Comparison of Bubble Size Distributions Inferred from Acoustic, Optical Visualisation, and Laser Diffraction

colloids and interfaces

Article Comparison of Bubble Size Distributions Inferred from Acoustic, Optical Visualisation, and Laser Diﬀraction

Pratik D Desai 1 , Woon Choon Ng 2, Michael J Hines 1, Yassir Riaz 3, Vaclav Tesar 4 and William B Zimmerman 3,*

1 Perlemax Ltd., 318 Broad Lane, Sheffield S3 7HQ, UK; [email protected] (P.D.D.); [email protected] (M.J.H.) 2 Department of Mechanical Engineering, Mappin Street, University of Sheffield, Sheffield S1 3JD, UK; MEP11WN@sheffield.ac.uk 3 Department of Chemical and Biological Engineering, Mappin Street, University of Sheffield, Sheffield S1 3JD, UK; YRiaz1@sheffield.ac.uk 4 Institute of Thermomechanics v.v.i., Czech Academy of Sciences, Dolejškova 5, 182 00 Praha-Kobylisy, Czech Republic; [email protected] * Correspondence: w.zimmerman@sheffield.ac.uk

Received: 25 August 2019; Accepted: 28 November 2019; Published: 5 December 2019

Abstract: Bubble measurement has been widely discussed in the literature and comparison studies have been widely performed to validate the results obtained for various forms of bubble size inferences. This paper explores three methods used to obtain a bubble size distribution—optical detection, laser diffraction and acoustic inferences—for a bubble cloud. Each of these methods has advantages and disadvantages due to their intrinsic inference methodology or design flaws due to lack of specificity in measurement. It is clearly demonstrated that seeing bubbles and hearing them are substantially and quantitatively different. The main hypothesis being tested is that for a bubble cloud, acoustic methods are able to detect smaller bubbles compared to the other techniques, as acoustic measurements depend on an intrinsic bubble property, whereas photonics and optical methods are unable to “see” a smaller bubble that is behind a larger bubble. Acoustic methods provide a real-time size distribution for a bubble cloud, whereas for other techniques, appropriate adjustments or compromises must be made in order to arrive at robust data. Acoustic bubble spectrometry consistently records smaller bubbles that were not detected by the other techniques. The difference is largest for acoustic methods and optical methods, with size differences ranging from 5–79% in average bubble size. Differences in size between laser diffraction and optical methods ranged from 5–68%. The differences between laser diffraction and acoustic methods are less, and range between 0% (i.e., in agreement) up to 49%. There is a wider difference observed between the optical method, laser diffraction and acoustic methods whilst good agreement between laser diffraction and acoustic methods. The significant disagreement between laser diffraction and acoustic method (35% and 49%) demonstrates the hypothesis, as there is a higher proportion of smaller bubbles in these measurements (i.e., the smaller bubbles ‘hide’ during measurement via laser diffraction). This study, which shows that acoustic bubble spectrometry is able to detect smaller bubbles than laser diffraction and optical techniques. This is supported by heat and mass transfer studies that show enhanced performance due to increased interfacial area of microbubbles, compared to fine bubbles.

Keywords: microbubbles; fluidics; fluidic oscillation; acoustic bubble spectrometry; laser diffraction

Colloids Interfaces 2019, 3, 65; doi:10.3390/colloids3040065 www.mdpi.com/journal/colloids Colloids Interfaces 2019, 3, 65 2 of 20

1. Introduction

Bubble Visualisation Techniques Bubbles ranging from (1 µm–1000 µm) in size are termed microbubbles. Although the actual definition of a microbubble depends on its application, for the purposes of this study, the aforementioned definition holds [1]. Bubbles have been visualised for over half a millennia with Newton’s observation of bubble formation with a pair of lenses, whilst the Berthelot tube method has long been known as a way to observe cavitation in liquids [2]. Reynolds discovered bubble formation by cavitation via the process of boiling [3]. Bubble visualisation is easier for fine bubbles or for sparse microbubbles generated by either energy intensive or low throughput methods. Single bubbles can be simply studied via a microscope or a lens. Characterising cloud bubble dynamics is more problematic. Common practice is to use optical imaging coupled with the volume fraction of the bubble by juxtaposing a control image (bubble-free) over the bubble cloud image, followed by using pixel data and a Hough transform to determine the void fraction. However, this does not necessarily provide any more information about the bubble size distribution (BSD). Therefore, optical methods were developed with algorithms relying on variety of techniques to estimate bubble sizes [4–11]. Interests in bubble cloud dynamics are largely focused on marine engineering and oceanic sciences. This is due to the high cost of producing microbubbles, thereby opposing the use of microbubbles for industrial purposes. Fluidic oscillation offers substantial reduction in energy costs for generating microbubbles with concomitant increase of throughput [12]. The Tesaˇr–Zimmermanfluidic oscillator [13]—a modified version of the feedback loop type oscillator—made it possible to use microbubbles economically for industrial applications with several applications explored for lab-scale [14] and large-scale industrial purposes. Several T-Junction devices [15,16] and sonication [17], amongst other techniques can now be used for generating a cloud of microbubbles with a wide size distribution. With the advent of such techniques, the methods for visualisation have simultaneously shifted from direct measurement using a microscope to indirect techniques for higher accuracy through the exploitation of properties exhibited by bubbles. The BSD depend on the methods used for obtaining the bubble size and the statistical analyses that accompany these methods. Methods used for inferring BSD include four-point optical probe [18–21], capacitance probes [22], electrical conductivity [23], video imaging [24–27], acoustical backscatter [28], acoustic resonator [29], acoustic pulse propagation sensor [29], laser diffraction [30], acoustic attenuation [31–33], University of Capetown Technique (UCT) bubble size sampler [34] and laser attenuation [35]. Several comparison studies have been performed on bubble visualization, such as [5], as well as work on resolving optical and acoustic methods [29,36,37] in order to merge the understanding of these techniques and try to obtain a better understanding of these visualisation systems. However, comparison studies for cloud bubble dynamics with an emphasis on detecting smaller bubbles have not been performed, nor studied in detail. Additionally, visual inspection, as can be seen in Figure1, show that for microbubble clouds, visual inferences cannot be made and size distributions need to be carefully obtained and analysed. Statistical analyses performed on the sizing by each method skews the size distribution and therefore the final average bubble size obtained could be quite different depending on the actual statistical analysis applied. A comparison study is performed for three classes of bubble sizing techniques, including optical, laser diffraction, and acoustic. Specifically, Dynaflow’s Acoustic Bubble Spectrometer (ABS), Malvern Instruments’ SprayTec, and high-speed photography (Photron FastCam S3). Each method offers its own advantages and disadvantages depending on the actual method of estimating the bubble size population. We test the hypothesis that for measuring a bubble cloud, an acoustic method is likely the method most representative of the cloud. There is a possibility that larger bubbles obscure the smaller bubbles in the cloud for the other methods. The other methods require a small sampling window/volume to garner the cloud information, which may also hamper their performance. Colloids Interfaces 2019, 3, 65 3 of 20

Colloids Interfaces 2018, 2, x FOR PEER REVIEW 3 of 20 This section discusses the distinct advantages oﬀered by the diﬀerent visualisation methods and otherThis capabilities. section discusses the distinct advantages offered by the different visualisation methods and other capabilities.

Figure 1. 1. PhotographicPhotographic Visualisation Visualisation of Cloud of Cloud Bubble Bubble Dynamics Dynamics (left) – control/steady (left)–control/ steadyflow, (right flow,) (oscillatoryright) oscillatory flow. Nothing flow. significant Nothing significant can be inferre cand visually—the be inferred visually—the major problem major when problem characterising when characterisingmicrobubble clouds. microbubble clouds. 2. Optical Methods 2. Optical Methods This is a direct form of measurement and visualisation, as well as the simplest method since it is a This is a direct form of measurement and visualisation, as well as the simplest method since it is quick and easy way to infer the BSD. a quick and easy way to infer the BSD. High-Speed Photography High-Speed Photography Optical methods usually involve a monochromatic light source and require the liquid to be transparentOptical to methods light. The usually greater involve the contrast a monochromatic between the bubble light source and the and background, require the the liquid more robustto be ittransparent is for automated to light. image The greater analysis. the High-speedcontrast betw photographyeen the bubble is commonly and the background, used due to the its more ease robust of use. Mostit is for high-speed automated cameras image analysis. have the High-speed ability to capture photography more than is commonly 500 frames used per seconddue to its (fps ease). of use. MostThe high-speed bubble generator cameras have is placed the ability in the centreto capture with more the light than source 500 frames and the per camera second placed (fps). opposite eachThe other bubble in order generator to obtain is placed the best in the contrast centre for with the the bubbles. light source Automated and the imagecamera analysis placed opposite is made easiereach other if there in isorder a good to contrastobtain the between best contrast the background for the bubbles. and the bubbles.Automated The image camera analysis need not is be made able toeasier capture if there more is thana good 2000 contrastfps to obtain between a BSD. the Thebackground simplicity and of thethe system bubbles. is oneThe ofcamera its key need advantages not be andable significantlyto capture more reduces than the 2000 costs fps ofto theobtain system. a BSD. Automated The simplicity image of analysis the system is possible is one byof simpleits key algorithmsadvantages by and using significantly any suitable reduces programming the costs languageof the system. viz. Octave, Automated ImageJ, image MATLAB, analysis Mathematica, is possible andby simple LabView. algorithms by using any suitable programming language viz. Octave, ImageJ, MATLAB, Mathematica,Image analysis and LabView. can also be performed manually. It can, therefore, provide bubble sizes without the needImage of computing analysis power can also (albeit be performed a cumbersome manually. approach). It can, Although therefore, this provide technique bubble is convenient sizes without for singlethe need bubbles, of computing cloud bubble power dynamics (albeit a presentcumbersome their own approach). drawbacks. Although Automated this technique image analysis is convenient cannot befor reliablysingle bubbles, used for cloud overlapping bubble bubbles,dynamics noncircular present their bubbles, own drawba and near-wallcks. Automated bubbles (the image bubbles analysis also needcannot to be be reliably in a single used plane). for over Dependinglapping onbubbles, the angle noncir used,cular the bubbles, bubble sizeand obtained near-wall is bubbles significantly (the dibubblesfferent. also A longneed working to be in focala single length plane). lens Depend could being used on the (to angle ensure used, wall the effects bubble are minimised)size obtained but is makessignificantly the process different. more A expensive long working and cumbersome. focal length lens could be used (to ensure wall effects are minimised)This problem but makes can bethe solved process by more using expensive multiple camerasand cumbersome. at the three focal planes but results in the needThis to develop problem a waycan be to solved accrue by synchronised using multiple information cameras at from the three the three focal cameras planes but and results then collate in the theneed information to develop togethera way to inaccrue order synchronised to obtain a bubble information spectrum. from Bubbles the three at cameras the wall, and partial then bubbles, collate noncircularthe information (spherical together for thein order 3D system) to obtain are nota bubble detected spectrum. by automated Bubbles image at the analysis. wall, partial These bubbles, features makesnoncircular the task (spherical tedious andfor the cumbersome, 3D system) while are introducingnot detected inference by automated errors. image analysis. These featuresDiff makeserent lenses the task are tedious required and for cumbersome, a particular while size range. introducing They cannotinference be errors. used simultaneously unlessDifferent another lenses camera are is used.required A comprehensive for a particular BSD size is range. therefore They diffi cannotcult to be obtain, used sosimultaneously only a certain sizeunless range another is observed camera is at used. a given A co time.mprehensive Once the BSD appropriate is therefore lens difficult has been to obtain, chosen so and only the a cameracertain focused,size range it cannotis observed detect at thea given other time. bubble Once size the ranges appropriate and cannot lens di hasfferentiate been chosen between and the the particles camera andfocused, bubbles it cannot if they detect are toothe small.other bubble Multiple size lenses ranges increase and cannot the costdifferentiate of the system, between the the number particles of measurements,and bubbles if andthey theare required too small. analyses Multiple and lenses comparisons. increase the cost of the system, the number of measurements, and the required analyses and comparisons. A number of additional analyses can be made using a high-speed camera. If the camera has a high frame rate, such as the Photron FastCam S3, the rise velocity of the bubble can be measured as

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A number of additional analyses can be made using a high-speed camera. If the camera has a high frame rate, such as the Photron FastCam S3, the rise velocity of the bubble can be measured as well as bubble formation dynamics, growth dynamics, conjunction and coalescence. Adil et al. [38] presents image analysis techniques for the rise velocity of a system with an ordinary camera.

