An Approximate Analytical Expression for the Probability of Attachment by Sliding

A mathematical model of continuous flotation deinking

“…For the same kind of intermediate flow over the bubble surface (see for example [6]) it follows from the work of Bloom and Heindel [5] that…”

“…For the probability (P c ) of collision and probability (P asl ) of adhesion by sliding we use, in this paper, new results which were developed in [4] and [5] respectively for 280 F. Bloom flotation deinking conditions. Beginning with P c , if u p represents the particle velocity, and Re p is the particle Reynolds number given by…”

Modeling local flotation frequency in a turbulent flow field

“…A completely different approach from the usual one described above, has been followed by these authors for the derivation of the attachment efficiency [16]. A detailed analysis of the forces governing the sliding process of a particle on the surface of a bubble was provided.…”

Movement of fine particles on an air bubble surface studied using high-speed video microscopy

“…The influence of the liquid velocity near the bubble surface on the sliding time and the bubble-particle attachment is now widely acknowledged. A simple stream function for intermediate Reynolds numbers was empirically developed by Yoon and Luttrell [12] and significantly simplifies the prediction of the particle sliding time [11,12]. The inertial effect on the particle sliding time was also investigated [7].…”

“…Since detailed knowledge of intermolecular and surface forces controlling bubble-particle attachment has been unavailable, the traditional modeling approach [5], based on the particle sliding time remains popular [6][7][8][9][10][11][12]. Sutherland [5] was the first who developed a contact time between a particle and a bubble during the sliding interaction and was able to determine the bubble-particle attachment efficiency as a function of the induction time, which is an integral measure of the physics and chemistry of the attachment process underlying the liquid film drainage and rupture and the motion of the three-phase contact line to form a stable contact.…”