A numerical extension of the "smooth profile method" is presently suggested to simulate the attachment of a colloidal particle to the surface of an immersed bubble. In this approach, the two fluid-particle boundaries and the fluidic boundary are replaced with diffuse interfaces. The method is tested under various capillary numbers. Upon attachment to a stable bubble, it is found that the method is capable of reproducing the three microprocesses associated with the particle attachment. The change in the trajectory as the particle approaches the fluidic interface, the collision process, and the sliding down the bubble surface are all captured. Potential application of the present method shows great promise in the field of froth flotation, where the capture of hydrophobic particles by rising bubbles is of primary importance. C 2016 Author(s).