3. Acoustic Methods Acoustic methods have been used for bubble sizing for almost half a century. Excellent reviews on bubble sizing using acoustic methods have been compiled [39]. Bubble acoustic responses include backscatter, attenuation, resonance and sound speed modulations in the medium [32]. This is made possible as a result of the substantial effect that a bubble has on the propagation of acoustic waves. A significant advance to demonstrate acoustic determination of the bubble sizes for bubble clouds was made in 1989 [40]. The relationship between complex sound speed in a bubbly medium (cm), and bubble free sound speed (c0), is defined by 2 2 Z c c ∞ an(a) 0 = 1 + 0 da (1) 2 2 2 2 c ( f ) π 0 f f + iδ f m R − a is the bubble radius(m), f is the insonant frequency (Hz), fR is the natural frequency of the bubble of size a, n(a) is the bubble density function and δ is bubble damping magnitude. This relationship by itself can be used for obtaining bubble size. However, there is a loss in fidelity, which is why other methods have been adopted for development. This along with the relation:

c2 0 = u( f ) iv( f ) (2) 2 cm( f ) − where u(f) is speed and phase speed (v(f)) is given by:

c2 0 (3) u( f )

And attenuation constant α is given by: ! 2π f v α( f ) = 20 log10 e (4) c0

This combination provides the bubble with a resonant frequency at which to oscillate. According to the solution of the Rayleigh–Plesset equation, the linear response of the bubble under continuous insonation and its nonlinear response, along with oscillation, is a property that is observed only for bubbles (not particles). These properties make this method favoured due to its speciﬁcity. Also, in the Rayleigh region, the insonation frequency is dependent on the sixth power of the radius thereby making it a highly speciﬁc method.

f r6 [3] (5) ∝ Several authors [41–51] have used hydrophones to infer bubble size, deploying these diﬀerent properties in order to obtain BSD for coated (polymeric shells/protein shells, liposomes) and uncoated (clear interface) bubbles. The drawback comes in the form of the complicated inversion observed due to the inverse of the ill posed Fredholm integral [52], which results in an enlarged eﬀect on the solution from small measurement errors. Colloids Interfaces 2018, 2, x FOR PEER REVIEW 5 of 20

Acoustic Bubble Spectrometry (ABS) by Dynaflow Acoustic bubble spectrometry (ABS), used in this study is based on an assumption known as the resonant bubble approximation (RBA). The system and the algorithm used for the bubble size measurementColloids is Interfacesdescrib2019ed, 3 well, 65 by [53]. 5 of 20 The main development made by Dynaflow is the algorithm based on constrained minimisation. A hydrophoneAcoustic is a Bubble microphone Spectrometry that (ABS) can by be Dynaflow used underwater. As sound travels much faster in water and attenuates Acousticslower than bubble with spectrometry air as the (ABS), medium used, inthe this design study of is basedthe hydrophone on an assumption has to known be modified as accordinglythe by resonant matching bubble its approximationacoustic impedance (RBA). The in systemwater [3]. and An the algorithmequiresponsive used for hydrophone the bubble size pair is used in thismeasurement system with is describedone utilised well byfor [53 generation]. and the other for the detection. MicrobubblesThe main oscillate development linearly made upon by Dynaflow ultrasonic is the insonation. algorithm based If onthe constrained mechanical minimisation. index of the A hydrophone is a microphone that can be used underwater. As sound travels much faster in water insonation andultrasound attenuates is slower high than enough, with air the as theoscillations medium, the become design ofnonlinear, the hydrophone increasing has to be the modified specificity, hence moreaccordingly effective by for matching sizing. its The acoustic acoustic impedance pressure in water has [3]. to An be equiresponsive increased hydrophoneto be able pairto cause is a nonlinear responseused in this and system a withcompression one utilised or for expansion, generation and which the other results for the in detection. the emissions of nonlinear signals and theirMicrobubbles respective oscillate harmonics linearly of upon the ultrasonic transmitted insonation. signal. If This the mechanical also causes index the of theacoustic impedanceinsonation of the bubble ultrasound to change is high with enough, respect the oscillations to water, become improving nonlinear, the signal. increasing This the can specificity, be thought hence more effective for sizing. The acoustic pressure has to be increased to be able to cause a nonlinear of as a contrastresponse enhancing and a compression effect of or the expansion, coating which on a resultscoated in medical the emissions microbubble. of nonlinear signals and their Initiallyrespective the two harmonics hydrophones of the transmitted are placed signal. opposite This also each causes other the acousticwith the impedance bubble generator of the bubble placed in the centre.to change The transmitter with respect toinsonates water, improving starting the fr signal.om a specific This can befrequency thought of and as a contrastperforms enhancing a frequency sweep. Thiseff ectsignal of the may coating or onmay a coated not be medical amplified microbubble. depending on the conditions. Whilst the receiver amplifies the Initiallysignal, thethe two data hydrophones obtained are is placed then oppositeinverted each by other bespoke with the software bubble generator provided placed by the in the centre. The transmitter insonates starting from a specific frequency and performs a frequency company. sweep.A zero This calibration signal may reading or may notis betaken amplified (P0 - dependinganalogous on to the any conditions. spectroscopic Whilst the method). receiver The productionamplifies of bubbles the signal, causes the a data change obtained in pressure is then inverted when by the bespoke bubble software cloud provided is insonated. by the company. This change is recordedA by zero the calibration transducers reading and is takencompared (P0 - analogous to the zero to any calibration spectroscopic reading. method). The production of The ABSbubbles (Figure causes 2) a changeprovides in pressure continuous, when thereal bubble time cloud bubble is insonated. size distribution This change that is recorded are extremely by specific tothe bubbles. transducers Using and compared an optimised to the zero octoph calibrationonic reading. system (four pairs of hydrophones), a The ABS (Figure2) provides continuous, real time bubble size distribution that are extremely −3 comprehensivespecific size to bubbles. distribution, Using an between optimised octophonic10 µm and system 2 mm. (four Void pairs offractions hydrophones), of down a comprehensive to 3 × 10 [53], can be measuredsize distribution, and verified between whilst 10 µm conducting and 2 mm. Void this fractions study. of down to 3 10 3 [53], can be measured × − and verified whilst conducting this study.

Figure 2. Schematic of the acoustic bubble spectrometer system comprised of bubble generating system Figure 2. Schematic(and hydrophones), of the signalacoustic ampliﬁer bubble and dataspectrometer processing. system comprised of bubble generating system (and hydrophones), signal amplifier and data processing. Skewed results are obtained if bubbles stick to the surface of the hydrophones. Since the hydrophones need to be submerged in the liquid, even small imperfections act as large centres for Skewed results are obtained if bubbles stick to the surface of the hydrophones. Since the bubble coalescence. Therefore, the hydrophones need to be regularly wiped and cleaned using hydrophoneswater need [54]. to be submerged in the liquid, even small imperfections act as large centres for bubble coalescence.The distinct Therefore, advantage the ofhydrophones acoustic spectrometry need to over belaser regularly diﬀraction wiped and opticaland cleaned methods using is that water [54]. bubbles in liquids are more transparent to acoustic waves than to light waves [36]. The distinctABS advantage can also be usedof acoustic to measure spectrometry the sound speed over of thelaser medium diffraction and therefore and optical determine methods the is viscosity or density of the medium. that bubbles in liquids are more transparent to acoustic waves than to light waves [36]. ABS can also be used to measure the sound speed of the medium and therefore determine the viscosity or density of the medium.

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4. Photonic Methods Photonic methods are most commonly used in particle sizing aside from optical imaging. Photonic methods are incredibly effective in terms of accuracy and range of the size distributions for small samples. The accuracy of photonic methods reduces for bubbles relative to particles not only due to the immanent property of the bubble but also due to total internal reflection that occurs upon illumination (presuming particles are opaque). Bubble opacity is not high so that the diaphanous behaviour exhibited by the bubbles affects the laser diffraction and scattering. Particles and bubbles interact with light (and sound) in three ways: absorption, emission and scattering. Assuming that the particles are spherical, the intensity of the scatter is measured and the BSD is inferred using Mie theory (assuming a noninteracting bubble cloud population). The scatter is dependent on the size of the particles, whilst the intensity is dependent on the number of particles. A bubble can be thought of as a dielectric sphere. An air filled bubble, with water as a medium, fits into this category. Mie theory describes diffraction, refraction and reflection (internal and external). Diffraction cannot tell the difference between a particle and bubble since it is independent of particle properties. Conversely, refraction and reflection are dependent on the type of particle and its refractive index. The refractive index, however, is fairly difficult to measure effectively. When light passes through a particle with an angle of incidence = 00, there is no change to the incident light. However, at all the other angles the three effects can be observed depending on the angle of incidence. Total internal reflection is observed for incident angles above the critical angle. Several devices used for particle sizing using photonic methods have been reviewed [30].

Malvern SprayTec According to Malvern Instruments, SprayTec uses dynamic light scattering (DLS) as a principle, and has a range with the 300 mm lens) between 0.1–900 µm (Dx(50): 0.5–600µm). The system measures droplet size distributions and requires the angular intensity of light scattered from a spray to be measured as it passes through a laser beam (based on transmittance and scattering). This scattering pattern is first recorded and then analysed using Fraunhofer and Mie scattering to yield a size distribution. Complete resolution of the size dispersion has been obtained through optimisation as well as using a patented multiple scattering algorithm ensuring up to 98% obscuration [55]. Figure3 shows a schematic of the SprayTec system. Two lasers, with collimating optics, are placed opposite each other with the test cell placed in the centre so that a small area of interest is measured. This was a modification made to the original setup as the usual method for measurement is spraying it in the space between the two lasers. The receiving lens adjusts itself—a self-correcting calibration system for alignment, which is critical for this measurement technique, and accounts for major errors and inconsistencies. This has been taken into account by the manufacturer by incorporating a separate collimator and an auto alignment feature embedded. The modification made here is to use a glass cell for bubble measurement while using a macro provided by Malvern Instruments to account for changes in refractive index. Bubbles are droplets with the phases inverted. Therefore, the SprayTec can be used for bubble size measurements especially for obtaining high density BSD [13,56]. Cloud bubble sizing might be a difficult phenomenon for laser diffraction techniques since the bubbles diffract far more than a particle with possibility of total internal reflection in a bubble. Since this principle depends on light diffraction and not a property exhibited specifically by bubbles alone, it cannot differentiate between bubble or particle. It is also affected by the diffractions caused by bubbles and particles in its vicinity and therefore some bubbles might be ‘hidden’. Photonic methods depend on the liquid being transparent to the wavelength of light but need not be transparent in the visible region. This gives an advantage to the photo-acoustic methods over optical methods. Arguably, there are fewer assumptions to be made for photonic methods, compared to acoustic methods for function inversion (a laser is essentially a monochromatic point source whereas the Colloids Interfaces 2019, 3, 65 7 of 20 insonation frequency is not as monodisperse). However, it is the inversion of the same ill-posed FredholmColloids integralInterfaces 2018 that, 2, makesx FOR PEER this REVIEW problem difficult [57]. 7 of 20

FigureFigure 3. 3. SprayTecSprayTec schematic. schematic.

