- Email: [email protected]
Comments on ‘fish hook effect in classifier efficiency curves’ in recent publications in Powder Technology
Powder Technology 286 (2015) 468–470
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Short communication
Comments on ‘fish hook effect in classifier efficiency curves’ in recent publications in Powder Technology K. Nageswararao Taijasa Consultants, 10-116, Visalakshi Nagar, Visakhapatnam 530 043, India
a r t i c l e
i n f o
Article history: Received 21 June 2015 Received in revised form 23 August 2015 Accepted 29 August 2015 Available online 31 August 2015 Keywords: Hydrocyclone Fish hook effect Efficiency curve Laser diffractometry Optical parameters Systematic errors
a b s t r a c t This note deals with reports of fish hook effect in classifier efficiency curves in recent publications in Powder Technology. Particle size characterisation methods followed in all of them are critically examined. It is shown that where the particle size distributions are determined by laser diffractometry, there is a distinct possibility that correct optical parameters of the test materials may not have been used. In one occurrence, where sieving is the method for measurement of particle size, sufficient details are not available. In another study, the method of size analysis is not disclosed. That is, in all the cases, the accuracy in estimating the efficiency and hence the quality of the data cannot be assessed. Consequentially, the results of all these reports on fish hook should be treated with caution. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Recently, Abdiollahzadeh et al. [1], Alves et al. [2], Altun and Benzer [3], Guizani et al. [4] and Eswaraiah et al. [5] reported fish hook effect in classifier efficiency curves. Of these, Eswaraiah et al. used sieving for characterisation of particle size distribution (PSD). While Guizani et al. have not mentioned the method of determining PSD; all others [1–3] have used laser diffractometry (LD). All reported the most common shape namely, a gradual decrease in efficiency to a minimum followed by a monotonic increase with size. In this note, we examine the robustness of the PSD data and hence the reliability of their results and conclusions with regard to fish hook.
2. Discussion In an earlier paper, we [6] conjectured that errors in PSD data are the sources of fish hooks. Our recent observations on the correlation between reported occurrences of fish hook and the method of characterisation of particle size [7] confirm this presumption. It is relevant to mention that most reports of fish hook are based on characterisation of PSDs by laser diffractometry including the three [1–3] for the current analysis. The result of PSD from laser diffractometry corresponds to that set of spherical particles which produces the same scattering pattern as the E-mail address: [email protected].
http://dx.doi.org/10.1016/j.powtec.2015.08.046 0032-5910/© 2015 Elsevier B.V. All rights reserved.
test material. This is obtained by comparing the actual pattern with that obtained by application of Mie theory (or Fraunhofer approximation of Mie theory in earlier instruments) for an initial guesstimate PSD; comparing the residuals between the theoretical and actual values and adjusting the PSDs to minimise the residuals; this process is repeated until the residuals reach an acceptable level. It may be noted that optical parameters of the test material namely the refractive index, RI; the imaginary refractive index IRI and the refractive index of the dispersing medium influence the scattering pattern particularly so, when the test material contains significant amount of sub sieve particles. In fact, ISO 13320 specifies that Mie theory should be applied for all b 50 μm particles. Noting that fish hook is reported in sub sieve range (b 30 μm) only, we emphasise that discussion on particle size analyses in this note is concerned only with such powders in which sub sieve material is significant. The impact of RI and IRI of the test material on PSD from laser diffractometry is well documented (for example, Jilavenkatesa et al. [8], Merkus [9], Beekman et al. [10], Mingard et al. [11] and Hackely et al. [12]). Specifically with regards to classifier efficiency, it is relevant to mention the recent experimental proof for fish hook phenomenon reported by Bourgeois and Majumder [13]. The efficiency curves generated by them from size distributions obtained from Mastersizer 2000 showed perfect separation of near zero sized particles prominently. Obviously, such curves are inconsistent with the experience and knowledge base on hydrocyclone practice accumulated over many years and could only be due to systematic errors in the size distribution data [14]. The most plausible explanation for their anomalous results is incorrect optical parameters of the test material. Because of this critical drawback,
K. Nageswararao / Powder Technology 286 (2015) 468–470
