This paper demonstrates the effects of both collector surface coverage and surface roughness on the work of particle-bubble adhesion and the probability of particle detachment from an air bubble. The work of adhesion and the probability of particle-bubble detachment change as a result of either surface coverage fraction or roughness ratio change or their combination. A modified Yoon-Luttrel model for a flotation rate constant has been introduced with respect to surface heterogeneity and roughness. The work of particle-bubble adhesion is calculated using variable surface coverage of collector on mineral surface and its roughness ratio and the probability of particle detachment from the air bubble has been estimated. These simulations have been made for galena and fluorite particles. (C) 2016 Elsevier B.V. All rights reserved.