OneOne of the of simplestthe simplest theories theories used used in in particle particle sizing through through laser laser diffraction diffraction is the is theFraunhofer Fraunhofer approximation.approximation. This This model model predicts predicts the the scattering scattering pattern pattern thatthat is created when when a asolid, solid, opaque opaque disc disc of a knownof a known size is size passed is passed through through a laser a laser beam. beam. This This means means that it it is is imperative imperative that that the thetransmission transmission of lightof light through through the the particle particle is assumedis assumed to to be be zero.zero. For a a bubble, bubble, that that never never happens. happens. This This model model is is satisfactorysatisfactory for largefor large particles particles (over (over 50- 50-µmµm diameter)diameter) but but it itdoes does not not describe describe the thescattering scattering exactly. exactly. The FraunhoferThe Fraunhofer approximation approximation is is no no longer longer usedused due to to the the assumptions, assumptions, which which do not do notnecessarily necessarily hold true for particles. However, they do hold true for bubbles. hold true for particles. However, they do hold true for bubbles. The particle is much larger than the wavelength of light employed. ISO 13320:2009 defines this The particle is much larger than the wavelength of light employed. ISO 13320:2009 defines this as as being greater than 40 times the wavelength of incident light (i.e., 25 µm when a He-Ne laser is µ beingused). greater The than other 40 approximation times the wavelength is that all sizes of incident of particle light scatter (i.e., with 25 equalm when efficiencies. a He-Ne That laser is isnot used). The othertrue, since approximation bubbles scatter is thatmore all than sizes particles of particle and a bubble scatter is with not opaque. equal e fficiencies. That is not true, since bubblesIt is for scatter the above more reasons than particles that Mie andtheory a bubble is utilised; is not all opaque.the particles are spherical. For bubbles Itsmaller is for than the above1 mm, reasonsthis approximation that Mie theory holds and is utilised; is also used all the for particlesthe RBA assumption are spherical. used For in bubblesthe smallerABS. than 1 mm, this approximation holds and is also used for the RBA assumption used in the ABS. However,However, refractive refractive indices indices for for the the material, material, mediummedium and and the the absorption absorption part part of the of refractive the refractive indexindex must must be be known known or estimated. estimated. These These can be canestimated be estimated for most substances for most and substances for bubbles—a and for comparatively a simpler prospect. Work has been conducted to demonstrate that laser diffraction is bubbles—a comparatively a simpler prospect. Work has been conducted to demonstrate that laser not very effective for obtaining cloud BSD [5]. Statistical methods need to be discussed since they are diffraction is not very effective for obtaining cloud BSD [5]. Statistical methods need to be discussed used in conjunction with any indirect forms of bubble size measurement. since they are used in conjunction with any indirect forms of bubble size measurement. 5. Statistical Analyses 5. Statistical Analyses Size distributions are expressed in terms of number averages (simple average based on the Sizenumber distributions of bubbles) are and expressed void fraction in terms averages of number (based on averages the volume (simple occu averagepied by the based bubbles). on the number of bubbles)In andparticle void sizing, fraction andaverages bubble sizing (based by onextens theion, volume there occupiedare several by methods the bubbles). to represent the InBSD. particle In the work sizing, presented and bubble herein, sizing there are by extension,quite a few larger there bubbles are several in the methods steady flow to condition represent the BSD.compared In the work to the presented oscillatory herein, flow condition. there are quiteHowever, a few with larger regard bubbles to the inbigger the steadybubbles, flow more condition are comparedproduced to the by the oscillatory steady flow, flow with condition. a significant However, contribution with to the regard BSD todue the to the bigger effect bubbles, of the volume more are on the average sizes. The volume of a larger bubble has a much higher weighting than the smaller produced by the steady flow, with a significant contribution to the BSD due to the effect of the volume bubble on gas throughput. Therefore, a bubble of 1 mm size has a 1000 times greater impact in terms on the average sizes. The volume of a larger bubble has a much higher weighting than the smaller of volumetric flowrate than a 100 µm bubble. This means that a thousand 100 µm bubbles would bubble on gas throughput. Therefore, a bubble of 1 mm size has a 1000 times greater impact in terms

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Colloids Interfaces 2018, 2, x FOR PEER REVIEW 8 of 20 of volumetric ﬂowrate than a 100 µm bubble. This means that a thousand 100 µm bubbles would needneed to to be be produced produced to to have have the the same same volume volume as as that that of of a a single single 1 1 mm mm bubble bubble resulting resulting in in a a skewed skewed BSDBSD due due to to this. this. Consider Consider 1000 1000 bubbles bubbles each each of of diameters diameters 1 1 µm,µm, 100 100 µm,µm, and and 500 500 µm.µm. Their Their number number contributioncontribution is is the the same same whereas whereas their volume contri contributionbution is much higher, as shown in Figure4 4..

Figure 4. Effect of volume contribution and number contribution on the average bubble size. Figure 4. Effect of volume contribution and number contribution on the average bubble size. Number mean is important when only the number of bubbles/particles is of interest. This is used Number mean is important when only the number of bubbles/particles is of interest. This is used when the number of bubbles is more important than obtaining the size (for example, applications such when the number of bubbles is more important than obtaining the size (for example, applications as dispersed air flotation and froth flotation). Differences in bubble size based on number mean and such as dispersed air flotation and froth flotation). Differences in bubble size based on number mean volume contribution has been described in the literature [58,59]. and volume contribution has been described in the literature [58,59]. Average bubble sizes vary with the particular data set being observed and are equally dependent Average bubble sizes vary with the particular data set being observed and are equally dependent on the analysis. However, this is amplified due to the change in the bubble dynamics. Analysis of on the analysis. However, this is amplified due to the change in the bubble dynamics. Analysis of single-bubble generation would not be a problem since both the average sizing values are fairly close single-bubble generation would not be a problem since both the average sizing values are fairly close to each other since the variance is lower. However, for cloud bubble dynamics, these effects become to each other since the variance is lower. However, for cloud bubble dynamics, these effects become prominent. When it comes to over 1 106–1 109 bubbles, even with a narrower size distribution, prominent. When it comes to over 1 × 106–1 ×× 109 bubbles, even with a narrower size distribution, large variances in bubble sizes are observed, depending on which method is used. For mass and heat large variances in bubble sizes are observed, depending on which method is used. For mass and heat transfer, it would generally be more appropriate to use void fraction for average bubble size for large transfer, it would generally be more appropriate to use void fraction for average bubble size for large sample sizes. The analysis utilises certain statistics (moments) used for calculating the different types sample sizes. The analysis utilises certain statistics (moments) used for calculating the different types of diameters. of diameters. The volume mean diameter is known as D4,3, also known as the third moment. The volume mean diameter is known as D4,3, also known as the third moment. Similarly, the Similarly, the surface area mean diameter is known as D3,2—the Sauter Mean Diameter [30,59,60]. surface area mean diameter is known as D3,2—the Sauter Mean Diameter [30,59,60]. The Specific Surface Area is the total area of the particles divided by their total weight. The Specific Surface Area is the total area of the particles divided by their total weight. Percentiles have been commonly used in particle sizing that determine the portion of particles Percentiles have been commonly used in particle sizing that determine the portion of particles which lie below or above the said percentage. which lie below or above the said percentage. Those used with particular emphasis are–Dx(10), Dx(50) and Dx(90). Those used with particular emphasis are – Dx(10), Dx(50) and Dx(90). These values are also used to calculate the span of a BSD, which is actually the width of the size These values are also used to calculate the span of a BSD, which is actually the width of the size distribution. This is done using distribution. This is done using Dx(90)–Dx(10) (6) 𝐷𝑥(90Dx)–𝐷𝑥(50) (10) (6) Percentiles become important in order to𝐷𝑥 characterise(50) the histogram and size distributions. All of these values can be found in the British Standard BS2955:1993 or the ISO 13320:2009. Percentiles become important in order to characterise the histogram and size distributions. 6. HypothesisAll of these values can be found in the British Standard BS2955:1993 or the ISO 13320:2009.

6. HypothesisThe hypothesis of this paper is that acoustic methods are most accurate for small microbubbles since they are speciﬁc to bubbles, they do not miss small bubbles (since they rely upon the RBA) and The hypothesis of this paper is that acoustic methods are most accurate for small microbubbles since they are specific to bubbles, they do not miss small bubbles (since they rely upon the RBA) and

Colloids Interfaces 2019, 3, 65 9 of 20 can also be used in particle based systems due to this property (they neglect particles). They can also be used holistically rather than taking small sample sizes. Microbubble size distributions cannot be visually determined but need careful measurement and analysis in order to better characterise the system. The use of the fluidic oscillator as a means of controlled microbubble generation mediated by frequency changes aids in testing the hypothesis as it generates microbubbles of different size distributions at various frequencies. The crux of the hypothesis lies in the smaller population of the bubbles in order to test whether they ‘hide’ among the larger ones, which can be achieved using the fluidic oscillator. Whilst larger bubbles are simple to generate, smaller bubbles generated with a ceramic sparger are not as simple unless noncoalescent media [61] or surfactants [62,63] are added, which affect the sizing and visualisation paradigms.

7. Methods and Materials

7.1. Sparger Sintered alumina spargers (2 µm average pore size, 2 off–50 cm2 area), which produces a cloud of fine bubbles approximately 500 µm in size under steady flow [58] is used as the sparger in this study. This sparger, when coupled with the fluidic oscillator, can generate down to 7 µm in average bubble size (number average) [58].

7.2. Fluidic Oscillator (FO) A ﬂuidic oscillator [64] (FO) is coupled with the accompanying pneumatic setup, Malvern SprayTec, Acoustic Bubble Spectrometer (ABS), High Speed Visualisation Setup, and frequency analysis kit. The frequency of the oscillator determines the rate of bubble generation.

7.3. Frequency Measurement and Fast Fourier Transform Impress G-1000 pressure transducers and ADXL335 accelerometers are used. Fast Fourier Transforms are workhorse algorithms in signal processing, converting a signal from one domain (time or space) and to the frequency domain (and the inverse). The associated power spectrum provides a facile estimate the frequency of the oscillatory ﬂow from the ﬂuidic oscillator. LabView was used to acquire the signal and process it.

7.4. Microbubble Generation Setup The global flow rate (see Figure5) is controlled by a flow meter while an accelerometer is placed at one of the legs in order to record the frequency of the FO for maintenance of experimental conditions. A relatively high global flow rate is required in order for the FO to oscillate, but the bleed valves control the flow rate that the spargers receive. Two configurations generating ten frequency conditions for bubble formation are used in the FO–sparger combination. Twelve averages were taken for the ABS, with four each for the optical and photonic method. There is less than 3% error in the readings estimated for the ABS and SprayTec, while the optical method has 5% error levels. Systemic conditions were kept as constant as possible whilst comparing the different characterisation methods in order to introduce the least amount of replication error as possible. Since each technique has their own drawbacks and advantages, slight variations to the actual methods were required. For example, photonic and optical (single camera systems) methods can only be used for a single plane to image accurately or in a small space, so extrapolations have to be made. The acoustic method can size the entire population, but the hydrophones require separate use for two equiresponsive diffusers. The equivalence of the double sparger/hydrophone system to a single sparger plume is the major replication assumption made. Colloids Interfaces 2018, 2, x FOR PEER REVIEW 9 of 20 can also be used in particle based systems due to this property (they neglect particles). They can also be used holistically rather than taking small sample sizes. Microbubble size distributions cannot be visually determined but need careful measurement and analysis in order to better characterise the system. The use of the fluidic oscillator as a means of controlled microbubble generation mediated by frequency changes aids in testing the hypothesis as it generates microbubbles of different size distributions at various frequencies. The crux of the hypothesis lies in the smaller population of the bubbles in order to test whether they ‘hide’ among the larger ones, which can be achieved using the fluidic oscillator. Whilst larger bubbles are simple to generate, smaller bubbles generated with a ceramic sparger are not as simple unless noncoalescent media [61] or surfactants [62,63] are added, which affect the sizing and visualisation paradigms.

7. Methods and Materials

7.1. Sparger

Sintered alumina spargers (2 µm average pore size, 2 off – 50 cm2 area), which produces a cloud of fine bubbles approximately 500 µm in size under steady flow [58] is used as the sparger in this study. This sparger, when coupled with the fluidic oscillator, can generate down to 7 µm in average bubble size (number average) [58].

7.2. Fluidic Oscillator (FO) A fluidic oscillator [64] (FO) is coupled with the accompanying pneumatic setup, Malvern SprayTec, Acoustic Bubble Spectrometer (ABS), High Speed Visualisation Setup, and frequency analysis kit. The frequency of the oscillator determines the rate of bubble generation.

7.3. Frequency Measurement and Fast Fourier Transform Impress G-1000 pressure transducers and ADXL335 accelerometers are used. Fast Fourier Transforms are workhorse algorithms in signal processing, converting a signal from one domain (time or space) and to the frequency domain (and the inverse). The associated power spectrum provides a facile estimate the frequency of the oscillatory flow from the fluidic oscillator. LabView was used to acquire the signal and process it.

7.4. Microbubble Generation Setup The global flow rate (see Figure 5) is controlled by a flow meter while an accelerometer is placed at one of the legs in order to record the frequency of the FO for maintenance of experimental conditions. A relatively high global flow rate is required in order for the FO to oscillate, but the bleed Colloidsvalves Interfaces control2019 the, 3flow, 65 rate that the spargers receive. Two configurations generating ten frequency10 of 20 conditions for bubble formation are used in the FO–sparger combination. Colloids Interfaces 2018, 2, x FOR PEER REVIEW 10 of 20

Twelve averages were taken for the ABS, with four each for the optical and photonic method. There is less than 3% error in the readings estimated for the ABS and SprayTec, while the optical method has 5% error levels. Systemic conditions were kept as constant as possible whilst comparing the different characterisation methods in order to introduce the least amount of replication error as possible. Since each technique has their own drawbacks and advantages, slight variations to the actual methods were required. For example, photonic and optical (single camera systems) methods can only be used for a single plane to image accurately or in a small space, so extrapolations have to be made. The acoustic method can size the entire population, but the hydrophones require separate use for two equiresponsive diffusers. The equivalence of the double sparger/hydrophone system to a single sparger plume is the major replicationFigure 5. Pneumatic assumption setup made. for bubble generation. Figure 5. Pneumatic setup for bubble generation. 7.5. Optical Optical Methods–High-Speed Methods–High-Speed Photography The visualisation visualisation device device (see (see Figure Figure 6)6) is is a a high-speed high-speed camera, camera, (Photron (Photron FastCam FastCam S3) S3) capable capable of 250,000of 250,000 fps fpswithwith a resolution a resolution of 1024 of 1024 × 10241024 and andprovided provided with with a lens a lens(Nikon (Nikon Nikkor Nikkor Lens, Lens, 1.8 D). 1.8 The D). × 3 regionThe region of interest of interest used usedwas 1.764 was 1.764 cm3 (this cm takes(this takesinto account into account the different the diff focalerent planes focal planes used in used order in toorder capture to capture sufficient suffi data).cient data). A single plane is used, as the image analysis so softwareftware is is not not designed designed for for a a cloud cloud of of bubbles. bubbles. Desai etet al.al [58[58]] is is the the only only other other significant significant work work done ondone 3D cloudon 3D bubble cloud dynamics, bubble dynamics, but no automated but no automatedimage analysis image on aanalysis 3D bubble on populationa 3D bubble has population been developed has been yet developed except attempting yet except to do attempting so [7]. It was to doassumed so [7]. It that was it wouldassumed be that an equiresponsive it would be an equiresponsive surface and that surface a single and plane that coulda single be plane representative could be representativeas a microcosm as of a themicrocosm overall cloud of the dynamical overall cloud system. dynamical The appropriateness system. The appropriateness of this assumption of this in assumptionrepresentativeness in representativeness is one area where is one errors area in where measurement errors in are measurement introduced. are introduced. The systemic conditions are kept constant as describeddescribed in the bubble generating system section.

