Different contact positions were selected by gradually increasing the offset distance from the vertical axis of the bubble. Three micrometer glass beads with varying hydrophobicities were adhered to the end of the force sensor, and an air bubble with a diameter of 950 μm was fixed at the bottom of the hydrophobic quartz cell. In this case, gas-liquid meniscus deformation during detachment is no longer always symmetrical. In this study, vertical adhesion force between particle and different positions on a bubble surface were measured using a micro-mechanical testing machine (MMTM) equipped with a single-axis capacitive micro-force sensor. However, the above works mainly focus on quantification of detachment (adhesion) forces based on symmetrical gas-liquid meniscus deformation, while forces with an asymmetric meniscus have been less investigated. With the invention of atomic force microscopy (AFM), it has become a universal approach to measure the interaction forces between micrometer-sized particles and bubbles (Butt, 1994, Xing et al., 2018, Ally et al., 2010, Knüpfer et al., 2017). (Feng and Nguyen, 2016, Feng and Nguyen, 2016). Recently, an analytical force balance was also used to measure detachment forces by Sherman et al. The oscillating bubble method was further used by other researchers to explore the effects of surface hydrophobicity, shape, and roughness on detachment behavior (Xu et al., 2011, Zhang et al., 2019, Xing et al., 2020). Holtham and Cheng (Holtham and Cheng, 1991) applied an oscillating bubble method to predict detachment forces based on Newton’s second law. (Schulze et al., 1989) used a centrifugal immersion method to determine the detachment force required for removal of a particle from a liquid interface. It should be noted that quantification of detachment force between bubble and particle is a primary task for validating the robustness of the theoretical model. Schulze (Wang et al., 2017) further developed Nutt’s theory by considering the kinetic energy of bubble-particle aggregates under turbulence. Historically, Nutt (Nutt, 1960) first analyzed the force required to detach a particle from a fluid interface. Among these, force balance analysis has always been of particular interest since the early days of flotation. Several theoretical models based on force balance, energy balance, and maximum floatable particle size have been successively proposed (Nguyen and Schulze, 2004, Wang et al., 2016, Ralston et al., 1999). Understanding the underlying mechanism of bubble-particle detachment is a prerequisite for achieving enhanced coarse particle flotation hence, it has received wide attention in recent years (Wang et al., 2016, Ralston et al., 1999, Nutt, 1960, Schulze, 1977). In contrast, the presence of an upper size limit for flotation is attributed to high probability of detachment caused by turbulence in pulp (Nguyen and Schulze, 2004, Wang et al., 2016, Ralston et al., 1999). To date, it has been well-recognized that decreased flotation recovery of micro-fine particles is mainly due to the low collision probability of bubbles and particles. The spring constants at different positions on the bubble surface were found to decrease with increasing offset distance, which were consistent with the variations in vertical adhesion force observed.įlotation is widely used to separate valuable minerals from ore using air bubbles, which is particularly effective in the narrow size range of approximately 45–250 μm, while out of this range recovery drops dramatically (Xing et al., 2017, Mankosa et al., 2018). ![]() Additionally, a linear region in the retraction force curves was always observed, illustrating that the bubble behaved as a Hooke’s spring under a vertical force. The decrease in the vertical component of the normal capillary force at the contact point might be the main reason for the decreased vertical adhesion force. The vertical adhesion force always decreased with increasing offset distance, regardless of particle hydrophobicity. The results showed that the back-calculated advancing contact angles of the hydrophilic, medium hydrophobic, and highly hydrophobic particles were 45, 86, and 124°, respectively. ![]() Three micrometer glass beads with varying hydrophobicities (hydrophilic, medium hydrophobic, and highly hydrophobic) were adhered to the end of the force sensor, and an air bubble with a diameter of 950 μm was fixed at the bottom of the hydrophobic quartz cell. In this study, vertical adhesion force between particle and different positions on a bubble surface were measured using a micro-mechanical testing machine (MMTM). Bubble-particle detachment is the key sub-process for determining the upper size limit of flotation.
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