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Behaviour of a galena particle in a thin film, revisiting dippenaar
International Journal of Mineral Processing 131 (2014) 1–6
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
Behaviour of a galena particle in a thin film, revisiting dippenaar Gareth D.M. Morris ⁎, Jan J. Cilliers Rio Tinto Centre for Advanced Minerals Recovery, Department of Earth Science and Engineering, Imperial College London, London SW7 2AZ, United Kingdom
a r t i c l e
i n f o
Article history: Received 21 January 2014 Received in revised form 28 May 2014 Accepted 26 July 2014 Available online 12 August 2014 Keywords: Flotation Particle bridging Film bursting High speed photography Simulation
a b s t r a c t Advances in technology over the past 30 years have drastically increased the frame rate and resolution at which the dynamics of thin film rupture and particle interaction can be imaged. A high speed camera (Phantom V7.1) was used to capture the bridging and rupture of a thin capillary film containing a particle of galena, revisiting work first published by Dippenaar (Dippenaar, A. 1982. The destabilisation of froth by solids. I. The mechanism of film rupture. Int. J. Min. Process., 9, 1–14.). The images were then compared to rendered models generated from simulations of an orthorhombic particle and capillary film under the same conditions, using the Surface Evolver program. These two sets of data are then used to build a more detailed picture of the behaviour of particles with sharp edges and corners as they bridge both sides of a thin liquid film. It has been observed that the liquid–vapour interface is highly distorted around the particle and that under certain conditions it can appear that the particle is drawing the film together to failure, whereas, in fact the film is being forced together behind the particle. The film failure is then due to contact between the opposite liquid–vapour interfaces, not the bridging dewetting mechanism as postulated by Dippenaar (1982). © 2014 Elsevier B.V. All rights reserved.
1. Introduction The mechanism through which particles stabilise or destroy films in a flotation froth is difficult to identify due to both the size and speed at which the phenomena occur. The particle-film interaction at the point of film rupture is a hugely important part of a flotation froth’s evolution and has a major impact on its physical properties and rheology as well as the efficiency of the whole process. It has therefore been the focus of much research to aid in the development of bubble film stability models. This paper revisits work published by Dippenaar (1982) that investigated the behaviour of a single galena particle in a thin liquid film. By using powerful modern modelling and imaging techniques it is possible to gain further insight into the interaction between the particle and the film at the moment of rupture. Previous analyses of the particle–film interaction have focused on the simplified two-dimensional case (2D) using circular particles in a single layer in a film (Ali et al., 2000; Denkov et al., 1992) in which the particle will destroy the film if the contact angle is greater than 90°. Garrett (1979) proposed the bridging dewetting mechanism that causes the failure of the bubble film; however, this also assumed spherical particles, flotation froths contain particles with irregular shapes and asperities which can interfere with this mechanism and complicate their interaction with the film. It is currently computationally intractable to simulate anything but the simplest of particle shapes attached to a liquid–vapour interface. Morris et al. (2011a) used Surface Evolver (Brakke, 1992) to develop a ⁎ Corresponding author. E-mail address: [email protected] (G.D.M. Morris).
http://dx.doi.org/10.1016/j.minpro.2014.07.004 0301-7516/© 2014 Elsevier B.V. All rights reserved.
method of simulating orthorhombic particles in a thin liquid film which were used to identify the stable orientations of cubes (Morris et al., 2010) and oblongs (Morris et al., 2011b) and their effect on film stability. De Graaf et al. (2009) also developed a numerical technique based on triangular tessellation to identify the adsorption free energy landscape for spheroidal, cylindrical and ellipsoidal particles at liquid– vapour (LV) interface. Lewandowski et al. (2008) also used Surface Evolver to investigate the self ordering of micro-particles at a liquid vapour interface. It is therefore well established that the interplay between a particle's shape and contact angle can have a large effect on its behaviour in the LV interface. Whilst it is relatively easy to analyse the shape of the film surrounding spherical particles in an ordered arrangement, when orthorhombic ones are considered the complexity of the LV-interfaces topology greatly increases. The interaction between the particles and the point at which the film fails becomes much more difficult to identify. Dippenaar (1982) investigated this using high speed imaging of a single galena particle sitting in a thin film supported by a capillary. The two stable orientations for a cubic particle at contact angles between 45° and 90° were identified (diagonal and horizontal) using a 2D analytical method. Morris et al. (2010) has since used 3D numerical simulation to identify a third energetically stable orientation (rotated) for a cubic particle, all three are shown in Fig. 1. Dippenaar's analysis of the high speed footage showed that the particle would adopt either a diagonal or horizontal orientation in the film when it bridged only one LV interface. As the film thinned and the lower part of the particle came into contact with the opposite LV interface it would react differently depending on the orientation; if it was horizontal it would move off to the side of the film until it thinned enough to
2
G.D.M. Morris, J.J. Cilliers / International Journal of Mineral Processing 131 (2014) 1–6
Fig. 1. Stable orientations for an orthorhombic particle, A—rotated, B—diagonal, and C—horizontal.