Figure 6. Setup for optical methods comparison study. Figure 6. Setup for optical methods comparison study.

7.6. Photonic Method–SprayTec SprayTec (see Figure 7) images a small sampling window. Within this field of vision, the statistical homogeneity and stationarity assumptions are made: bubbles are being produced equally from all regions of the spargers and that surface imperfections are negligible. The uniformity of this

Colloids Interfaces 2019, 3, 65 11 of 20

7.6. Photonic Method–SprayTec SprayTec (see Figure7) images a small sampling window. Within this ﬁeld of vision, the statistical homogeneity and stationarity assumptions are made: bubbles are being produced equally from all Colloids InterfacesInterfaces 2018 2018, ,2 2, ,x x FOR FOR PEER PEER REVIEW REVIEW 11 of 11 20 of 20 regions of the spargers and that surface imperfections are negligible. The uniformity of this assumption is theassumption same problem is is the the same same as observed problem problem as for as observed observed optical methods.for for op opticaltical Themethods. methods. gamut The The of gamut the gamut bubble of theof the bubble population bubble population population is possible onlyis forpossiblepossible a small onlyonly test forfor cell aa smallsmall in case test test of cell bubblecell in in case case generation. of of bubble bubble Usuallygeneration. generation. itis Usually notUsually required it isit notis whennot required required compared when when to a spray.compared The SprayTec toto a a spray. spray. is The ableThe SprayTec SprayTec to infer is BSDs is able able to whilst to infe infer automaticallyBSDsr BSDs whilst whilst automatically automatically adjusting foradjusting adjusting the change for forthe the inchange refractive change indexin refractiverefractive due to the indexindex addition due due to to of the the the addition addition test cell. of of th For the etest an test example,cell. cell. For For an seean example, example, Figure see8. see Figure Figure 8. 8.

Figure 7. SprayTec setup – addition of fluidic oscillator and sparger into the modified SprayTec Figure 7. SprayTec setup–addition of ﬂuidic oscillator and sparger into the modiﬁed SprayTec system systemFigure (see7. SprayTec Figure 4 forsetup the standard– addition system). of fluidic oscillator and sparger into the modified SprayTec (seesystem Figure (see4 for Figure the standard 4 for the system).standard system).

Figure 8. Example of spectrum for SprayTec. The red line is the cumulative volume graph. The BSD is Figure 8. Example of spectrum for SprayTec. The red line is the cumulative volume graph. The BSD provided with volume frequency as a metric. is provided with volume frequency as a metric. Figure 8. Example of spectrum for SprayTec. The red line is the cumulative volume graph. The BSD is provided with volume frequency as a metric.

Colloids Interfaces 2019, 3, 65 12 of 20 Colloids Interfaces 2018, 2, x FOR PEER REVIEW 12 of 20

The 300 mmmm lenslens waswas usedused withwith particulateparticulate refractiverefractive indexindex setset atat 11+0.01I,+0.01I, dispersant refractive indexindex setset atat 1.33.1.33. The particle density was 1.231.23 gg/cm/cm33 with residual set at 2.15% for the data. The transmission measurement involves a spatial filteringfiltering of the collimated laser beam pre andand postpost transmissiontransmission through through the the bubble bubble cloud. cloud. The The spatial spat filterial filter is the is pinhole the pinhole at the centreat the ofcentre the detector of the array.detector As array. well as As being well usedas being to ensure used theto ensure detector the array, detector it is centredarray, it onis centred the laser on beam the laser and also beam rejects and anyalso scatteredrejects any light. scattered This islight. important, This is important, as it removes as it backscatter removes backscatter for most cases.for most However, cases. However, for high scatterers,for high scatterers, such as bubbles,such as bubbles, due to concentration due to concentrat effects,ion effects, multiple multiple scattering scattering inevitably inevitably causes causes some lightsome to light be rescatteredto be rescattered back toback a near-zero to a near-zero scattering scattering angle. angle. The laserThe laser used used in SprayTec in SprayTec is a 632.8 is a 632.8 nm, 2mWnm, 2mW helium-neon helium-neon laser. Thelaser. transmitter The transmitter contains contains the He:Ne the laser He:Ne source laser which source produces which aproduces collimated a beamcollimated of 10 beam mm diameter of 10 mm with diameter a wavelength with a wavelength of 632.8 nm. of 632.8 nm. The detectors (over 30 ofof them),them), withwith thethe useuse ofof high-ehigh-efficiencyfficiency spatialspatial filtering,filtering, meansmeans thethe concentration calculation is reliable overover aa muchmuch widerwider concentrationconcentration range than a method based on measuring total scattered energy. ThisThis methodmethod requiresrequires nono calibrationcalibration andand isis ableable to carry out bubble sizing inin realreal time.time. The media set are water andand air.air.

7.7. Acoustic Method–Acoustic Bubble Spectrometer (ABS) The measurements involvinginvolving thethe ABS used four pairs of hydrophones with resonant frequencies at 5050 kHz,kHz, 150150 kHz,kHz, 250250 kHzkHz andand 500500 kHz.kHz. This ensured that the entire gamut of the BSDBSD couldcould bebe observed. TheThe hydrophones hydrophones were were placed placed opposite opposi eachte othereach andother the and bubbles the insonatedbubbles byinsonated ultrasound. by Theultrasound. frequency The of insonationfrequency determinesof insonation bubble determ sizeines and attenuationbubble sizeprovides and attenuation the number provides of bubbles. the Thenumber bubble of sizesbubbles. obtained The bubble are for sizes the entire obtained sparger are andfor arethe nearentire real sparger time measurements. and are near real Figure time9 showsmeasurements. the setup Figure for the 9 experiment shows the setup with thefor ABS.the experiment with the ABS.

Figure 9. Setup for the ABS—addition ofof thethe fluidicfluidic oscillator oscillator to to an an octophonic octophonic ABS ABS system system (see (see Figure Figure2 for2 for standard standard stereophonic stereophonic ABS ABS setup). setup). 8. Results 8. Results A comparison is made on the bubble sizing with the three methods. To ensure repeatability A comparison is made on the bubble sizing with the three methods. To ensure repeatability of of bubble sizes, the frequencies of oscillation was measured using accelerometers and a pressure bubble sizes, the frequencies of oscillation was measured using accelerometers and a pressure transducer. Figures 10 and 11 show the average bubble sizes estimated for the spargers at different FO transducer. Figure 10 and Figure 11 show the average bubble sizes estimated for the spargers at frequencies at different configurations using the three visualisation methods. different FO frequencies at different configurations using the three visualisation methods.

Colloids Interfaces 2018, 2, x FOR PEER REVIEW 13 of 20

Colloids InterfacesColloids 2018 Interfaces, 2, x FOR 2018 PEER, 2, xREVIEW FOR PEER REVIEW 13 of 20 13 of 20 Colloids InterfacesColloidsColloids Interfaces 2018Interfaces, 2, x2019 2018FOR, ,3 PEER2,, 65 x FOR REVIEW PEER REVIEW 13 of 20 13 of of 20 20

Figure 10. Average BUBBLE SIZES at different frequencies of bubble generation for different methods

( - ABS , - SprayTec, - optical methods ). Figure 10. AverageFigure 10. BUBBLE Average SIZES BUBBLE at different SIZES frequencieat differents frequencieof bubble generations of bubble forgeneration different for methods different methods Figure 10.FigureFigure Average 10.10. AverageAverage BUBBLE BUBBLEBUBBLE SIZES at SIZES SIZESdifferent atat didifferent frequencieﬀerent frequenciesfrequencies of bubbles ofof generation bubblebubble generationgeneration for different forfor didifferent methodsﬀerent methodsmethods The acoustic method shows an average bubble size with smaller bubbles than the other methods. ( Even -( ABS( for , conditions -ABS, - ABS , with - SprayTec,-SprayTec, the same - SprayTec, average -optical bubbl- optical methodse size,methods - optical their ). ). respective methods ). BSD is different. ( ( - ABS , - ABS , - SprayTec, - SprayTec, - optical -methods optical methods ). ). The acousticThe method acoustic shows method an average shows an bubble average size bubble with smaller size with bubbles smaller than bubbles the other than methods. the other methods. The acousticThe acoustic method method shows an shows average an average bubble sizebubble with size smaller with smallerbubbles bubbles than the than other the methods. other methods. Even for conditionsEven for conditions with the same with average the same bubbl averagee size, bubbl theire respectivesize, their respectiveBSD is different. BSD is different. Even forEven conditions for conditions with the with same the average same average bubble size,bubbl theire size, respective their respective BSD is different.BSD is different.

FigureFigure 11.11. AverageAverage bubblebubble sizes at didifferentﬀerent frequencies of bubble generation generation fo forr different diﬀerent methods methods (

( -ABS, -SprayTec, -optical methods ). - ABS , - SprayTec, - optical methods ). Figure 11. AverageFigure 11. bubble Average sizes bubble at different sizes atfrequencies different frequenciesof bubble generation of bubble fogenerationr different fo methodsr different ( methods ( Figure 11.TheFigure Average acoustic 11. Average bubble method sizes bubble shows at differentsizes an at average different frequencies bubble frequencies of bubble size withof generation bubble smaller generation fo bubblesr different fo thanr different methods the other methods ( methods. ( EvenAlthough for conditions the SprayTec with the sameseems average to correlate bubble well size, with their the respective high-speed BSD camera is different. and the ABS, the - ABSaverage , bubble- ABS - SprayTec, , sizes obtained - SprayTec, by - optical the ABS methods -are optical lower. ). methods Substantial ). data is condensed into a single point, - ABSAlthough ,- ABS the , - SprayTec SprayTec, - SprayTec, seems to correlate - optical -methods welloptical with methods ). the high-speed ). camera and the ABS, the average bubbleresulting sizes in a obtainedloss of fidelity by the and ABS understanding. are lower. Substantial The window data used is for condensed bubble sizing into aalso single influences point, Although Althoughthe SprayTec the seemsSprayTec to correlateseems to well correlate with wellthe high-speed with the high-speed camera and camera the ABS, and thethe ABS, the Althoughresultingthe determinationAlthough the in aSprayTec loss the of ofSprayTec fidelity theseems bubble and toseems correlate understanding.size. to Forcorrelate well ABS, with thewell The thesizes windowwith high-speed obtained the used high-speed can forcamera bubblebe smaller cameraand sizing the ifand ABS,using also the influencesthe aABS, smaller the average bubbleaverage sizes bubble obtained sizes by obtained the ABS by are the lower. ABS Suarebstantial lower. Su databstantial is condensed data is condensed into a single into point, a single point, averagetheacquisitionaverage bubble determination sizesbubble window. obtained sizes of Due theobtained by bubble tothe the ABS by number size. the are ABS lower. For average are ABS, Su lower.bstantial the calculations, sizesSubstantial data obtained is the condensed data average can is condensed be bubble smallerinto a single sizes into if using become apoint, single a smaller point,much resulting inresulting a loss of in fidelity a loss andof fidelity understanding. and understanding. 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Colloids Interfaces 2018, 2, x FOR PEER REVIEW 14 of 20

the accuracy is reduced for a polydisperse distribution, but increased accuracy for a narrower size distribution. The averaging performed reduces the induced errors. The ABS records a much larger sample size, due to the volume subtended by the hydrophones being much larger. This results in a more comprehensive BSD.