their ‘proof of existence of fish hook’ could be viewed as an excellent example of repeatable yet irreproducible efficiency curves. Fish hooks reported by Zhu and Liow [15] are similarly based on PSDs obtained from Mastersizer 2000. Significantly, they did not ascertain the values of optical parameters of test materials. They used the refractive index values for their test materials from Malvern database and the manufacturer's data. They have not experimentally determined the extinction coefficients (IRI) either [16]. It is noteworthy that although reproducibility of their data was questioned [17], it was not asserted [16]. For robustness of PSD results from LD, picking a representative sample [18] is undoubtedly a primary requisite. Additionally, Rawle [19] suggests that RI should be determined accurate up to 2 decimal places using Becke line method. He reiterates the necessity to determine the imaginary refractive index experimentally with known volume concentration [20]. While he opines that value of IRI accurate to an order of magnitude is acceptable, Beckman Coulter [21] suggest the tolerance limit of a factor of three. For all particulate systems in which b 30 μm fraction is considerable, incorrect optical parameters influence the distribution as well as key points such as x10 (size at which 10% of the sample is finer) etc. on the distribution curve [8–12,19,22 etc.] appreciably. Indeed, the PSD results with inaccurate optical parameters can be highly misleading so much so that Keck and Muller [22] rightly remark: “that any laser diffraction data without information of the optical parameters and/or without measuring the parameters used, as well as data using guessed optical parameters must be doubted”. They estimate that probably at least 90% of all the size analysis data published for submicron particles are unreliable. Suffice it to say that the reliability of PSDs from laser diffractometry is totally dependent on the reliability of the optical properties of the test material as elaborated in the foregoing. Furthermore, it appears to be a good practice to check some results by alternate methods to enhance the reliability of the data (Ray et al. [23], Santos et al. [24]). The fish hooks reported by Abdiollahzadeh et al. [1], Alves et al. [2], Altun and Benzer [3] are to be viewed in this background. Spherical aluminium, glass sand and flake aluminium powder with mean (d50) particle sizes of 18.28 μm, 17.50 μm and 20.18 μm respectively were the feed materials used by Abdiollahzadeh et al. [1]. The feed to reverse flow cyclones investigated by Alves et al. [2] consisted of biomass boiler exhausts with median diameter varying from 1.1 μm to 2.7 μm. Cement was the feed to high efficiency air classifiers studied by Altun and Benzer [3]. While the mean diameter of feed to classifiers varied between 32 and 46 μm, the range was from 12 to 15 μm for the product in their investigations. Conspicuously, the authors [1–3] neither specified the values of the optical parameters of their test materials nor how they were determined. It is likely that they determined the PSDs with assumed/guessed optical parameters, attracting errors as a result. Furthermore, errors in determining the classifier efficiency are compounded as it involves more than one PSD data. Consequentially, the efficiency curves showing fish hooks reported by them [1–3] should be treated with caution. Although, laser diffractometry is more common these days for characterisation of particles in the ‘sub sieve’ (b30 μm) range, sieving too could be considered for the same. Woven wire sieves with nominal apertures of 32 μm, 25 μm, 20 μm and precision sieves made from electro-etched nickel plate with apertures in the range of 5–30 μm are available in the market. Specially designed sieve shakers for handling such special purpose screens and other accessories for maintenance are also available. Guidelines which include the amount of sample; number of screens in the stack; the maximum height the material could rise; time of sieving; care required in handling and usage and method of checking for damage of screens etc. are also provided by the manufacturers. The study of a circulating air classifier by Eswaraiah et al. [5] is one recent example where sizing is done by sieve analysis. Their CFD simulations indicate occurrence of fish hook in sub sieve range (10–25 μm) in agreement with typical experimentally determined efficiency curves (Fig. 1). Conspicuously, they have not given any details regarding the
469
Fig. 1. Typical efficiency curves for classification of fly ash in a circulating air classifier at two different wheel speeds. These efficiency curves are the first to report fish hook based on sizing by sieve analysis. The fish hook is in 10–25 μm as per CFD simulations (Eswaraiah et al. [5]).
screens used, particularly those with apertures of b 30 μm. As such, it is impossible to assess the precision and accuracy of the only report on fish hook which is determined from PSDs by sieve analysis. The recent report of fish hook effect in classification curve of cement in a dynamic separator by Guizani et al. [4] is based on more uncertainty. The experimentally determined curve (Fig. 2) is in close agreement with their CFD simulation results. However, the authors have not mentioned even the mode of characterisation of PSDs. In view of the above, the reliability of the data on which fish hooks are reported by Eswaraiah et al. and Guizani et al. is subject to uncertainty and their observations too are to be treated with caution.
