Dear Student,
Hydrometallurgy is one of the methods for such separation. It is divided into 3 segments
1. Leaching
2. Concentration and purification of solution
3. Recovery of metal/ metal compound
The third step can be done by electrolysis or precipitation.
Most recently, David Clarke and William Bonificio devised a new method to separate rare earth metals by using bacteria filters and solutions with pH around 3.
Regards