9. Discussion The results in Figure 10 and Figure 11 demonstrate that there is a certain size difference obtained for the various conditions. This is due to the loss in fidelity due to the reduction of an extremely large dataset into a singular point. Since bubble sizing normally deals with the number average, it is used here. For Figure 12, the bubbles formed are recorded over several averages for an acquisition time of 200 ms in order to collate the maximum breadth of information achievable with the available computational power. This is for a normalised volume of 1 cm3 and the y-axis is a logarithmic scale. As can be seen, the bubbles smaller than 150 µm are recorded for both SprayTec and the ABS. A general trend that was observed is that the average measured by ABS is smaller than the SprayTec or the high-speed camera. Several averages are taken for the SprayTec automatically, which enhances accuracy, especially for narrow size distributions. High-speed photography and the SprayTec cannot differentiate between bubbles and particles whereas the ABS measures only bubble size. ABS also obtains the gamut of the bubble size within the volume of liquid between the two Colloidshydrophones. Interfaces 2019 However,, 3, 65 this also means that one has to use larger bins, shorter acquisition times14 and of 20 high-speed acquisition, i.e., a powerful computing package. Figure 13 is an example of a BSD expandedthe accuracy from is a reduced single point for a from polydisperse Figure 11. distribution, The differences but in increased the bubble accuracy sizes for for the a three narrower methods size candistribution. be seen here. The Whilst averaging the average performed bubble reduces size themight induced be similar, errors. the The BSD ABS is quite records different. a much larger sampleFigure size, 12 due is a to BSD the expanded volume subtended from another by the point hydrophones from Figure being 10. However, much larger. it can This be clearly results seen in a thatmore the comprehensive BSDs are different BSD. and just merely balanced out even with the averaging performed. The ABS and SprayTec measure the smaller bubbles and these bubbles are not accounted for by the optical methods.9. Discussion There are also larger bubbles observed but the per cm3 figure is a construct in some sense for the SprayTec and the optical method. This is because optical methods measure a plane and not a The results in Figures 10 and 11 demonstrate that there is a certain size diﬀerence obtained for the significant depth. The depth has to be introduced artificially and expanded. Likewise, for the various conditions. This is due to the loss in ﬁdelity due to the reduction of an extremely large dataset SprayTec the volume has to be modified appropriately in order to get values per cm3. The ABS on the into a singular point. Since bubble sizing normally deals with the number average, it is used here. other hand, has to be reduced by calculations as the gamut and volume captured is larger than 1 cm3. This For Figure 12, the bubbles formed are recorded over several averages for an acquisition time brings about a more statistically significant value but has the drawback that salient features can sometimes of 200 ms in order to collate the maximum breadth of information achievable with the available be missed due to lack of computing power. The BSD would be better for the SprayTec if the sampling computational power. This is for a normalised volume of 1 cm3 and the y-axis is a logarithmic scale. chamber were designed accordingly so as to be able to collate a comprehensive size distribution. As can be seen, the bubbles smaller than 150 µm are recorded for both SprayTec and the ABS.

( ,, p) 100000

10000

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1 <150 150-250 250-350 350-450 450-550 550-650 650-750 >750 ColloidsColloids InterfacesColloids Interfaces Interfaces 2018 ,2018 2, x 2018 ,FOR 2, x, FOR2PEER, x FOR PEER REVIEW PEER REVIEW REVIEW Bubble Diameter (µm) 15 of 15 20 of 15 20 of 20

FigureFigure 12.FigureFigure BSD 12. BSD12.for 12. BSDcondition forBSD conditionfor for condition conditionat 257Hz at 257Hz at in at 257Hz 257HzFigure in Figure in in10. Figure Figure 10. 10. 10 -. Optical - Optical-Optical - methodOptical method method, method, , , - SprayTec,-SprayTec, - SprayTec, - SprayTec, -Acoustic - Acoustic - Acoustic- bubbleAcoustic bubbl bubbl spectrometry.e spectrometry.bubble spectrometry.e spectrometry. A general trend that was observed is that the average measured by ABS is smaller than the SprayTec or the high-speed camera. Several averages are taken for the SprayTec automatically, which enhances

accuracy, especially100001000010000 for narrow size distributions. High-speed photography and the SprayTec cannot differentiate between bubbles and particles whereas the ABS measures only bubble size. ABS also obtains the gamut of the bubble size within the volume of liquid between the two hydrophones. 3 3 However, this10003 1000 also1000 means that one has to use larger bins, shorter acquisition times and high-speed acquisition, i.e., a powerful computing package. Figure 13 is an example of a BSD expanded from a single point from Figure 11. The differences in the bubble sizes for the three methods can be seen here. Number/cm Number/cm Whilst the average100 Number/cm 100 100 bubble size might be similar, the BSD is quite different. Figure 12 is a BSD expanded from another point from Figure 10. However, it can be clearly seen that the BSDs are different and just merely balanced out even with the averaging performed. The ABS 10 10 and SprayTec measure10 the smaller bubbles and these bubbles are not accounted for by the optical methods. There are also larger bubbles observed but the per cm3 figure is a construct in some sense for the SprayTec and the optical method. This is because optical methods measure a plane and not a 1 1 1 significant depth.<150 The<150 depth 150-250<150 150-250 has 150-250 250-350 to 250-350be introduced 250-350 350-450 350-450 350-450 450-550 artificially 450-550 450-550 550-650 550-650 and 550-650 650-750 expanded.650-750 650-750 >750 >750 Likewise, >750 for the SprayTec BubbleBubble DiameterBubble Diameter Diameter(µm) (µm) (µm) the volume has to be modified appropriately in order to get values per cm3. The ABS on the other hand, has to be reduced by calculations as the gamut and volume captured is larger than 1 cm3. This brings

FigureFigure 13.Figure BSD13. BSD13. for BSD thefor dataforthe thedata poi datant poi – ntpoi265Hz –nt 265Hz – in 265Hz Figure in Figure in 10.Figure 10. 10. - Optical - Optical - Opticalmethod method method, , -, SprayTec, - SprayTec, - SprayTec,

- Acoustic - Acoustic - Acoustic bubble bubble spectrometry.bubble spectrometry. spectrometry.

TheThe ABSThe ABS needs ABS needs to needs have to have to the have samplingthe thesampling sampling chamber chamber chamber big enbigough bigenough en forough thefor forhydrophonesthe thehydrophones hydrophones to fit to in, fit to in in, fit order inin, order in order to obtainto obtainto aobtain BSD. a BSD. aWith BSD. With this With thisin place,this in place, in the place, ABSthe theABS can ABS canalso can al beso alused beso usedbe outside used outside outside the liquidthe theliquid andliquid and in anotherand in another in another liquid liquid liquid if theif acoustictheif theacoustic acoustic impedance impedance impedance is matched. is matched. is matched. This This means This means thatmeans that the that ABSthe theABS can ABS canbe usedcan be used be in used optically in optically in optically opaque opaque opaque media. media. media. LiquidsLiquidsLiquids usually usually usually have have ahave higher a highera higheracoustic acoustic acoustic transparency transparency transparency over over optical over optical opticaltransparency. transparency. transparency. If theIf theacousticIf theacoustic acoustic impedanceimpedanceimpedance of the of theliquidof theliquid isliquid known, is known, is known, and and the and theresona theresona ntresona frequencynt frequencynt frequency of the of thehydrophoneof thehydrophone hydrophone can canbe can obtained,be obtained,be obtained, ABSABS canABS canbe usedcan be usedbe for used thefor forthebubble thebubble bubblesizing sizing insizing a invariety a in variety a varietyof liquids. of liquids. of liquids. This This is Thisnot is nottrue is nottrue for true opticalfor foroptical opticalmethods methods methods nor nor nor for photonicfor forphotonic photonic methods. methods. methods. PhotonicPhotonicPhotonic methods methods methods depend depend depend on diffractionon diffractionon diffraction and and ther and therefore therefore areefore arenot are notspecific notspecific specific to bubbles. to bubbles.to bubbles. The The ABS The ABS is ABS is is bubblebubble bubblespecific, specific, specific, while while optical while optical opticalmethods methods methods tend tend to tendmiss to miss toth missis thdistinctionis th distinctionis distinction and and also and also have also have problems have problems problems with with non- with non- non- circularcircularcircular or overlapping or overlappingor overlapping bubbles. bubbles. bubbles. Bubbles Bu bblesBu withbbles with neighbouring with neighbouring neighbouring particles particles particles affect affect the affect theBSD theBSD obtained BSD obtained obtained with with with SprayTec,SprayTec,SprayTec, while while image while image analysisimage analysis analysis is made is made is difficult made difficult difficult for overlappingfor foroverlapping overlapping or coalescing or coalescing or coalescing bubbles. bubbles. bubbles. Scattering Scattering Scattering of of of laserlaser lightlaser light is light very is veryis sensitive very sensitive sensitive to changesto changesto changes in anyin any ininherent any inherent inherent conditions conditions conditions (temperature, (temperature, (temperature, contamination, contamination, contamination, smallersmallersmaller bubbles, bubbles, bubbles, smudges, smudges, smudges, etc.), etc.), resulting etc.), resulting resulting in errors in errors in inerrors measurement. in measurement. in measurement. Scattering Scattering Scattering also also neglects also neglects neglects smaller smaller smaller bubblesbubblesbubbles as they as theyas ‘hide’ they ‘hide’ behind ‘hide’ behind behindthe thlargere thlargere bubbles.larger bubbles. bubbles. Both Both SprayTec Both SprayTec SprayTec and and the and theABS theABS depend ABS depend depend on inversionson inversionson inversions as wellas aswell as well statisticalas asstatistical statistical techniques techniques techniques in orderin orderin toorder inferto inferto ainfer BSD.a BSD.a InversionBSD. Inversion Inversion propagates propagates propagates errors errors errorsin thein thein the measurementmeasurementmeasurement to errors to errors to inerrors the in estimatedthe in theestimated estimated BSD. BSD. BSD. TheThe ceramicThe ceramic ceramic spargers spargers spargers are arecommercially arecommercially commercially availabl availabl available microbubblee microbubblee microbubble generators generators generators and and are and aresupposed aresupposed supposed to to to be equiresponsive.be equiresponsive.be equiresponsive. This This is Thisalso is also anis also assumptionan assumptionan assumption that that introduces that introduces introduces errors errors inerrors the in the systemin thesystem systemas not as notonlyas notonly does only does does this thiscreatethis create ancreate erroran erroran for error thefor forthethree thethree methods three methods methods but butcan but canalso can also introduce also introduce introduce errors errors witherrors with the with theABS theABS since ABS since it since treats it treats it treats bubblebubble bubbleclouds clouds cloudsfrom from two from two spargers two spargers spargers at the at thesameat thesame time. same time. Smaller time. Smaller Smaller bubble bubble bubblesizes sizes might sizes might bemight observedbe observedbe observed using using using acousticacousticacoustic methods methods methods since since liquids since liquids liquidsare aremore aremore transparent more transparent transparent to sound to sound to thansound than light. than light. The light. The bubbles The bubbles bubbles are twoare aretwo phase two phase phase entitiesentitiesentities with with distinct with distinct distinct boundaries, boundaries, boundaries, possibly possibly possibly able able to scable toatter sc toatter lightscatter light in light such in such in a waysuch a way that a way that the that entirethe theentire population entire population population is notis notmeasured.is notmeasured. measured. As demonstrated As demonstratedAs demonstrated previously, previously, previously, acoust acoustic acoust methodsic methodsic methods are moreare aremore consistent more consistent consistent for bubblefor bubblefor bubblesizing sizing sizing withwith thewith abilitythe theability toability provide to provide to provide a wider a wider a range wider range BSD. range BSD. BSD. In caseIn case Inof caseoptical of optical of opticaland and photonic and photonic photonic techniques, techniques, techniques, vigne vignetting vignetting mighttting might affect might affect the affect resultsthe theresults resultsdue due to thedue to incorrectthe to theincorrect incorrect measurementmeasurementmeasurement of light of light of scattering light scattering scattering angles angles resultingangles resulting resulting from from incorrect from incorrect incorrect focusing. focusing. focusing. This This is Thiseasier is easier is to easier correct to correct to correctfor for for opticaloptical opticalmethods methods methods but butnot but notso with notso with so photonic with photonic photonic methods. methods. methods. Optical Optical Optical methods methods methods also also suffer also suffer from suffer from the from factthe the factthat fact that the that the the lenseslenses andlenses and focusing and focusing focusing ability ability canability canvery can very limited. very limited. limited. The The bubble The bubble bubblesize size can size canbe eithercan be eitherbe magnified either magnified magnified and and a small and a small a ROI small ROI ROI

Colloids Interfaces 2019, 3, 65 15 of 20 Colloids Interfaces 2018, 2, x FOR PEER REVIEW 15 of 20

about a more statistically signiﬁcant value but has the drawback that salient features can sometimes be missedFigure due 12. to BSD lack for of condition computing at 257Hz power. in Figure The BSD 10. would - Optical be better method for the , SprayTec - SprayTec, if the sampling chamber- Acoustic were bubbl designede spectrometry. accordingly so as to be able to collate a comprehensive size distribution.