2.1. General remarks Fish hook in efficiency curves has been a topic of interest in more than 200 publications. Current state of understanding on this phenomenon can be summarised as follows [6,7,14,17,25–27]:
Fig. 2. Efficiency curve of cement classified in a dynamic separator. The method of characterisation of particle size distributions is not specified (Guizani et al. [4]).
470
K. Nageswararao / Powder Technology 286 (2015) 468–470
• it is reasonable to accept that all reported occurrences of fish hook are repeatable. However, the conditions under which it is reproducible have not been stated so that they could be corroborated by independent investigators. As such, it cannot be described as a scientifically significant physical effect (Popper [28]); and • the passive acceptance of this phenomenon is attributable to the indiscriminate use of repeatability and reproducibility in fish hook literature.
3. Summary and conclusions Results and conclusions based on size distribution data from laser diffractometry are as reliable as the data inputs, namely, the refractive index, imaginary refractive index of the test material and the refractive index of the dispersing medium. Assumed values of these optical parameters could result in particle size distributions of unknown accuracy and precision. The errors are compounded when such data are used for calculation of classifier efficiency curves. The observations of Abdiollahzadeh et al. [1], Alves et al. [2] and Altun and Benzer [3] on fish hook are subject to this limitation and should be treated with caution. The fish hook in efficiency curves reported by Eswaraiah et al. [5] in the sub sieve range based on characterisation of particle size by sieving technique too is subject to the limitation regarding the reliability of their base data. Due to lack of knowledge on the method of characterisation of particle size, fish hook in efficiency curves reported by Guizani et al. [4] too is subject to the limitation of uncertainty. Acknowledgements I am highly obliged to Sri Satya Simha, now with Mawarid Mining LLC, Oman for introducing the Works of Sri Aurobindo on Nature, which have a profound influence on my understanding of particulate systems. Lengthy discussions with Dr K Badarinath, Assistant Professor, Department of Mechanical and Aerospace Engineering, Indian Institute of Technology, Hyderabad were particularly useful. References [1] L. Abdollahzadeh, M. Habibian, R. Etezazian, S. Naseri, Study of particle's shape factor, inlet velocity and feed concentration on mini-hydrocyclone classification and fishhook effect, Powder Technol. 285 (2015) 294–301. [2] A. Alves, J. Pava, R. Salcedo, Cyclone optimization including particle clustering, Powder Technol. 272 (2015) 14–22. [3] O. Altun, H. Benzer, Selection and mathematical modelling of high efficiency air classifiers, Powder Technol. 264 (2014) 1–8. [4] R. Guizani, I. Mokni, H. Mhiri, P. Bournot, CFD modeling and analysis of the fish-hook effect on the rotor separator's efficiency, Powder Technol. 264 (2014) 149–157. [5] C. Eswaraiah, S.I. Angadi, B.K. Mishra, Mechanism of particle separation and analysis of fish-hook phenomenon in a circulating air classifier, Powder Technol. 218 (2012) 57–63.