rupture, but if it was diagonal it would either rotate to horizontal and behave as before or adopt a rotated orientation. When the particles adopted a rotated orientation the opposite sides of the LV interface would draw up the sides of the particle and rupture the film. This bridging dewetting phenomenon was proposed by Garrett (1979), but was developed with spherical particles where the film distortion around the particle is much less pronounced. The phenomenon of particles moving out of the centre of the film was also noted by Qu (2012) who observed hydrophobic coal particles being forced out of the centre of the film as it thinned, leaving an area of empty, thin film before rupture. The distortion of the film surrounding non-spherical particles can be quite severe, causing them to exhibit interesting packing phenomena. Botto et al. (2012)) whereby their contact angle and shape interact with the curvature of the LV interface to allow some control on their behaviour in the film. This interaction of non-spherical particles in a liquid film is beyond the scope of this paper; however, it will affect their packing arrangement and therefore the film loading and stability (Bournival and Ata, 2010; Morris et al., 2011c). It also highlights the rather extreme distortion that a LV interface can undergo when close to a particle. 2. Materials and methods
the camera was mounted on a sliding bed which was used to focus on the capillary film and particle along the Y-axis (this setup is shown in Fig. 2). For vertical filming the camera was mounted on a tripod and rotated down to image down the Z-axis, videoing from above the film (this setup is not shown in Fig. 2). Finally a Solarc GE ELSV-60 RVI Light Source was used to illuminate the area of interest. The whole setup for filming horizontally is shown in Fig. 2. 2.2. Procedure Liquid was drawn from the capillary, or injected into it, using a manually operated syringe. It was possible to accurately control the thickness of the film by monitoring it in the camera viewer. The film was thinned until the lower point of any attached particle was within 40 μm of the opposite LV interface. After this point the film was allowed to thin naturally due to evaporation whilst being filmed by the camera. The camera was mounted in one of two positions, horizontally or vertically. In the former, the film could be videoed from the side and the movement of the three point contact (TPC) over the particle surface captured accurately. In the latter, the exact point where the film ruptures can be identified, as well as the particle position at the point of film failure.
2.1. High speed photography rig 2.3. Materials The rig used to capture the videos of particle film bridging is shown in Fig. 2. It consists of a capillary holder (machined from Perspex) for the film mounted with control in 3 axes to position the area of interest in front of the camera. A Vision Research Phantom V7.1 (on loan from the EPSRC equipment loan pool) was used to capture the images and was mounted with a Canon EOS Macro Lens. For horizontal filming
The films in the capillary were made with de-ionised water and the galena particles were hand ground in a pestle and mortar with water. The freshly ground particles were then wet sized and mixed in a stirred solution of 100 ppm sodiumisobutylxanthate (SIBX) for 1 h after which they were washed several times with de-ionised water and stored in a
Fig. 2. The high speed rig used to capture the moment a film breaks with the particle in it. A—camera/lens, B—capillary/area of interest, and C—light source. X, Y and Z in the detail of the capillary holder show the axis used to discuss film shape and particle positions.
G.D.M. Morris, J.J. Cilliers / International Journal of Mineral Processing 131 (2014) 1–6
3
Fig. 3. The Surface Evolver model used to simulate film shape surrounding an orthorhombic particle.
clean beaker under de-ionised water. Samples were made and used fresh every day. Contact angle tests on a polished plate of galena treated in the same way showed contact angles of 80° ± 10°, providing a similar range to those used in Dippenaar's work (80° ± 8°).
The model was run for several capillary pressures corresponding to a film that was just touching both sides of the particle to one which has failed. Three particle positions (centre, 1.5rp and 3rp from the centre) and two orientations (horizontal and rotated) were also modelled. 3. Results and discussion
2.4. Surface Evolver model The Surface Evolver model used is based upon those previously described in Morris et al. (2011a,c). The particles used in the experiments were below 200 μm in length meaning the Bond number (Bo) was roughly 0.03 allowing gravity to be ignored. Dippenaar (1982) also reported that particles of galena up to this size did not pull any observable dimple in the LV interface. All length (L) and pressure (P) terms in the model have been non-dimensionalised using particle radius (rp) and surface tension of the water (γLV) as shown in Eqs. (1) and (2). The ⁎ denotes non-dimensionalisation of a parameter.
L ¼
P ¼
L rp
ð1Þ
Prp γ
ð2Þ
The model of the particle and film is constructed in Surface Evolver as shown in Fig. 3. The curvature of the two LV interfaces is controlled by altering the volume of gas for each volume associated with the LV interfaces; they are kept the same at all times. The particle position is user defined, as is the rotation of the particle. The ratio of the size of the particle and the diameter of the capillary was matched to the experimental conditions.
