An edge finishing apparatus includes a surface, a fluid delivery device configured to deliver at least one magnetorheological polishing fluid (MPF) ribbon to the at least one well, at least one magnet placed adjacent to the surface to selectively apply a magnetic field in a vicinity of the surface, and at least one holder placed in opposing relation to the surface, the at least one holder being configured to support at least one article such that an edge of the at least one article can be selectively immersed in the MPF ribbon delivered to the at least one well.