[6] K. Nageswararao, A critical analysis of fish-hook effect in hydrocyclone classifiers, Chem. Eng. J. 80 (1–3) (2000) 251–256. [7] K. Nageswararao, R.A. Medronho, Fish hook effect in centrifugal classifiers — a further analysis, Int. J. Miner. Process. 132 (2014) 43–58. [8] A. Jillavenkatesa, S.J. Dapkaunas, L.H. Lum, Particle Size Characterization, Special Publication 960–1, National Institute of Standards and Technology, US Department of Commerce, Gaithersburg, MD, USA, 2001. [9] H.G. Merkus, Particle Size Measurements — Fundamentals, Practice, Quality, Springer, 2009. [10] A. Beekman, D. Shan, A. Ali, W. Dai, S. Ward-Smith, M. Goldenberg, Micrometerscale particle sizing by laser diffraction: critical Impact of the Imaginary component of Refractive Index, Pharm. Res. 22 (4) (2005) 518–522. [11] K. Mingard, R. Morrell, P. Jackson, S. Lawson, S. Patel, R. Buxton, Good Practice Guide for Improving the Consistency of Particle Size Measurement, A National Measurement Good Practice Guide No. 111, National Physical Laboratory, Hampton Road, Teddington, Middlesex, UK, 2009. [12] V. Hackley, L.S. Lum, V. Gintautas, C.F. Ferraris, Particle Size Analysis by Laser Diffraction Spectrometry: Application to Cementitious Powders, NISTIR 7097, US Department of Commerce, Technology Administration, National Institute of Standards and Technology, Gaithersburg, MD, USA, 2004. [13] F. Bourgeois, A.K. Majumder, Is the fish-hook effect in hydrocyclones a real phenomenon? Powder Technol. 237 (2013) 367–375. [14] K. Nageswararao, Comment on: ‘Is the fish-hook effect in hydrocyclones a real phenomenon?’ by F. Bourgeois and A. K. Majumder [powder technology 237 (2013) 367–375], Powder Technol. 262 (2014) 194–197. [15] G. Zhu, J.L. Liow, Experimental study of particle separation and the fish hook effect in a mini-hydrocyclone, Chem. Eng. Sci. 111 (2014) 94–105. [16] G. Zhu, J.L. Liow, A. Neely, Response to comment on “Experimental study of particle separation and the fish hook effect in a mini-hydrocyclone [Chem. Eng. Sci. 111 (2014) 94–105]”, Chem. Eng. Sci. 122 (2015) 104–105. [17] K. Nageswararao, Comment on: ‘Experimental study of particle separation and the fish hook effect in a mini-hydrocyclone’ by G. Zhu and J. L. Liow [chemical engineering science 111 (2014) 94–105], Chem. Eng. Sci. 122 (2015) 182–184. [18] A.F. Rawle, Representative sampling — another Cinderella of particle size analysis, The 7th World Congress on Particle Technology (WCPT7), Procedia Eng. 102 (2015) 1707–1713. [19] A.F. Rawle, Best practice in laser diffraction — a robustness study of the optical properties of silica, The 7th World Congress on Particle Technology (WCPT7), Procedia Eng. 102 (2015) 182–189. [20] Malvern instruments Ltd., Determination of the Particle Absorption for Laser Diffraction Size Calculations, 2009 (Application Note: MRK1309-1). [21] Beckman Coulter Inc., LS 13320 Laser Diffraction Particle Size Analyzer, Instructions for Use, PN B05577AB, October 2011. [22] C.M. Keck, R.H. Muller, Size analysis of submicron particles by laser diffractometry — 90% of the published measurements are false, Int. J. Pharm. 355 (1–2) (2008) 150–163. [23] M.B. Ray, A.C. Hoffmann, R.S. Postma, Performance of different analytical methods in evaluating grade efficiency of centrifugal separators, J. Aerosol Sci. 31 (5) (2000) 563–581. [24] A.C. Santos, J. Cunha, F. Veiga, A. Cordeiro-da-Silva, A.J. Ribeiro, Ultrasonication of insulin-loaded microgel particles produced by internal gelation: impact on particle's size and insulin bioactivity, Carbohydr. Polym. 98 (2) (2013) 1397–1408. [25] K. Nageswararao, Normalisation of the efficiency curves of hydrocyclone classifiers, Miner. Eng. 12 (1) (1999) 107–118. [26] K. Nageswararao, Reduced efficiency curves of industrial hydrocyclones — an analysis for plant practice, Miner. Eng. 12 (5) (1999) 517–544. [27] K. Nageswararao, D.M. Wiseman, T.J. Napier-Munn, Two empirical hydrocyclone models revisited, Miner. Eng. 17 (5) (2004) 671–687. [28] K.R. Popper, The Logic of Scientific Discovery, Routledge, London, 1992 (Logik der Forschung First published, 1935 by Verlag von Julius Springer, Vienna, Austria).