10000

3 1000

Number/cm 100

1 <150 150-250 250-350 350-450 450-550 550-650 650-750 >750 Colloids Interfaces 2018, 2, x FOR PEER REVIEWBubble Diameter (µm) 15 of 20 Colloids Interfaces 2018, 2, x FOR PEER REVIEW 15 of 20 Colloids Interfaces 2018, 2, x FOR PEER REVIEW 15 of 20

Figure 13. Figure FigureBSD BSD 12.for 12. forBSD the BSD the fordata for datacondition conditionpoi point –nt–265Hz 265Hzat at257Hz 257Hz in in Figure in Figure Figure Figure 10. 10. 1010. . - Optical --Optical Optical - Optical method method method, method , , , - -SprayTec,SprayTec, - SprayTec, - SprayTec, - Acoustic bubble spectrometry. -Acoustic- Acoustic bubble bubbl spectrometry.e spectrometry. Figure 12. BSD for condition at 257Hz in Figure 10. - Optical method , - SprayTec, - Acoustic bubble spectrometry. - Acoustic bubble spectrometry. The ABS needs to have the sampling chamber big enough for the hydrophones to ﬁt in, in order The ABS needs to have the sampling chamber big enough for the hydrophones to fit in, in order to obtain a BSD. With this in place, the ABS can also be used outside the liquid and in another liquid to obtain a BSD. With this in place, the ABS can also be used outside the liquid and in another liquid if the acoustic impedance10000 is10000 matched. This means that the ABS can be used in optically opaque if the acoustic impedance is matched. This means that the ABS can be used in optically opaque media. media. Liquids usually have a higher acoustic transparency over optical transparency. If the acoustic 10000 Liquids usually have a higher acoustic transparency over optical transparency. If the acoustic impedance of the liquid is known, and the resonant frequency of the hydrophone can be obtained, 3 impedance of the liquid is3 1000known,1000 and the resonant frequency of the hydrophone can be obtained, ABS can be used for the bubble sizing in a variety of liquids. This is not true for optical methods nor ABS can be used for the bubble sizing in a variety of liquids. This is not true for optical methods nor 3 1000 for photonic methods. for photonic methods.

Photonic methods dependNumber/cm on diffraction and therefore are not specific to bubbles. The ABS is Photonic methods dependNumber/cm 100100 on diffraction and therefore are not specific to bubbles. The ABS is bubble specific, while optical methods tend to miss this distinction and also have problems with

Number/cm bubble specific, while optical methods tend to miss this distinction and also have problems with non- 100 non-circular or overlapping bubbles. Bubbles with neighbouring particles affect the BSD obtained with circular or overlapping bubbles. Bubbles with neighbouring particles affect the BSD obtained with SprayTec, while image analysis1010 is made difficult for overlapping or coalescing bubbles. Scattering of SprayTec, while image analysis is made difficult for overlapping or coalescing bubbles. Scattering of laser light is very sensitive to changes in any inherent conditions (temperature, contamination, 10 laser light is very sensitive to changes in any inherent conditions (temperature, contamination, smaller bubbles, smudges, etc.), resulting in errors in measurement. Scattering also neglects smaller smaller bubbles, smudges, etc.), resulting in errors in measurement. Scattering also neglects smaller bubbles as they ‘hide’ behind1 the1 larger bubbles. Both SprayTec and the ABS depend on inversions as bubbles as they ‘hide’ behind the<150 larger<150 150-250 bubbles. 150-250 250-350 250-350 Both 350-450 SprayTec 350-450 450-550 450-550 and 550-650 the 550-650 ABS 650-750 650-750 depend >750 >750 on inversions well as statistical techniques in order to infer a BSD. InversionBubbleBubble Diameter Diameter propagates (µm) (µm) errors in the measurement to 1 as well as statistical techniques in order to infer a BSD. Inversion propagates errors in the <150 150-250 250-350 350-450 450-550 550-650 650-750 >750 errors in the estimated BSD. Bubble Diameter (µm) measurement to errors in the estimated BSD. The ceramic spargers are commercially available microbubble generators and are supposed to be The ceramic spargers are commercially available microbubble generators and are supposed to equiresponsive.FigureFigure This 13. 13. is BSD alsoBSD for an for the assumption the data data poi point thatnt – 265Hz– introduces265Hz in in Figure Figure errors 10. 10. in the - Optical system- Optical method as method not only, , does - SprayTec, - SprayTec, this be equiresponsive. This is also an assumption that introduces errors in the system as not only does create an error for the three methods but can also introduce errors with the ABS since it treats bubble Figure 13. BSD for the data point – 265Hz in Figure 10. - Optical method , - SprayTec,this create an error for - Acoustic the three bubble methods spectrometry. but can also introduce errors with the ABS since it treats clouds from two spargers - Acoustic at bubble the same spectrometry. time. Smaller bubble sizes might be observed using acoustic bubble clouds from two spargers at the same time. Smaller bubble sizes might be observed using - Acoustic bubble spectrometry. methods since liquids are more transparent to sound than light. The bubbles are two phase entities acoustic methodsTheThe ABS since ABS needs needsliquids to to haveare have more the the sampling transparent sampling chamber chamber to sound big big thanen enoughough light. for for The the the bubbleshydrophones hydrophones are two to to phasefit fit in, in, in in order order with distinct boundaries, possibly able to scatter light in such a way that the entire population is not entities withtoto obtain obtain distinct a aBSD. boundaries,BSD. With With this this possibly in in place, place, able the the toABS ABSscatter can can allight alsoso be in be usedsuch used aoutside wayoutside that the the the liquid liquid entire and and population in in another another liquid liquid The ABS needs to have the sampling chamber big enough for the hydrophones to fitmeasured. in, in order As demonstrated previously, acoustic methods are more consistent for bubble sizing with is not measured.if ifthe the acoustic acoustic As demonstrated impedance impedance is previously, ismatched. matched. This acoust This means meansic methods that that the the are ABS ABS more can can consistent be be used used in infor optically optically bubble opaque sizing opaque media. media. to obtain a BSD. With this in place, the ABS can also be used outside the liquid and in anotherthe ability liquid to provide a wider range BSD. with theLiquids abilityLiquids tousually provideusually have ahave wider a ahigher rangehigher acousticBSD. acoustic transparency transparency over over optical optical transparency. transparency. If Ifthe the acoustic acoustic if the acoustic impedance is matched. This means that the ABS can be used in optically opaqueIn media. case of optical and photonic techniques, vignetting might affect the results due to the incorrect In caseimpedanceimpedance of optical of of andthe the photonicliquid liquid is is known,techniques, known, and and vigne the the resonatting resona mightntnt frequency frequency affect the of ofresults the the hydrophone hydrophone due to the incorrectcan can be be obtained, obtained, Liquids usually have a higher acoustic transparency over optical transparency. Ifmeasurement the acoustic of light scattering angles resulting from incorrect focusing. This is easier to correct for measurementABS ofcan light be usedscattering for the angles bubble resulting sizing in from a variety incorrect of liquids. focusing. This This is not is easier true for to opticalcorrect methodsfor nor impedance of the liquid is known, and the resonant frequency of the hydrophone can be obtained,ABS can be used for the bubble sizing in a variety of liquids. This is not true for optical methods nor optical methodsfor photonic but not methods. so with photonic methods. Optical methods also suffer from the fact that the ABS can be used for the bubble sizing in a variety of liquids. This is not true for optical methodsfor nor photonic methods. lenses and focusingPhotonic ability methods can very depend limited. on The diffraction bubble sizeand canther beefore either are magnified not specific and to a bubbles. small ROI The ABS is for photonic methods. Photonic methods depend on diffraction and therefore are not specific to bubbles. The ABS is bubble specific, while optical methods tend to miss this distinction and also have problems with non- Photonic methods depend on diffraction and therefore are not specific to bubbles. The ABSbubble is specific, while optical methods tend to miss this distinction and also have problems with non- circularcircular or or overlapping overlapping bubbles. bubbles. Bu Bubblesbbles with with neighbouring neighbouring particles particles affect affect the the BSD BSD obtained obtained with with bubble specific, while optical methods tend to miss this distinction and also have problems with non- SprayTec, while image analysis is made difficult for overlapping or coalescing bubbles. Scattering of circular or overlapping bubbles. Bubbles with neighbouring particles affect the BSD obtainedSprayTec, with while image analysis is made difficult for overlapping or coalescing bubbles. Scattering of laser light is very sensitive to changes in any inherent conditions (temperature, contamination, SprayTec, while image analysis is made difficult for overlapping or coalescing bubbles. Scatteringlaser of light is very sensitive to changes in any inherent conditions (temperature, contamination, smaller bubbles, smudges, etc.), resulting in errors in measurement. Scattering also neglects smaller laser light is very sensitive to changes in any inherent conditions (temperature, contamination,smaller bubbles, smudges, etc.), resulting in errors in measurement. Scattering also neglects smaller bubbles as they ‘hide’ behind the larger bubbles. Both SprayTec and the ABS depend on inversions smaller bubbles, smudges, etc.), resulting in errors in measurement. Scattering also neglects smallerbubbles as they ‘hide’ behind the larger bubbles. Both SprayTec and the ABS depend on inversions as well as statistical techniques in order to infer a BSD. Inversion propagates errors in the bubbles as they ‘hide’ behind the larger bubbles. Both SprayTec and the ABS depend on inversionsas well as statistical techniques in order to infer a BSD. Inversion propagates errors in the measurement to errors in the estimated BSD. as well as statistical techniques in order to infer a BSD. Inversion propagates errors inmeasurement the to errors in the estimated BSD. TheThe ceramic ceramic spargers spargers are are commercially commercially availabl available emicrobubble microbubble generators generators and and are are supposed supposed to to measurement to errors in the estimated BSD. be equiresponsive. This is also an assumption that introduces errors in the system as not only does The ceramic spargers are commercially available microbubble generators and are supposedbe equiresponsive.to This is also an assumption that introduces errors in the system as not only does this create an error for the three methods but can also introduce errors with the ABS since it treats be equiresponsive. This is also an assumption that introduces errors in the system as not onlythis does create an error for the three methods but can also introduce errors with the ABS since it treats bubble clouds from two spargers at the same time. Smaller bubble sizes might be observed using this create an error for the three methods but can also introduce errors with the ABS since it treatsbubble clouds from two spargers at the same time. Smaller bubble sizes might be observed using acoustic methods since liquids are more transparent to sound than light. The bubbles are two phase bubble clouds from two spargers at the same time. Smaller bubble sizes might be observed usingacoustic methods since liquids are more transparent to sound than light. The bubbles are two phase entities with distinct boundaries, possibly able to scatter light in such a way that the entire population acoustic methods since liquids are more transparent to sound than light. The bubbles are two phaseentities with distinct boundaries, possibly able to scatter light in such a way that the entire population is isnot not measured. measured. As As demonstrated demonstrated previously, previously, acoust acoustic icmethods methods are are more more consistent consistent for for bubble bubble sizing sizing entities with distinct boundaries, possibly able to scatter light in such a way that the entire population with the ability to provide a wider range BSD. is not measured. As demonstrated previously, acoustic methods are more consistent for bubble sizingwith the ability to provide a wider range BSD. In case of optical and photonic techniques, vignetting might affect the results due to the incorrect with the ability to provide a wider range BSD. In case of optical and photonic techniques, vignetting might affect the results due to the incorrect measurement of light scattering angles resulting from incorrect focusing. This is easier to correct for In case of optical and photonic techniques, vignetting might affect the results due to the incorrectmeasurement of light scattering angles resulting from incorrect focusing. This is easier to correct for optical methods but not so with photonic methods. Optical methods also suffer from the fact that the measurement of light scattering angles resulting from incorrect focusing. This is easier to correctoptical for methods but not so with photonic methods. Optical methods also suffer from the fact that the lenses and focusing ability can very limited. The bubble size can be either magnified and a small ROI optical methods but not so with photonic methods. Optical methods also suffer from the fact thatlenses the and focusing ability can very limited. The bubble size can be either magnified and a small ROI lenses and focusing ability can very limited. The bubble size can be either magnified and a small ROI

