how frictional drag controls the operational range of magnetic separators. These insights support improved design, process adjustment, and greater reliability in dry magnetic separation. References 41, tables 7, figures 12.