An acoustic technique for measurement of bubble solids mass loading – (a) Fundamental study of single bubble Wen Zhang ⇑ , Steven J. Spencer, Peter Coghill Lucas Heights Research Laboratory, CSIRO Process Science and Engineering, Locked Bag 2005, Kirrawee, New South Wales 2232, Australia article info Article history: Available online 6 March 2012 Keywords: Flotation bubbles On-line analysis Process instrumentation abstract This paper investigates a promising acoustic emission (AE) technique for estimating solids mass loading on pulp bubbles, with potential for on-line monitoring of attached solids in industrial flotation cells. It is observed that the coating of solids on a bubble surface results in a decrease in the fundamental (Minna- ert) AE resonance frequency. Analytical models are derived to relate the resonance frequency of a loaded bubble to its size, attached solids mass loading and geometrical covering of particles. The AE resulting from induced pulsations of a solids loaded bubble is measured and linked with high-speed photographic recordings of the oscillations. These experiments have been performed for the attachment of a mono- layer, multilayer and cluster of particles onto a gas bubble. The efficacy of the monitoring approach for these types of solids loading is demonstrated and a comparison is made of the sophistication of modelling necessary for adequate prediction of attached solids mass loading. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Bubble solids loading (attachment) is one of the key processes related to flotation performance (Bradshaw and O’Connor, 1996; Ross, 1997). On-line measurement of solids mass loading on bub- bles in industry flotation cells is clearly highly desirable for process optimisation purposes. One approach reported in the literature is a device using the positive displacement principle to collect solids laden bubbles at different depths in the pulp phase of a flotation machine and accumulate them into a reservoir, allowing the solids load to be weighed (Dyer, 1995; Moys et al., 2010; Seaman et al., 2004). Reproducible bubble load measurements have been re- ported using this technique. However, the limitations of this instrument include a large sample mass (i.e., at least 200 g of solids (Bhondayi, 2010)) required for accurate estimation of solids loading and loss of attached fine particles with the displaced water during bubble bursting in the reservoir. Video image analysis and direct sampling of the froth surface have also been combined to measure the bubble solids loading in the froth phase (Barbian et al., 2007; Sadr-Kazemi and Cilliers, 2000; Ventura-Medina et al., 2004). This technique uses a micro- scope glass to sample the curved surface of a single bubble, with calculation of the bubble solids loading as the amount of solids on the slide over the surface area of the bubble. Under steady state conditions, this technique requires that the upper surface of the froth be video recorded for off-line image processing. In this paper, an acoustic emission technique is investigated for measurement of pulp bubble solids mass loading. The strong acoustic resonance and scattering properties associated with a bubble immersed in a liquid make acoustic techniques potentially useful for estimation of pulp bubble properties and dynamics. The acoustic resonance frequency for a freely oscillating bubble may be defined as (Minnaert, 1993) f 0 ¼ 1 2pR 0 ffiffiffiffiffiffiffiffiffiffiffi 3jP 0 q l s : ð1Þ Here f 0 is the fundamental resonance frequency, R 0 is the bubble equilibrium radius, j is the polytropic index, P 0 is the absolute liquid pressure, and q l is the liquid density. Thus, the bubble equi- librium radius can be estimated from knowledge of the acoustic res- onance frequency. Solids attachment on a bubble surface alters bubble dynamics. As intuitively expected, the added mass causes a decrease in the acoustic resonance frequency associated with the original un- loaded bubble. In this paper, theoretical formulae are derived to re- late bubble attached mass loading and distribution to acoustic resonance frequency. The resonance frequency of the attached sol- ids loaded bubble is found to be a function of the unloaded bubble resonance frequency, the bubble equilibrium radius, the solids mass loading, the thickness of the attached solid–liquid agglomer- ate layer and the solids coverage angle. The resonance of a particle- laden bubble is measured to validate the model, where active acoustic techniques are applied to force the bubble into linear oscillation. A variety of solids attachment geometries on the gas 0892-6875/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2012.02.007 ⇑ Corresponding author. Tel.: +61 2 9710 6744; fax: +61 2 9710 6789. E-mail address: W.Zhang@csiro.au (W. Zhang). Minerals Engineering 36–38 (2012) 45–52 Contents lists available at SciVerse ScienceDirect Minerals Engineering journal homepage: www.elsevier.com/locate/mineng