A series of films were taken of a single galena particle in the capillary, using the camera to film either side-on or vertically. Side on images allow comparison to Dippenaar's (1982) work, but the images from above allow the evaluation of more information about the physics of the film rupture. When a film bursts the initial hole that forms expands rapidly. The speed at which this rupture front expands was measured for three sets of experiments filmed from above. The radius of the rupture was measured using ImageJ and the diameter of the capillary used for scale (3 mm); an example set of images are shown in Fig. 4. The speed of the film rupture front for three cases is shown in Fig. 5 along with the radius of the ruptured hole, both as a function of time from the initial film failure. The speeds and distances were measured using video taken at 26,143 fps. There is a rapid drop off in the speed of the rupture front after the initial failure of the film but what should be noted is that in Dippenaar's paper a maximum film speed of 5000 fps was achieved and for the results that were analysed for the galena particles in a film the speed was only 1500 fps. Therefore, assuming that the first frame captured the very moment the film burst (best case scenario) the next frame would be at either 0.2 ms (5000 fps) or 0.66 ms (1500 fps) during which time the bursting front will have travelled roughly either 350 μm or 600 μm respectively, a distance greater than the particle sizes used in the experiments. These values are calculated from the fitted curve, shown as the solid black line in the right graph in Fig. 5. The speed of the bursting front drops off very quickly as the film gets thicker due to the small radius of curvature of the LV interface (the
Fig. 4. Rupture of a thin liquid film in a capillary, filmed from above. A—un-ruptured film, white circle highlights the capillary edge, diameter 3 mm. B—first frame showing rupture of the film. White circle highlights the rupture front. C—expanding hole in the film.
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Fig. 5. Speed of film rupture (in metres per second) as a function of time from rupture (milliseconds) is shown on the left. The radius of the ruptured hole (in mm) as a function of time from rupture (milliseconds) is shown on the right.
capillary is either 2 or 3 mm high). The high speeds discussed above are only applicable in the first few hundred milliseconds; however, this is more than enough time to blur the line between particle bridging film failure or ‘natural’ film failure where the opposite LV interfaces come into contact with each other at the thinnest point. If there is a particle in the film, at lower film speeds it is difficult to identify the origin of the film failure. If the film is videoed from the side it is much harder to identify the exact location of the failure, with or without a particle present as there is no Y-axis information. Therefore if the film bursts behind the particle (from the camera's perspective) and too low a frame rate is used the results can look like the particle has bridged the film. Side on viewing does allow the curvature of the film and the shape of the TPC on the particle to be distinguished though. When a SIBX treated galena
particle was added to the film and Dippenaar's experiments were recreated it was found that the particle rarely burst the film directly but was often squeezed out of the thinnest part of the film, where failure eventually occurred. However, it was noted that this behaviour was exacerbated if the capillary was not completely level. Fig. 6 shows a film containing a galena particle in the lead up to and moment of failure. The particle can be seen to be in a rotated orientation but when it touches the lower meniscus it is moved to the side of the capillary, away from the thinnest part of the film. When the film fails, even at 4000 fps it is not possible to identify whether the point of failure is at the particle wall or the thinnest part of the film due to motion blur. Comparing the analyses from the video shown in Fig. 4 and that of Dippenaar the time between particle contact with the lower meniscus and film failure was between 13.5 ms and 18.75 ms for these
Fig. 6. Selected frames showing a film rupture with a galena particle attached to the LV interfaces, taken at 4000 fps with an exposure of 100 μs. The width of each image is 3 mm. 1—particle about to come into contact with lower meniscus (0 ms). 2—particle touched lower meniscus (10 ms). 3—particle touching both sides of the LV, just before film fails (23.75 ms). 4—film fails (24 ms).
G.D.M. Morris, J.J. Cilliers / International Journal of Mineral Processing 131 (2014) 1–6
5
Fig. 7. The film distortion around a cubic particle in a capillary film displaced 3 units along the X-axis. A—view of the YZ plane, B—view of the XZ plane, and C—cross-section of the XZ plane showing the film distortion.
