Maximum bubble loads: Experimental measurement vs. analytical estimation P.M. Gallegos-Acevedo * , R. Pe´rez-Garibay, A. Uribe-Salas CINVESTAV-IPN (Unidad Saltillo), Carr. Saltillo-Monterrey KM 13, Ramos Arizpe, Coahuila, CP 25000, Me´xico Received 26 January 2005; accepted 4 April 2005 Available online 31 May 2005 Abstract This paper presents an experimental technique to measure maximum bubble loads, which are then compared with geometrical model estimations. The geometrical models studied assume that a particle monolayer, having a square arrangement, covers the entire bubble surface. Comparison of the experimental and analytical results gave a fairly high statistical correlation (R 2 = 0.89), when a shape factor was used for particle volume estimation (k = 0.32–0.41; [Kelly, E.G., Spottiswood, D.J. Introduction to Mineral Processing, John Wiley & Sons, 1982, p. 491]). This supports the applicability of geometrical models for maximum bubble load estimation. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Froth flotation; Mineralized bubbles; Carrying capacity 1. Introduction One objective of some researchers interested in froth flotation is mathematical modeling of the mass flow rate of solids in the concentrate. For others, these models are important for optimizing and evaluating flotation pro- cess performance. However, these models must previ- ously be validated, by comparison with experimental results reported by reliable techniques. For this reason, the first part of this paper describes the experimental methodology used to measure maximum bubble loads, and the second part compares the analytical predictions against the experimental measurements. This work con- tributes to the study of bubble loading, and is the previ- ous stage to modeling the concentrate solids mass flow. 2. Background Some authors have approached the study of maxi- mum bubble loads through statistical correlations, such as neural networks (Gupta et al., 1999), while other have used semiempirical models based on physical rela- tionships or practical knowledge of the phenomenon (Espinosa-Gomez et al., 1988). Only few researchers have reported work on the analytical modeling of bub- ble loading (Vera et al., 2002; Zheng et al., 2004; Zheng and Knopjes, 2004). According to these reports, the bubble diameter, particle density, particle diameter, par- ticle shape, and the geometrical particle arrangement are important variables for bubble load estimation. A commonly used technique to measure bubble diameter is photography (Chen et al., 2001; Grau and Heiskanen, 2002; Ata et al., 2003; Hernandez-Aguilar et al., 2004). In these papers, a common characteristic of the experimental set-up is the presence of a flat sec- tion in order to accurately visualize the bubbles and to avoid image distortion. 0892-6875/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2005.04.002 * Corresponding author. Tel.: +52 844 438 9646; fax: +52 844 438 9610 E-mail address: patricia.gallegos@cinvestav.edu.mx (P.M. Gallegos- Acevedo). This article is also available online at: www.elsevier.com/locate/mineng Minerals Engineering 19 (2006) 12–18