Chemical Engineering and Processing 49 (2010) 622–627 Contents lists available at ScienceDirect Chemical Engineering and Processing: Process Intensiﬁcation journal homepage: www.elsevier.com/locate/cep Bubble–particle collision and attachment probability on ﬁne particles ﬂotation B. Shahbazi a,∗ , B. Rezai b , S.M. Javad Koleini c a Mining Department, Research and Science Branch, Islamic Azad University, Tehran, Iran b Amirkabir University of Technology, Tehran, Iran c Tarbiat Modares University, Tehran, Iran article info Article history: Received 11 February 2009 Received in revised form 4 April 2010 Accepted 23 April 2010 Available online 20 May 2010 Keywords: Flotation Fine particles Hydrodynamic Collision Attachment abstract Particle size is an important parameter in ﬂotation and has been the focus of ﬂotation research for decades. The difﬁculty in ﬂoating ﬁne particles is attributed to the low probability of bubble–particle collision. In this research, the inﬂuence of hydrodynamic parameters on collision probability of ﬁne particles was investigated. Collision probability was obtained using Stokes, intermediate I and intermediate II and potential equations. Maximum collision probability was 5.65% obtained with impeller speed of 1100 rpm, air ﬂow rate of 30 l/h and particle size of 50 m. Also, attachment probability under Stokes ﬂow, turbulent and potential ﬂow conditions was calculated 100, 99.49 and 81.87% respectively. Maximum attachment probability was obtained with impeller speed of 700 rpm, contact angle of 90 ◦ , particle size of 20 m and air ﬂow rate of 15 l/h. Collision angles were obtained between 60.71 ◦ and 60.18 ◦ and attachment angles were obtained between 9.15 ◦ and 59.83 ◦ . © 2010 Elsevier B.V. All rights reserved. 1. Introduction For ﬂotation occurring under quiescent conditions, one can calculate the probability of collision using stream functions. The stream functions used by earlier workers are applicable for bubbles that are either too large or too small [1], while those developed in recent years are useful for ﬂotation size bubbles [2,3]. However, most of the ﬂotation machines are operated under intensely agi- tated conditions, which make it difﬁcult to use the interceptional collision models based on stream functions. Under such conditions, models based on microturbulence may be more useful [4]. Froth ﬂotation is widely used for separating different minerals from each other. However, its inﬂuence is limited to a relatively narrow particle size range of 10–100 m [5–7]. Although the effect of particle size on ﬂotation performance has been widely studied to date [5,6,8–10], and many important physico-chemical factors related to particle size have been identiﬁed, the net effect of these factors are very difﬁcult to predict. For example, in particle–bubble interaction, particle size is known to play a critical role in the prob- ability of particles colliding with bubbles, attachment of particles to bubbles after collision, as well as remaining attached in the pulp phase [11,12]. Fine particles typically show slow recovery rates, owing to decreased particle–bubble collisions, and are prone to entrain- ment. Moreover, very small particles tend to have large speciﬁc ∗ Corresponding author. Tel.: +98 2182883516; fax: +98 2182884324. E-mail address: bzshahbazi@yahoo.com (B. Shahbazi). areas, which can lead to excessive adsorption of reagents, and other effects associated with chemically active particles. These factors can have a considerable impact on grades and recoveries, depending on the dominant effects in operation [13,14]. Efﬁciency of the bubble–particle stability depends on the particle size, particle hydrophobicity and external detaching forces. Even in the ﬂotation of ﬁne particles, the bubble–particle detachment can signiﬁcantly inﬂuence the kinetics of ﬂotation taking place in mechanical cells by intensive turbulent agitation [15]. For these ﬁne particles, the bubble–particle detachment is often neglected. In this research a theoretical analysis of ﬁne particle ﬂota- tion was investigated based on experimental measurement of bubble size and raise velocity. Using Stokes equation collision probability was obtained very low while using potential equa- tion collision probability was exaggerated. According to this study, for ﬁne particles, best equation for calculating collision probabil- ity are intermediate equations cause to collision probability by these equations can be estimated between Stokes and potential equations. Also, for ﬁne particles with different air ﬂow rates and impeller speeds, collision angle was obtained between 63.18 ◦ and 60.71 ◦ . Furthermore, attachment probability of ﬁne particles was cal- culated under turbulent and Stokes conditions. Stokes equation is more useful for column ﬂotation and when the attachment proba- bility was calculated under Stokes ﬂow conditions, the probability was exaggerated. So, attachment probability was calculated under turbulent ﬂow conditions that is more suitable for mechanical ﬂota- tion. Finally, after calculating collision probability by intermediate I equation and attachment probability under turbulent ﬂow condi- 0255-2701/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2010.04.009