Dynamic interactions of fine solids with boundary-layer flows, formed on different interfaces, are studied. The procedure for the mathematical modeling of the perturbation, that an individual solid sphere creates in the background field, is reviewed. It is established that the tangential mobilities of the interfaces, where these layers are formed, play an important role in the interactions. So, two major cases are particularly specified: a rising bubble and a solid wall. Depending on the type of the perturbation, the particles may be divided into three major groups: small, medium-sized and large. The first group induces a purely viscous transverse disturbance in the outer stream, the second -- a prevailing viscous perturbation, and with larger solids a gradual transfer towards predominantly longitudinal inertial interaction is observed. An important moment in the analysis is the possibility this classification of the particles to be presented via general criteria, containing only parameters of the background flow. The basic result is that small and medium-sized particles are usually entrapped inside the boundary-layer regions. The presence of one particle inside the layer retards the background flow. Therefore, if a second solid enters this already slower flow region, it is retarded additionally and the tendency for its detention inside the boundary layer is stronger, etc. The proposed model investigation gives a concise explanation for the observed entrapment of fine solids in many flotation and separation processes. It also offers an additional clarification for the role of the tangential sliding and normal approach of the particle in the elementary act of the flotation processes.