Finely crushed and sized quartz particles were flotated both continuously and countercurrently with a bench-scale column notation cell. The particles mere not notable at pH 7 in the absence of the collector. The particles were flotated by making them hydrophobic with a typical, familiar, cationic surfactant, n-dodecyltrimethylammonium bromide, as a collector. The observed particle concentration profiles that formed along the column for varying collector concentrations were linearly correlated with the column height on a semilogarithmic scale. To simulate the aforementioned particle concentration profiles and the particle removabilities, we proposed a set of free settling and sedimentation model equations that involve a collision and attachment probability or a collection probability between a rising bubble and a particle. A traditional stagewise model was employed to solve the aforementioned equations, and their solutions were tested to determine whether or not they can simulate the observed profiles and removabilities. The results indicate that the mathematical model equations supported the observed linear profiles and the removabilities, which strongly depended on the collector concentrations and were compatible with those observed for the Denver-type flotation machine. From the observed rate constant at a high collector concentration, the collection probability value was deduced and its magnitude could be supported by a theoretical model proposed by other investigators.