Contents lists available at ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
Short communication
Comments on ‘fish hook effect in classifier efficiency curves’ in recent publications in Powder Technology K. Nageswararao Taijasa Consultants, 10-116, Visalakshi Nagar, Visakhapatnam 530 043, India
a r t i c l e
i n f o
Article history: Received 21 June 2015 Received in revised form 23 August 2015 Accepted 29 August 2015 Available online 31 August 2015 Keywords: Hydrocyclone Fish hook effect Efficiency curve Laser diffractometry Optical parameters Systematic errors
a b s t r a c t This note deals with reports of fish hook effect in classifier efficiency curves in recent publications in Powder Technology. Particle size characterisation methods followed in all of them are critically examined. It is shown that where the particle size distributions are determined by laser diffractometry, there is a distinct possibility that correct optical parameters of the test materials may not have been used. In one occurrence, where sieving is the method for measurement of particle size, sufficient details are not available. In another study, the method of size analysis is not disclosed. That is, in all the cases, the accuracy in estimating the efficiency and hence the quality of the data cannot be assessed. Consequentially, the results of all these reports on fish hook should be treated with caution. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Recently, Abdiollahzadeh et al. [1], Alves et al. [2], Altun and Benzer [3], Guizani et al. [4] and Eswaraiah et al. [5] reported fish hook effect in classifier efficiency curves. Of these, Eswaraiah et al. used sieving for characterisation of particle size distribution (PSD). While Guizani et al. have not mentioned the method of determining PSD; all others [1–3] have used laser diffractometry (LD). All reported the most common shape namely, a gradual decrease in efficiency to a minimum followed by a monotonic increase with size. In this note, we examine the robustness of the PSD data and hence the reliability of their results and conclusions with regard to fish hook.
2. Discussion In an earlier paper, we [6] conjectured that errors in PSD data are the sources of fish hooks. Our recent observations on the correlation between reported occurrences of fish hook and the method of characterisation of particle size [7] confirm this presumption. It is relevant to mention that most reports of fish hook are based on characterisation of PSDs by laser diffractometry including the three [1–3] for the current analysis. The result of PSD from laser diffractometry corresponds to that set of spherical particles which produces the same scattering pattern as the E-mail address: [email protected].
http://dx.doi.org/10.1016/j.powtec.2015.08.046 0032-5910/© 2015 Elsevier B.V. All rights reserved.
test material. This is obtained by comparing the actual pattern with that obtained by application of Mie theory (or Fraunhofer approximation of Mie theory in earlier instruments) for an initial guesstimate PSD; comparing the residuals between the theoretical and actual values and adjusting the PSDs to minimise the residuals; this process is repeated until the residuals reach an acceptable level. It may be noted that optical parameters of the test material namely the refractive index, RI; the imaginary refractive index IRI and the refractive index of the dispersing medium influence the scattering pattern particularly so, when the test material contains significant amount of sub sieve particles. In fact, ISO 13320 specifies that Mie theory should be applied for all b 50 μm particles. Noting that fish hook is reported in sub sieve range (b 30 μm) only, we emphasise that discussion on particle size analyses in this note is concerned only with such powders in which sub sieve material is significant. The impact of RI and IRI of the test material on PSD from laser diffractometry is well documented (for example, Jilavenkatesa et al. [8], Merkus [9], Beekman et al. [10], Mingard et al. [11] and Hackely et al. [12]). Specifically with regards to classifier efficiency, it is relevant to mention the recent experimental proof for fish hook phenomenon reported by Bourgeois and Majumder [13]. The efficiency curves generated by them from size distributions obtained from Mastersizer 2000 showed perfect separation of near zero sized particles prominently. Obviously, such curves are inconsistent with the experience and knowledge base on hydrocyclone practice accumulated over many years and could only be due to systematic errors in the size distribution data [14]. The most plausible explanation for their anomalous results is incorrect optical parameters of the test material. Because of this critical drawback,
K. Nageswararao / Powder Technology 286 (2015) 468–470