Fig. 8. Raytraced rendered images of Surface Evolver model with XP = 300 μm, P⁎ = 0.118. Image on the left is viewing the YZ plane and image on the right is viewing the XZ plane.
experiments and roughly 10 ms for Dippenaar's. Although Dippenaar reported longer induction times in other experiments. However, whilst the induction times are similar, the views are from different angles, the images in Fig. 4 clearly show the particle positioned off centre from the thinnest point of the film. The images shown span roughly 0.2 ms meaning the particle appears stationary, but as the film thinned towards failure, the particle moved from a central position to the one shown in Fig. 4. It is therefore possible that Dippenaar's observations were of a particle moving out of the centre of the film and what appeared to be the film riding up the particle faces, is in fact the film curving behind the particle. To identify the location at which the film fails a Surface Evolver model of the system was created with a cubic particle placed in the film in the position shown in Fig. 6–3. The completed models can then be analysed in more detail, without the effects of glare and blur shown in the videos. Analysis of the particle position in Fig. 6 shows it to be offset from the centre by 300 μm along the X-axis, the models used equivalent particle positions (XP) of 0 μm (0), 150 μm (1.5rp) and 300 μm (3rp) from the centre of the capillary. At a P⁎ of 0.1187 and XP of 300 μm in the Surface
Evolver model the film is about to rupture, but not at the particle's surface. Instead the film is thinnest closer to the centre of the capillary. At higher capillary pressure the film fails at this point, away from the particle; however, if the system is viewed in the YZ plane it appears as if the film is being drawn together by the particle. Fig. 8 shows the two views from Fig. 7 after rendering with raytracing software (3Ds Max). This shows how the harsh lighting required for high speed photography coupled with the intense optical distortion from the curved surface of the LV interfaces combines to make accurate analysis of the film shape difficult from only one point of reference. When the side on view from Fig. 8 is shown in comparison with a still taken from experiments with the capillary ring it can be seen that just before the film ruptures the film shape is closely matched (Fig. 9). So far this work has only referenced the case where the particle has moved away from the thinnest point in the film. If we run a simulation with the particle at the centre of the film, with a contact angle of 80° and in a rotated orientation the expected result would be for the film to rupture at the particle's surface as reported by Dippenaar. Instead due to the highly distorted interfacial curvature around the particle the film
Fig. 9. Comparison of high speed photography still and raytraced simulation.
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film can rupture away from the particle, whilst appearing to be drawn together by the particle. In a sense the film is still destroyed by the particle as its highly distorted shape around the particle is what forces the opposite sides together, but the TPC is not drawn together at the particle surface for contact angles below 90° as discussed by Dippenaar (1982). Even at very high speed (N4000 fps) it is still difficult to reliably capture the moment of film rupture. The high curvature of the LV interfaces arising from the thickness of capillary cells used will also affect the particle behaviour and film shape. In a flotation froth bubbles have a radius much greater than the roughly 1.5 mm diameter studied here. However analysis of bubble radius on particle behaviour is beyond the scope of this manuscript. Acknowledgments The authors would like to thank Rio Tinto and Imperial College London for the support they have provided to do this research as well as the EPSRC Engineering Instrument Pool whose loan of a Phantom 7.1T made the capture of the images used possible. Fig. 10. The points at which a film and a capillary will fail when containing a cubic particle with a contact angle of 80°. The lower film surface pushing through the upper surface is shown in dark grey.
actually ruptures away from the particle surface (Fig. 10). In the case of contact angles above 90° this will not be the case, but even up to 88° as in Dippenaar's work the film will fail away from the particle. Clearly if the particle has a contact angle above 90° it will bridge the film, but below 90° whilst the particle will draw the film together it causes rupture by forcing the LV interfaces together, but at some small distance away from the particle surface. 4. Conclusions This manuscript presents a discussion of the processes through which a thin liquid film is destroyed by an orthorhombic particle. It compares the results from two sets of experiments using different equipment and viewing angles to re-interpret the findings of Dippenaar (1982). The speed at which a film burst and the scale at which it interacts with particles make identifying the exact point film rupture a complex task. The bright light and optical distortion present in high speed photography of the system make it difficult to identify exactly what is happening. However by filming the process along different axes and modelling the film shape in Surface Evolver it has been shown that the
References Ali, S.A., Gauglitz, P.A., Rossen, W.R., 2000. Stability of solids-coated liquid layers between bubbles. Ind. Eng. Chem. Res. 39 (8), 2742–2745. Botto, L.,Lewandowski, E.P.,Cavallaro, M., Stebe, K.J., 2012. Capillary interactions between anisotropic particles. Soft Matter 8 (39), 9957. Bournival, G., Ata, S., 2010. Packing of particles on the surface of bubbles. Miner. Eng. 23 (2), 111–116. Brakke, K., 1992. Exp. Math. 1, 141–165. De Graaf, J., Dijkstra, M., van Roij, R., 2009. Triangular tessellation scheme for the adsorption free energy at the liquid–liquid interface: towards nonconvex patterned colloids. Phys. Rev. E. 80 (5), 1–19. Denkov, N., Ivanov, I., Kralchevsky, P.,Wasan, D., 1992. A possible mechanism of stabilization of emulsions by solid particles. J. Colloid Interface Sci. 150 (2), 589–593. Dippenaar, A., 1982. The destabilisation of froth by solids. I. The mechanism of film rupture. Int. J. Miner. Process. 9, 1–14. Garrett, P., 1979. The effect of polytetrafluoroethylene particles on the foamability of aqueous surfactant solutions. J. Colloid Interface Sci. 69 (1), 107–121. Lewandowski, E.P., Bernate, J.A., Searson, P.C., Stebe, K.J., 2008. Rotation and alignment of anisotropic particles on nonplanar interfaces. Langmuir 24 (17), 9302–9307. Morris, G., Neethling, S.J., Cilliers, J.J., 2010. The effects of hydrophobicity and orientation of cubic particles on the stability of thin films. Miner. Eng. 23 (11–13), 979–984. Morris, G., Neethling, S.J., Cilliers, J.J., 2011a. A model for investigating the behaviour of non-spherical particles at interfaces. J. Colloid Interface Sci. 354 (1), 380–385. Morris, G., Neethling, S.J., Cilliers, J.J., 2011b. An investigation of the stable orientations of orthorhombic particles in a thin film and their effect on its critical failure pressure. J. Colloid Interface Sci. 361 (1), 370–380. Morris, G., Neethling, S.J., Cilliers, J.J., 2011c. Modelling the self orientation of particles in a film. Miner. Eng. 33, 87–92. Qu, X., 2012. Correlation of air recovery with froth stability and separation efficiency in coal flotation. (Thesis) The University of Queensland.