Colloids Interfaces 2019, 3, 65 16 of 20

Colloids Interfaces 2018, 2, x FOR PEER REVIEW 16 of 20 optical methods but not so with photonic methods. Optical methods also suffer from the fact that thecan lensesbe used, and otherwise focusing abilitya broader can veryregion limited. but a The larger bubble ROI size is used. can be This either means magnified that sub-150 and a small µm ROImeasurements can be used, would otherwise result ain broader a substantial region redaction but a larger for bubbles ROI is used. being This measured. means that sub-150 µm measurementsA point from would Figure result 11 in is a expanded substantial into redaction a BSD forin Figure bubbles 14. being The measured.ABS consistently measures smallerA pointbubbles from resulting Figure 11in isa smaller expanded BSD into and a BSDmuch in larger Figure number 14. The of ABS bubbles, consistently which would measures be smallerseverely bubblesskewed resultingfor the other in atwo smaller methods BSD due and to much the problems larger number of ‘hidden’ of bubbles, bubbles whichand overlapping would be severelybubbles. skewedThese, however, for the other are twonot methodsmissed by due the to AB theS. problems Thus, the of obtained ‘hidden’ bubblesBSDs vary and considerably. overlapping bubbles.When volume These, averages however, are are taken, not smaller missed bybubbles the ABS. do not Thus, contribute the obtained as much BSDs as the vary larger considerably. bubbles. WhenHowever, volume the problem averages with are taken,this measurement smaller bubbles is that do whilst not contribute it will reconcile as much the asdata the obtained larger bubbles. for the However,acoustic method the problem and SprayTec with this mo measurementre successfully, is that it shows whilst itmuch will reconcilelarger average the data bubble obtained size for the acousticoptical method, method since and SprayTec then the morevolume successfully, contributions it shows become much much larger larger. average Just bubbleas a billion size for 1 µm the opticalbubbles method, occupy sincethe same then thevolume volume as a contributions single 1 mm become bubble, much the bubbles larger. Just >750 as µm a billion will have 1 µm a bubbles larger occupycontribution. the same This volume will result as a singlein a much 1 mm larger bubble, average the bubbles bubble>750 sizeµ form will the haveoptical a larger method. contribution. The D50 and D4,3 are also, therefore, not that useful for this exchange. This also removes the effect that the This will result in a much larger average bubble size for the optical method. The D50 and D4,3 are also, therefore,small bubbles not that have useful on forthe thisBSD. exchange. The smaller This alsobubbles removes have the a emuchffect that higher the smallimpact bubbles on transport have on thephenomena BSD. The due smaller to their bubbles high have internal a much convection/mix higher impacting on as transport well as the phenomena rate of transfer due to their[65]. highThis internalmeans that convection with singular/mixing values as well in asbubble the rate sizes, of on transfere can have [65]. similar This means values that for with the system singular but values highly in bubblevaried performances sizes, one can that have are similar not effectively values for descr the systemibed. Since but highly the transport variedperformances phenomena associated that are not is ehighlyffectively dependent described. on Sincethe size the of transport the bubbles phenomena in question, associated the composition is highly dependent of the bubble on the sizecloud of can the bubblesmake a large in question, difference. the composition of the bubble cloud can make a large difference.

10000000

1000000

100000 3

10000

1000 Number/cm 100

1 <150 150-250 250-350 350-450 450-550 550-650 650-750 >750 Bubble Diameter (µm)

Figure 14. ShowsShows BSD BSD for for 87Hz 87Hz condition condition in in Figure Figure 11. 11 The. The bubble bubble size size difference diﬀerence is not is not as high as high in the in ColloidsColloidsColloids Interfaces Interfaces Interfacesthe 2018 points2018, 2 ,2018 x, FOR2, but,x 2 FOR, PEERx thereFOR PEER REVIEW PEER is REVIEW a substantialREVIEW BSD observed for bubbles smaller than 150 µm. The 15 of bubbles15 20 15 of 20 of 20 points but there is a substantial BSD observed for bubbles smaller than 150 µm. The bubbles recorded recorded are two orders of magnitude larger than the ones observed by SprayTec and over nine orders are two orders of magnitude larger than the ones observed by SprayTec and over nine orders of

FigureFigureFigure 12.of BSD12. magnitude 12. BSD for BSD conditionfor for condition as condition compared at 257Hz at 257Hz at 257Hz toin Figure optical in Figurein Figure 10. methods. 10. 10. - Optical - Optical-Optical - Optical method method method, method , , , - SprayTec,-SprayTec, - SprayTec, - SprayTec, -Acoustic magnitude as compared to optical methods. - Optical method , - SprayTec, - - Acoustic- Acoustic- Acousticbubble bubbl bubbl e spectrometry.bubbl spectrometry.e spectrometry.e spectrometry. Acoustic bubble spectrometry. 10. Conclusions 10. Conclusions Each of these methods offers distinct drawbacks and advantages. SprayTecEach10000 of these10000 and10000 methods the ABS are offers indirect distinct methods drawbacks used forand inferring advantages. BSD but offer near real time results withSprayTec enormous and acquisition the ABS capabilities. are indirect High-speedmethods used photography for inferring/videography BSD but offer are near a direct real time method results but arewith not enormous as effective acquisition for bubble capabilities. cloud dynamics, High-sp requiringeed photography/videography post processing and image are analysis.a direct method 3 3 but are not1000 as3 1000effective1000 for bubble cloud dynamics, requiring post processing and image analysis. The SprayTec needs an appropriately sized chamber for sampling to engender the gamut of the bubble spectra and is better for a smaller sample whereas the ABS is better for a larger system. The Number/cm Number/cm 100Number/cm 100100

10 10 10

1 1 1 <150<150<150 150-250 150-250 150-250 250-350 250-350 250-350 350-450 350-450 350-450 450-550 450-550 450-550 550-650 550-650 550-650 650-750 650-750 650-750 >750 >750 >750 BubbleBubble DiameterBubble Diameter Diameter (µm) (µm) (µm)

FigureFigureFigure 13. BSD13. 13. BSD for BSD forthe for thedata the data poi data ntpoi –point 265Hz –nt 265Hz – 265Hz in Figure in Figurein Figure 10. 10. 10. - Optical - Optical - Optical method method method , , , - SprayTec, - SprayTec, - SprayTec,

- Acoustic - Acoustic - Acoustic bubble bubble bubble spectrometry. spectrometry. spectrometry.

TheThe ABSThe ABS needs ABS needs needs to have to haveto thehave thesampling the sampling sampling chamber chamber chamber big bigen bigough en oughen forough forthe for thehydrophones the hydrophones hydrophones to fit to in,tofit fitinin, orderin, in inorder order to obtainto toobtain obtain a BSD. a BSD. a WithBSD. With thisWith this in this place, in inplace, place, the theABS the ABS can ABS can al canso al beso al usedsobe beused outsideused outside outside the theliquid the liquid liquid and and in and another in inanother another liquid liquid liquid if theif theacousticif the acoustic acoustic impedance impedance impedance is matched. is matched.is matched. This This means This means means that that the that theABS the ABS can ABS can be can usedbe beused inused optically in opticallyin optically opaque opaque opaque media. media. media. LiquidsLiquidsLiquids usually usually usually have have havea highera highera higher acoustic acoustic acoustic transparency transparency transparency over over opticalover optical optical transparency. transparency. transparency. If theIf If theacoustic the acoustic acoustic impedanceimpedanceimpedance of theof of theliquid the liquid liquid is known, is known,is known, and and the and theresona the resona resonant frequencynt ntfrequency frequency of theof of thehydrophone the hydrophone hydrophone can can be can obtained,be beobtained, obtained, ABSABS canABS can be can usedbe beused forused forthe for thebubble the bubble bubble sizing sizing sizing in a in variety ina variety a variety of liquids. of ofliquids. liquids. This This is This not is not istrue not true for true foroptical for optical optical methods methods methods nor nor nor for forphotonicfor photonic photonic methods. methods. methods. PhotonicPhotonicPhotonic methods methods methods depend depend depend on ondiffraction on diffraction diffraction and and ther and therefore therefore eforeare arenot are not specific not specific specific to bubbles.to tobubbles. bubbles. The The ABS The ABS isABS is is bubblebubblebubble specific, specific, specific, while while whileoptical optical optical methods methods methods tend tend to tend miss to missto th missis th distinction isth distinctionis distinction and and also and also have also have problemshave problems problems with with non- with non- non- circularcircularcircular or overlappingor oroverlapping overlapping bubbles. bubbles. bubbles. Bu bblesBu Bubbles bbleswith with neighbouringwith neighbouring neighbouring particles particles particles affect affect affectthe theBSD the BSD obtainedBSD obtained obtained with with with SprayTec,SprayTec,SprayTec, while while whileimage image image analysis analysis analysis is made is madeis madedifficult difficult difficult for foroverlapping for overlapping overlapping or coalescingor orcoalescing coalescing bubbles. bubbles. bubbles. Scattering Scattering Scattering of of of laserlaser laserlight light islight veryis isvery sensitivevery sensitive sensitive to changesto tochanges changes in anyin inany inherentany inherent inherent conditions conditions conditions (temperature, (temperature, (temperature, contamination, contamination, contamination, smallersmallersmaller bubbles, bubbles, bubbles, smudges, smudges, smudges, etc.), etc.), resultingetc.), resulting resulting in errorsin inerrors errors in measurement.in inmeasurement. measurement. Scattering Scattering Scattering also also neglects also neglects neglects smaller smaller smaller bubblesbubblesbubbles as theyas asthey ‘hide’they ‘hide’ ‘hide’ behind behind behind the thlarger eth largere larger bubbles. bubbles. bubbles. Both Both SprayTecBoth SprayTec SprayTec and and the and theABS the ABS depend ABS depend depend on oninversions on inversions inversions as aswell aswell aswell asstatistical asstatistical statistical techniques techniques techniques in inorder inorder orderto toinfer toinfer infera BSD.a BSD.a BSD.Inversion Inversion Inversion propagates propagates propagates errors errors errors in inthe in the the measurementmeasurementmeasurement to errors to toerrors errors in the in intheestimated the estimated estimated BSD. BSD. BSD. TheThe ceramicThe ceramic ceramic spargers spargers spargers are arecommercially are commercially commercially availabl availabl available microbubblee microbubblee microbubble generators generators generators and and are and aresupposed are supposed supposed to to to be equiresponsive.be beequiresponsive. equiresponsive. This This is This also is alsois an also assumptionan anassumption assumption that that introduces that introduces introduces errors errors errors in thein in thesystem the system system as notas asnot only not only doesonly does does thisthis createthis create create an erroran anerror errorfor forthe for thethree the three threemethods methods methods but but can but can also can also introduce also introduce introduce errors errors errors with with thewith theABS the ABS sinceABS since sinceit treats it treatsit treats bubblebubblebubble clouds clouds clouds from from twofrom two spargers two spargers spargers at theat at thesame the same sametime. time. time.Smaller Smaller Smaller bubble bubble bubble sizes sizes mightsizes might might be observedbe beobserved observed using using using acousticacousticacoustic methods methods methods since since liquidssince liquids liquids are aremore are more moretransparent transparent transparent to sound to tosound sound than than light.than light. light.The The bubbles The bubbles bubbles are aretwo are two phase two phase phase entitiesentitiesentities with with distinct with distinct distinct boundaries, boundaries, boundaries, possibly possibly possibly able able to able sc toatter sctoatter sc lightatter light in light such in suchin a such way a way a that way that the that theentire the entire entire population population population is notis not ismeasured. not measured. measured. As demonstratedAs As demonstrated demonstrated previously, previously, previously, acoust acoust acoustic methodsic methodsic methods are aremore are more consistentmore consistent consistent for forbubble for bubble bubble sizing sizing sizing withwith thewith theability the ability ability to provide to toprovide provide a wider a wider a wider range range rangeBSD. BSD. BSD. In caseIn Incase of case optical of opticalof optical and and photonic and photonic photonic techniques, techniques, techniques, vigne vigne ttingvignetting mighttting might might affect affect affectthe theresults the results results due due to due the to thetoincorrect the incorrect incorrect measurementmeasurementmeasurement of light of oflight scatteringlight scattering scattering angles angles angles resulting resulting resulting from from incorrectfrom incorrect incorrect focusing. focusing. focusing. This This is This easier is easieris easier to correct to tocorrect correct for for for opticalopticaloptical methods methods methods but but not but not so not withso sowith photonic with photonic photonic methods. methods. methods. Optical Optical Optical methods methods methods also also suffer also suffer suffer from from thefrom thefact the fact that fact that the that the the lenseslenseslenses and and focusing and focusing focusing ability ability ability can can very can very limited. very limited. limited. The The bubble The bubble bubble size size can size can be can eitherbe beeither either magnified magnified magnified and and a andsmall a small a smallROI ROI ROI

ColloidsColloids Interfaces Interfaces 20182019, 2, x, 3FOR, 65 PEER REVIEW 17 of 17 20 of 20

