Despite the relevance of the Kelvin force in many physical and electrochemical systems involving magnetic species, the underlying convective flows are scarcely understood. For that purpose, we simulate a simplified rare-earth system in the presence of competing Kelvin and gravity forces. The results are experimentally validated using interferometry and microscopic particle image velocimetry. Based on the excellent agreement of numerical and experimental results, the underlying mechanism of ions' magnetic separation can be explained, which paves the way for a prospective application in rare-earth beneficiation.