Contents lists available at ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
Behaviour of a galena particle in a thin film, revisiting dippenaar Gareth D.M. Morris ⁎, Jan J. Cilliers Rio Tinto Centre for Advanced Minerals Recovery, Department of Earth Science and Engineering, Imperial College London, London SW7 2AZ, United Kingdom
a r t i c l e
i n f o
Article history: Received 21 January 2014 Received in revised form 28 May 2014 Accepted 26 July 2014 Available online 12 August 2014 Keywords: Flotation Particle bridging Film bursting High speed photography Simulation
a b s t r a c t Advances in technology over the past 30 years have drastically increased the frame rate and resolution at which the dynamics of thin film rupture and particle interaction can be imaged. A high speed camera (Phantom V7.1) was used to capture the bridging and rupture of a thin capillary film containing a particle of galena, revisiting work first published by Dippenaar (Dippenaar, A. 1982. The destabilisation of froth by solids. I. The mechanism of film rupture. Int. J. Min. Process., 9, 1–14.). The images were then compared to rendered models generated from simulations of an orthorhombic particle and capillary film under the same conditions, using the Surface Evolver program. These two sets of data are then used to build a more detailed picture of the behaviour of particles with sharp edges and corners as they bridge both sides of a thin liquid film. It has been observed that the liquid–vapour interface is highly distorted around the particle and that under certain conditions it can appear that the particle is drawing the film together to failure, whereas, in fact the film is being forced together behind the particle. The film failure is then due to contact between the opposite liquid–vapour interfaces, not the bridging dewetting mechanism as postulated by Dippenaar (1982). © 2014 Elsevier B.V. All rights reserved.
1. Introduction The mechanism through which particles stabilise or destroy films in a flotation froth is difficult to identify due to both the size and speed at which the phenomena occur. The particle-film interaction at the point of film rupture is a hugely important part of a flotation froth’s evolution and has a major impact on its physical properties and rheology as well as the efficiency of the whole process. It has therefore been the focus of much research to aid in the development of bubble film stability models. This paper revisits work published by Dippenaar (1982) that investigated the behaviour of a single galena particle in a thin liquid film. By using powerful modern modelling and imaging techniques it is possible to gain further insight into the interaction between the particle and the film at the moment of rupture. Previous analyses of the particle–film interaction have focused on the simplified two-dimensional case (2D) using circular particles in a single layer in a film (Ali et al., 2000; Denkov et al., 1992) in which the particle will destroy the film if the contact angle is greater than 90°. Garrett (1979) proposed the bridging dewetting mechanism that causes the failure of the bubble film; however, this also assumed spherical particles, flotation froths contain particles with irregular shapes and asperities which can interfere with this mechanism and complicate their interaction with the film. It is currently computationally intractable to simulate anything but the simplest of particle shapes attached to a liquid–vapour interface. Morris et al. (2011a) used Surface Evolver (Brakke, 1992) to develop a ⁎ Corresponding author. E-mail address: [email protected] (G.D.M. Morris).
http://dx.doi.org/10.1016/j.minpro.2014.07.004 0301-7516/© 2014 Elsevier B.V. All rights reserved.
