Entrapment efficiencies of hydrodynamic boundary layers on rising bubbles

Hydrodynamic Boundary Layers at Solid Wall—A Tool for Separation of Fine Solids

A theoretical study is performed about the hydrodynamic interaction of fine species entrapped in the boundary layer (BL) at solid wall (plate). The key starting point is the analysis of the disturbance introduced by solid spheres in the background fluid flow. For a neutrally buoyant entity, the type of interaction is determined by the size of the spheres as compared to the thickness of the BL region. The result is granulometric separation of the solids inside the BL domain at the wall. The most important result in view of potential applications concerns the so-called small particles Rp < L/ReL5/4 (ReL is the Reynolds number of the background flow and Rp is the radius of the entrapped sphere). In the case of non-neutrally buoyant particles, gravity interferes with the separation effect. Important factor in this case is the relative density of the solid species as compared to this of the fluid. In view of further practical uses, particles within the range of Δρ/ρ < Fr2/ReL1/2 (Fr is Froude number and Δρ/ρ is the relative density of the entrapped solids) are systematically studied. The trajectories inside the BL region of the captured species are calculated. The obtained data show that there are preferred regions along the wall where the fine solids are detained. The results are important for the assessment of the general efficiency of entrapment and segregation of fine species in the vicinity of solid walls and have high potential for further design of industrial separation processes.