Apparatus is provided featuring a first and second cells. The first cell receives an ore slurry having mineral particles of interest, receives unexpanded polymer microspheres comprising a surface having mineral collector chemistry attached thereto with molecules for attaching the mineral particles of interest, causes the unexpanded polymer microspheres to expand substantially in volume into expanded polymer microspheres having a substantially increased sphere surface area, and provides an expanded polymer microsphere foam layer comprising the expanded polymer microspheres with attached mineral particles of interest. The second cell receives the expanded polymer microsphere foam layer, and causes the expanded polymer microspheres to collapse substantially in volume into collapsed polymer microspheres having a substantially reduced sphere surface area that results in a mechanical shearing off of the attached mineral particles of interest. The second cell may also provide a mineral concentrate output having the mineral particles of interest.