method of simulating orthorhombic particles in a thin liquid film which were used to identify the stable orientations of cubes (Morris et al., 2010) and oblongs (Morris et al., 2011b) and their effect on film stability. De Graaf et al. (2009) also developed a numerical technique based on triangular tessellation to identify the adsorption free energy landscape for spheroidal, cylindrical and ellipsoidal particles at liquid– vapour (LV) interface. Lewandowski et al. (2008) also used Surface Evolver to investigate the self ordering of micro-particles at a liquid vapour interface. It is therefore well established that the interplay between a particle's shape and contact angle can have a large effect on its behaviour in the LV interface. Whilst it is relatively easy to analyse the shape of the film surrounding spherical particles in an ordered arrangement, when orthorhombic ones are considered the complexity of the LV-interfaces topology greatly increases. The interaction between the particles and the point at which the film fails becomes much more difficult to identify. Dippenaar (1982) investigated this using high speed imaging of a single galena particle sitting in a thin film supported by a capillary. The two stable orientations for a cubic particle at contact angles between 45° and 90° were identified (diagonal and horizontal) using a 2D analytical method. Morris et al. (2010) has since used 3D numerical simulation to identify a third energetically stable orientation (rotated) for a cubic particle, all three are shown in Fig. 1. Dippenaar's analysis of the high speed footage showed that the particle would adopt either a diagonal or horizontal orientation in the film when it bridged only one LV interface. As the film thinned and the lower part of the particle came into contact with the opposite LV interface it would react differently depending on the orientation; if it was horizontal it would move off to the side of the film until it thinned enough to
2
G.D.M. Morris, J.J. Cilliers / International Journal of Mineral Processing 131 (2014) 1–6
Fig. 1. Stable orientations for an orthorhombic particle, A—rotated, B—diagonal, and C—horizontal.
rupture, but if it was diagonal it would either rotate to horizontal and behave as before or adopt a rotated orientation. When the particles adopted a rotated orientation the opposite sides of the LV interface would draw up the sides of the particle and rupture the film. This bridging dewetting phenomenon was proposed by Garrett (1979), but was developed with spherical particles where the film distortion around the particle is much less pronounced. The phenomenon of particles moving out of the centre of the film was also noted by Qu (2012) who observed hydrophobic coal particles being forced out of the centre of the film as it thinned, leaving an area of empty, thin film before rupture. The distortion of the film surrounding non-spherical particles can be quite severe, causing them to exhibit interesting packing phenomena. Botto et al. (2012)) whereby their contact angle and shape interact with the curvature of the LV interface to allow some control on their behaviour in the film. This interaction of non-spherical particles in a liquid film is beyond the scope of this paper; however, it will affect their packing arrangement and therefore the film loading and stability (Bournival and Ata, 2010; Morris et al., 2011c). It also highlights the rather extreme distortion that a LV interface can undergo when close to a particle. 2. Materials and methods
the camera was mounted on a sliding bed which was used to focus on the capillary film and particle along the Y-axis (this setup is shown in Fig. 2). For vertical filming the camera was mounted on a tripod and rotated down to image down the Z-axis, videoing from above the film (this setup is not shown in Fig. 2). Finally a Solarc GE ELSV-60 RVI Light Source was used to illuminate the area of interest. The whole setup for filming horizontally is shown in Fig. 2. 2.2. Procedure Liquid was drawn from the capillary, or injected into it, using a manually operated syringe. It was possible to accurately control the thickness of the film by monitoring it in the camera viewer. The film was thinned until the lower point of any attached particle was within 40 μm of the opposite LV interface. After this point the film was allowed to thin naturally due to evaporation whilst being filmed by the camera. The camera was mounted in one of two positions, horizontally or vertically. In the former, the film could be videoed from the side and the movement of the three point contact (TPC) over the particle surface captured accurately. In the latter, the exact point where the film ruptures can be identified, as well as the particle position at the point of film failure.
2.1. High speed photography rig 2.3. Materials The rig used to capture the videos of particle film bridging is shown in Fig. 2. It consists of a capillary holder (machined from Perspex) for the film mounted with control in 3 axes to position the area of interest in front of the camera. A Vision Research Phantom V7.1 (on loan from the EPSRC equipment loan pool) was used to capture the images and was mounted with a Canon EOS Macro Lens. For horizontal filming
The films in the capillary were made with de-ionised water and the galena particles were hand ground in a pestle and mortar with water. The freshly ground particles were then wet sized and mixed in a stirred solution of 100 ppm sodiumisobutylxanthate (SIBX) for 1 h after which they were washed several times with de-ionised water and stored in a
Fig. 2. The high speed rig used to capture the moment a film breaks with the particle in it. A—camera/lens, B—capillary/area of interest, and C—light source. X, Y and Z in the detail of the capillary holder show the axis used to discuss film shape and particle positions.
G.D.M. Morris, J.J. Cilliers / International Journal of Mineral Processing 131 (2014) 1–6
3
Fig. 3. The Surface Evolver model used to simulate film shape surrounding an orthorhombic particle.
clean beaker under de-ionised water. Samples were made and used fresh every day. Contact angle tests on a polished plate of galena treated in the same way showed contact angles of 80° ± 10°, providing a similar range to those used in Dippenaar's work (80° ± 8°).