ABS operatesThe SprayTec more effectively needs an appropriatelywhen the hydropho sized chambernes are for placed sampling in the to engenderliquid medium the gamut whereas of the the ColloidsColloids InterfacesColloids Interfaces 2018Interfaces ,2018 2, x 2018,FOR 2, x, FORPEER2, x FOR PEER REVIEW PEER REVIEW REVIEW 17 of 17 20 of 17 20 of 20 lasersbubble need spectrato have and a clear is better path for to a smallertraverse sample through. whereas the ABS is better for a larger system. The ABS operatesThe ABS more does eff notectively require when a thesampling hydrophones chamber are placedto be transparent in the liquid mediumwhereas whereas SprayTec the and lasers high- ABSABS operatesABS operates operates more more effectively more effectively effectively when when the when hydrophothe thehydropho hydrophones nesare nesplacedare areplaced inplaced the in liquidthe in theliquid medium liquid medium medium whereas whereas whereas the the the speedneed photography to have a clear have path this to traverseprerequisite. through. An acoustically transparent substance need not be an laserslasers needlasers need to needhave to have toa clearhave a clear patha clear path to pathtraverse to traverse to traverse through. through. through. The ABS does not require a sampling chamber to be transparent whereas SprayTec and high-speed Theoptically TheABSThe ABS does transparent ABS does not does notrequire notrequire one. requirea sampling a sampling a sampling chamber chamber chamber to be to transparent be to transparentbe transparent whereas whereas whereas SprayTec SprayTec SprayTec and andhigh- and high- high- photography have this prerequisite. An acoustically transparent substance need not be an optically speedspeed photographyspeed Therefore,photography photography have application-specific have this have thisprerequisite. this prerequisite. prerequisite. constraintsAn Anacou Anacoustically acou willstically stically transparentdictate transparent transparent which substance systemsubstance substance need ought need not need to notbe be annot beused. anbe an transparent one. opticallyopticallyoptically transparentBubble transparent transparent sizes one. obtained one. one. are smaller when the ABS is used because the gamut of the bubble spectra Therefore, application-specific constraints will dictate which system ought to be used. Therefore,is obtainedTherefore,Therefore, application-specific for application-specific this application-specific system whereas constraints constraints constraintsSprayTec will willdictate canwill dictate onwhichdictately which observe system which system aoughtsystem small ought to ought section. be to used. be to used. beA planeused. had to be used Bubble sizes obtained are smaller when the ABS is used because the gamut of the bubble spectra Bubblefor Bubblethe sizesBubblehigh-speed sizes obtained sizes obtained obtained photography are smallerare aresmaller smallerwhen due when the towhen ABSthecomplications theABS is used ABS is used becauseis used becauserelating because the gamutthe to thegamutthe of gamut overlapping the of bubblethe of thebubble spectrabubble bubbles spectra spectra as well as is obtained for this system whereas SprayTec can only observe a small section. A plane had to be used is obtainedis obtainedis obtained for this for thissystemfor this system whereassystem whereas whereas SprayTec SprayTec SprayTec can oncanly canon observely on observely observe a small a small section.a small section. section. A plane A plane A had plane hadto be had to used be to used be used imagefor analysis the high-speed for cloud photography bubble dynamics. due to complications relating to the overlapping bubbles as well as for thefor high-speedthefor thehigh-speed high-speed photography photography photography due dueto complicationsdue to complications to complications relating relating relating to the to overlappingthe to theoverlapping overlapping bubbles bubbles bubbles as well as well as well as as imageFigure analysis 15 shows for the cloud percentage bubble dynamics. differences between pairs of methods among the three different imageimage analysisimage analysis analysis for cloudfor cloudfor bubble cloud bubble dynamics.bubble dynamics. dynamics. visualisationFigure techniques. 15 shows the It is percentage observed di that,fferences as per between the hypothesis, pairs of methods there is among a wide the difference three different with the FigureFigure 15Figure shows 15 shows 15 the shows percentagethe thepercentage percentage differences differences differences between between between pairs pairs of pairsmethods of methods of methods among among theamong threethe thethree different three different different ABS-Opticalvisualisation (79%) techniques. and SprayTec-Optical It is observed that,(68%)-based as per the systems. hypothesis, There there is is closer a wide agreement difference withwith the visualisationvisualisationvisualisation techniques. techniques. techniques. It is Itobserved is It observed is observed that, that, as that,per as theper as hypothesis,perthe thehypothesis, hypothesis, there there is therea wideis a iswide differencea wide difference difference with with the with the the ABS theand ABS-Optical SprayTec (79%)due andto the SprayTec-Optical controlled conditio (68%)-basedns in systems. this experimental There is closer setup agreement (nearly with zero ABS-OpticalABS-OpticalABS-Optical (79%) (79%) and (79%) andSprayTec-Optical and SprayTec-Optical SprayTec-Optical (68%)-based (68%)-based (68%)-based systems. systems. systems. There There is There closer is closer is agreement closer agreement agreement with with the with the the the ABS and SprayTec due to the controlled conditions in this experimental setup (nearly zero ABSABS particulates/additives/contaminationandABS andSprayTec and SprayTec SprayTec due dueto due theto thetocontrolled thecontrolled controlled conditioin theconditio conditiotestns innswa thisinnster) thisin experimentaland this experimental the experimental reasons setup setupdiscussed (nearlysetup (nearly (nearly zeropreviously zero zero agree particulates/additives/contamination in the test water) and the reasons discussed previously agree particulates/additives/contaminationparticulates/additives/contaminationwithparticulates/additives/contamination the close alignment with in the thein testthe inresults. thetestwa ter) testwa One ter)andwa ter) andpoint,the and reasonsthe thetherereasons reasons discussed is discusseda largediscussed previously discrepancypreviously previously agree agree between agree the with the close alignment with the results. One point, there is a large discrepancy between the withwith SprayTecthewith theclose theclose andalignment close alignment ABS alignment (49%, with with asthe withper theresults. Figure theresults. results.One 14) One point,at One87 point, Hz therepoint, condition, there is there a islarge a is andlarge adiscrepancy largethe discrepancy hypothesis discrepancy between between being between the tested. the the Smaller SprayTec and ABS (49%, as per Figure 14) at 87 Hz condition, and the hypothesis being tested. SprayTecSprayTecbubblesSprayTec and andABSare and ABShidden (49%, ABS (49%, as (49%,from per as Figureper asthe perFigure SprayTec 14) Figure at 14) 87 at14) Hz and87 at condition, Hz 87 Optical condition,Hz condition, andtype andthe systems, and hypothesisthe hypothesisthe hypothesisbut being not being for tested. being the tested. ABSSmaller tested. Smaller – isSmaller seen herein. Smaller bubbles are hidden from the SprayTec and Optical type systems, but not for the ABS–is bubblesbubblesSimilarly,bubbles are hiddenare arehiddenthe hiddenfrom 257-Hz from the from pointSprayTecthe theSprayTec shows SprayTec and andnearlyOptical and Optical 38%Opticaltype type discsystems, type systems,repancy systems, but not butbetween butfornot the notfor SprayTec ABSthefor theABS – is ABS seen– andis –seen herein.is ABS, seen herein. herein.which can be seen herein. Similarly, the 257-Hz point shows nearly 38% discrepancy between SprayTec and ABS, Similarly,Similarly,observedSimilarly, the 257-Hzthe in the257-Hz the 257-Hzpoint BSD point shows (as point shows seen nearly shows innearly Figure38% nearly 38% disc 38%12), discrepancy discwhererepancyrepancy between the between smallerbetween SprayTec SprayTec bubbles SprayTec and andABS, were and ABS, which ABS, not which can beingwhich canbe recordedcanbe be for which can be observed in the BSD (as seen in Figure 12), where the smaller bubbles were not being observedobservedobserved in the in BSDthe in theBSD (as BSD seen(as seen(as in seenFigure in Figure in 12),Figure 12),where 12),where thewhere smallerthe thesmaller smallerbubbles bubbles bubbles were were not were notbeing notbeing recorded being recorded recorded for for for the SprayTec.recorded for When the SprayTec. the bubble When throughput the bubble is throughputlow, the differences is low, the between differences the between SprayTec the SprayTecand ABS are the SprayTec.the theSprayTec. SprayTec. When When the When bubblethe thebubble throughputbubble throughput throughput is low, is low, the is low, differencesthe thedifferences differences between between between the SprayTecthe theSprayTec SprayTec and andABS and ABS are ABS are are reducedand ABSsignificantly, are reduced and significantly, the averaging and the results averaging in equal results average in equal bubble average size, bubble even size, though even though there is a reducedreducedreduced significantly, significantly, significantly, and andthe and averagingthe theaveraging averaging results results inresults equal in equal in average equal average average bubble bubble size,bubble size, even size, even though even though thoughthere there is therea is a is a differencethere is in a the diff erenceBSD (as in theseen BSD in Figure (as seen 13). in Figure It seems 13). likely It seems that likely the thatcause the of cause the discrepancy of the discrepancy between differencedifferencedifference in the in BSDthe in theBSD (as BSD seen (as seen(as in Figureseen in Figure in 13).Figure 13).It seems 13).It seems It likely seems likely that likely thatthe that causethe thcause eof cause the of discrepancythe of thediscrepancy discrepancy between between between the twobetween techniques the two at techniques high bubble at high throughput bubble throughput is as a result is as a of result bubble–bubble of bubble–bubble interactions interactions and and that if the twothe the twotechniques two techniques techniques at high at high bubbleat high bubble throughputbubble throughput throughput is as is a asresult is a as result aof result bubble–bubble of bubble–bubble of bubble–bubble interactions interactions interactions and andthat and thatif that if if that if it is not possible to measure at low bubble throughputs then modifications to Mie theory being it is itnotit is isit not possible isnot notpossible possible possible to measure to tomeasureto measuremeasure at low at low bubbleatat low lowbubble bubble throbubble throughputs throughputs throughputs thenughputs then modification then modification then modification modifications to sMie tos Mietotheory Mie stheory to beingtheoryMie being theory being being implemented into the analysis may result in a more robust analysis. implementedimplementedimplementedimplemented into intothe into into analysisthe the theanalysis analysisanalysis may may result maymay result in result resulta inmore a in more in robusta morea morerobust analysis.robust robust analysis. analysis. analysis.

FigureFigure 15.Figure 15.Percentage 15.Percentage Percentage Difference Difference Difference in averagein averagein averagebubbl bubble bubblsizese sizes efor sizes forthe forthepairs thepairs among pairs among amongthe thethree thethree three characterizationcharacterizationcharacterization FigureFigure 15. 15.PercentagePercentage DiDifferenceﬀerence in averagein average bubble sizesbubbl fore thesizes pairs for among the thepairs three characterisationamong the three characterization methods. methods. methods. (methods. ( (- (Spraytec- ( - -(Spraytec- (Spraytec- - (Spraytec- Optical), Optical), Optical), Optical), -(ABS- -(ABS- -(ABS- SprayTec), -(ABS- SprayTec), SprayTec), SprayTec), -(ABS-Optical)). - (AB - S-Optical)). (AB - S-Optical)).(ABS-Optical)).

DependingDepending methods.Depending on the on( uses,the on uses,the availability, - uses,(Spraytec- availability, availability, Optical),expertise expertise expertise and andthe -(ABS- and application,the application,the SprayTec), application, different different different methods methods - (AB methods canS-Optical)). becan used canbe used be used to computeto computeto compute the BSDthe theBSD and BSD andupon and upon significant upon significant significant infe rence,infe inference, accuraterence, accurate accurate BSDs BSDs can BSDs canbe estimated. canbe estimated. be estimated. Depending on the uses, availability, expertise and the application, different methods can be used to compute the BSD and upon significant inference, accurate BSDs can be estimated.

Colloids Interfaces 2019, 3, 65 18 of 20

Depending on the uses, availability, expertise and the application, diﬀerent methods can be used to compute the BSD and upon signiﬁcant inference, accurate BSDs can be estimated.

Author Contributions: P.D.D. and W.B.Z. wrote the paper, formulated the hypothesis, and conceptualised the framework for the paper. W.C.N., V.T., and Y.R. conducted experiments. W.C.N. designed the graphics and images in the paper. P.D.D., W.B.Z., V.T., and M.J.H. supervised the work. Funding: The authors acknowledge gratefully the Engineering and Physical Sciences Research Council (EPSRC) for supporting this work financially (Grant no. EP/K001329/1).This work was carried out as part of the “4CU” programme grant, aimed at sustainable conversion of carbon dioxide into fuels, led by the University of Sheffield and carried out in collaboration with the University of Manchester, Queens University Belfast and University College London. Pratik Desai and Michael J. Hines would like to thank R3 Water FP7 grant. Pratik Desai and William B. Zimmerman would like to thank the EPSRC (EP/I019790/1, EP/P030238/1, EP/N011511/1) and Innovate UK for the IBCatalyst–Bioethanol Grant and Energy Catalyst Round 4 Award (Anaerobic Digestion). Acknowledgments: Pratik Desai would like to thank GK for inspiration and Professor Joshua “Jim” Swithenbank (co-inventor of particle sizing by Fraunhofer diffraction, popularised as the Malvern Instrument) for splendid conversations. Conflicts of Interest: The authors declare no conflict of interest.

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