The model was run for several capillary pressures corresponding to a film that was just touching both sides of the particle to one which has failed. Three particle positions (centre, 1.5rp and 3rp from the centre) and two orientations (horizontal and rotated) were also modelled. 3. Results and discussion
2.4. Surface Evolver model The Surface Evolver model used is based upon those previously described in Morris et al. (2011a,c). The particles used in the experiments were below 200 μm in length meaning the Bond number (Bo) was roughly 0.03 allowing gravity to be ignored. Dippenaar (1982) also reported that particles of galena up to this size did not pull any observable dimple in the LV interface. All length (L) and pressure (P) terms in the model have been non-dimensionalised using particle radius (rp) and surface tension of the water (γLV) as shown in Eqs. (1) and (2). The ⁎ denotes non-dimensionalisation of a parameter.
L ¼
P ¼
L rp
ð1Þ
Prp γ
ð2Þ
The model of the particle and film is constructed in Surface Evolver as shown in Fig. 3. The curvature of the two LV interfaces is controlled by altering the volume of gas for each volume associated with the LV interfaces; they are kept the same at all times. The particle position is user defined, as is the rotation of the particle. The ratio of the size of the particle and the diameter of the capillary was matched to the experimental conditions.
A series of films were taken of a single galena particle in the capillary, using the camera to film either side-on or vertically. Side on images allow comparison to Dippenaar's (1982) work, but the images from above allow the evaluation of more information about the physics of the film rupture. When a film bursts the initial hole that forms expands rapidly. The speed at which this rupture front expands was measured for three sets of experiments filmed from above. The radius of the rupture was measured using ImageJ and the diameter of the capillary used for scale (3 mm); an example set of images are shown in Fig. 4. The speed of the film rupture front for three cases is shown in Fig. 5 along with the radius of the ruptured hole, both as a function of time from the initial film failure. The speeds and distances were measured using video taken at 26,143 fps. There is a rapid drop off in the speed of the rupture front after the initial failure of the film but what should be noted is that in Dippenaar's paper a maximum film speed of 5000 fps was achieved and for the results that were analysed for the galena particles in a film the speed was only 1500 fps. Therefore, assuming that the first frame captured the very moment the film burst (best case scenario) the next frame would be at either 0.2 ms (5000 fps) or 0.66 ms (1500 fps) during which time the bursting front will have travelled roughly either 350 μm or 600 μm respectively, a distance greater than the particle sizes used in the experiments. These values are calculated from the fitted curve, shown as the solid black line in the right graph in Fig. 5. The speed of the bursting front drops off very quickly as the film gets thicker due to the small radius of curvature of the LV interface (the
Fig. 4. Rupture of a thin liquid film in a capillary, filmed from above. A—un-ruptured film, white circle highlights the capillary edge, diameter 3 mm. B—first frame showing rupture of the film. White circle highlights the rupture front. C—expanding hole in the film.
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Fig. 5. Speed of film rupture (in metres per second) as a function of time from rupture (milliseconds) is shown on the left. The radius of the ruptured hole (in mm) as a function of time from rupture (milliseconds) is shown on the right.
capillary is either 2 or 3 mm high). The high speeds discussed above are only applicable in the first few hundred milliseconds; however, this is more than enough time to blur the line between particle bridging film failure or ‘natural’ film failure where the opposite LV interfaces come into contact with each other at the thinnest point. If there is a particle in the film, at lower film speeds it is difficult to identify the origin of the film failure. If the film is videoed from the side it is much harder to identify the exact location of the failure, with or without a particle present as there is no Y-axis information. Therefore if the film bursts behind the particle (from the camera's perspective) and too low a frame rate is used the results can look like the particle has bridged the film. Side on viewing does allow the curvature of the film and the shape of the TPC on the particle to be distinguished though. When a SIBX treated galena
particle was added to the film and Dippenaar's experiments were recreated it was found that the particle rarely burst the film directly but was often squeezed out of the thinnest part of the film, where failure eventually occurred. However, it was noted that this behaviour was exacerbated if the capillary was not completely level. Fig. 6 shows a film containing a galena particle in the lead up to and moment of failure. The particle can be seen to be in a rotated orientation but when it touches the lower meniscus it is moved to the side of the capillary, away from the thinnest part of the film. When the film fails, even at 4000 fps it is not possible to identify whether the point of failure is at the particle wall or the thinnest part of the film due to motion blur. Comparing the analyses from the video shown in Fig. 4 and that of Dippenaar the time between particle contact with the lower meniscus and film failure was between 13.5 ms and 18.75 ms for these
Fig. 6. Selected frames showing a film rupture with a galena particle attached to the LV interfaces, taken at 4000 fps with an exposure of 100 μs. The width of each image is 3 mm. 1—particle about to come into contact with lower meniscus (0 ms). 2—particle touched lower meniscus (10 ms). 3—particle touching both sides of the LV, just before film fails (23.75 ms). 4—film fails (24 ms).
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Fig. 7. The film distortion around a cubic particle in a capillary film displaced 3 units along the X-axis. A—view of the YZ plane, B—view of the XZ plane, and C—cross-section of the XZ plane showing the film distortion.
Fig. 8. Raytraced rendered images of Surface Evolver model with XP = 300 μm, P⁎ = 0.118. Image on the left is viewing the YZ plane and image on the right is viewing the XZ plane.
experiments and roughly 10 ms for Dippenaar's. Although Dippenaar reported longer induction times in other experiments. However, whilst the induction times are similar, the views are from different angles, the images in Fig. 4 clearly show the particle positioned off centre from the thinnest point of the film. The images shown span roughly 0.2 ms meaning the particle appears stationary, but as the film thinned towards failure, the particle moved from a central position to the one shown in Fig. 4. It is therefore possible that Dippenaar's observations were of a particle moving out of the centre of the film and what appeared to be the film riding up the particle faces, is in fact the film curving behind the particle. To identify the location at which the film fails a Surface Evolver model of the system was created with a cubic particle placed in the film in the position shown in Fig. 6–3. The completed models can then be analysed in more detail, without the effects of glare and blur shown in the videos. Analysis of the particle position in Fig. 6 shows it to be offset from the centre by 300 μm along the X-axis, the models used equivalent particle positions (XP) of 0 μm (0), 150 μm (1.5rp) and 300 μm (3rp) from the centre of the capillary. At a P⁎ of 0.1187 and XP of 300 μm in the Surface
Evolver model the film is about to rupture, but not at the particle's surface. Instead the film is thinnest closer to the centre of the capillary. At higher capillary pressure the film fails at this point, away from the particle; however, if the system is viewed in the YZ plane it appears as if the film is being drawn together by the particle. Fig. 8 shows the two views from Fig. 7 after rendering with raytracing software (3Ds Max). This shows how the harsh lighting required for high speed photography coupled with the intense optical distortion from the curved surface of the LV interfaces combines to make accurate analysis of the film shape difficult from only one point of reference. When the side on view from Fig. 8 is shown in comparison with a still taken from experiments with the capillary ring it can be seen that just before the film ruptures the film shape is closely matched (Fig. 9). So far this work has only referenced the case where the particle has moved away from the thinnest point in the film. If we run a simulation with the particle at the centre of the film, with a contact angle of 80° and in a rotated orientation the expected result would be for the film to rupture at the particle's surface as reported by Dippenaar. Instead due to the highly distorted interfacial curvature around the particle the film
Fig. 9. Comparison of high speed photography still and raytraced simulation.
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film can rupture away from the particle, whilst appearing to be drawn together by the particle. In a sense the film is still destroyed by the particle as its highly distorted shape around the particle is what forces the opposite sides together, but the TPC is not drawn together at the particle surface for contact angles below 90° as discussed by Dippenaar (1982). Even at very high speed (N4000 fps) it is still difficult to reliably capture the moment of film rupture. The high curvature of the LV interfaces arising from the thickness of capillary cells used will also affect the particle behaviour and film shape. In a flotation froth bubbles have a radius much greater than the roughly 1.5 mm diameter studied here. However analysis of bubble radius on particle behaviour is beyond the scope of this manuscript. Acknowledgments The authors would like to thank Rio Tinto and Imperial College London for the support they have provided to do this research as well as the EPSRC Engineering Instrument Pool whose loan of a Phantom 7.1T made the capture of the images used possible. Fig. 10. The points at which a film and a capillary will fail when containing a cubic particle with a contact angle of 80°. The lower film surface pushing through the upper surface is shown in dark grey.
actually ruptures away from the particle surface (Fig. 10). In the case of contact angles above 90° this will not be the case, but even up to 88° as in Dippenaar's work the film will fail away from the particle. Clearly if the particle has a contact angle above 90° it will bridge the film, but below 90° whilst the particle will draw the film together it causes rupture by forcing the LV interfaces together, but at some small distance away from the particle surface. 4. Conclusions This manuscript presents a discussion of the processes through which a thin liquid film is destroyed by an orthorhombic particle. It compares the results from two sets of experiments using different equipment and viewing angles to re-interpret the findings of Dippenaar (1982). The speed at which a film burst and the scale at which it interacts with particles make identifying the exact point film rupture a complex task. The bright light and optical distortion present in high speed photography of the system make it difficult to identify exactly what is happening. However by filming the process along different axes and modelling the film shape in Surface Evolver it has been shown that the
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