their ‘proof of existence of fish hook’ could be viewed as an excellent example of repeatable yet irreproducible efficiency curves. Fish hooks reported by Zhu and Liow [15] are similarly based on PSDs obtained from Mastersizer 2000. Significantly, they did not ascertain the values of optical parameters of test materials. They used the refractive index values for their test materials from Malvern database and the manufacturer's data. They have not experimentally determined the extinction coefficients (IRI) either [16]. It is noteworthy that although reproducibility of their data was questioned [17], it was not asserted [16]. For robustness of PSD results from LD, picking a representative sample [18] is undoubtedly a primary requisite. Additionally, Rawle [19] suggests that RI should be determined accurate up to 2 decimal places using Becke line method. He reiterates the necessity to determine the imaginary refractive index experimentally with known volume concentration [20]. While he opines that value of IRI accurate to an order of magnitude is acceptable, Beckman Coulter [21] suggest the tolerance limit of a factor of three. For all particulate systems in which b 30 μm fraction is considerable, incorrect optical parameters influence the distribution as well as key points such as x10 (size at which 10% of the sample is finer) etc. on the distribution curve [8–12,19,22 etc.] appreciably. Indeed, the PSD results with inaccurate optical parameters can be highly misleading so much so that Keck and Muller [22] rightly remark: “that any laser diffraction data without information of the optical parameters and/or without measuring the parameters used, as well as data using guessed optical parameters must be doubted”. They estimate that probably at least 90% of all the size analysis data published for submicron particles are unreliable. Suffice it to say that the reliability of PSDs from laser diffractometry is totally dependent on the reliability of the optical properties of the test material as elaborated in the foregoing. Furthermore, it appears to be a good practice to check some results by alternate methods to enhance the reliability of the data (Ray et al. [23], Santos et al. [24]). The fish hooks reported by Abdiollahzadeh et al. [1], Alves et al. [2], Altun and Benzer [3] are to be viewed in this background. Spherical aluminium, glass sand and flake aluminium powder with mean (d50) particle sizes of 18.28 μm, 17.50 μm and 20.18 μm respectively were the feed materials used by Abdiollahzadeh et al. [1]. The feed to reverse flow cyclones investigated by Alves et al. [2] consisted of biomass boiler exhausts with median diameter varying from 1.1 μm to 2.7 μm. Cement was the feed to high efficiency air classifiers studied by Altun and Benzer [3]. While the mean diameter of feed to classifiers varied between 32 and 46 μm, the range was from 12 to 15 μm for the product in their investigations. Conspicuously, the authors [1–3] neither specified the values of the optical parameters of their test materials nor how they were determined. It is likely that they determined the PSDs with assumed/guessed optical parameters, attracting errors as a result. Furthermore, errors in determining the classifier efficiency are compounded as it involves more than one PSD data. Consequentially, the efficiency curves showing fish hooks reported by them [1–3] should be treated with caution. Although, laser diffractometry is more common these days for characterisation of particles in the ‘sub sieve’ (b30 μm) range, sieving too could be considered for the same. Woven wire sieves with nominal apertures of 32 μm, 25 μm, 20 μm and precision sieves made from electro-etched nickel plate with apertures in the range of 5–30 μm are available in the market. Specially designed sieve shakers for handling such special purpose screens and other accessories for maintenance are also available. Guidelines which include the amount of sample; number of screens in the stack; the maximum height the material could rise; time of sieving; care required in handling and usage and method of checking for damage of screens etc. are also provided by the manufacturers. The study of a circulating air classifier by Eswaraiah et al. [5] is one recent example where sizing is done by sieve analysis. Their CFD simulations indicate occurrence of fish hook in sub sieve range (10–25 μm) in agreement with typical experimentally determined efficiency curves (Fig. 1). Conspicuously, they have not given any details regarding the
469
Fig. 1. Typical efficiency curves for classification of fly ash in a circulating air classifier at two different wheel speeds. These efficiency curves are the first to report fish hook based on sizing by sieve analysis. The fish hook is in 10–25 μm as per CFD simulations (Eswaraiah et al. [5]).
screens used, particularly those with apertures of b 30 μm. As such, it is impossible to assess the precision and accuracy of the only report on fish hook which is determined from PSDs by sieve analysis. The recent report of fish hook effect in classification curve of cement in a dynamic separator by Guizani et al. [4] is based on more uncertainty. The experimentally determined curve (Fig. 2) is in close agreement with their CFD simulation results. However, the authors have not mentioned even the mode of characterisation of PSDs. In view of the above, the reliability of the data on which fish hooks are reported by Eswaraiah et al. and Guizani et al. is subject to uncertainty and their observations too are to be treated with caution.
2.1. General remarks Fish hook in efficiency curves has been a topic of interest in more than 200 publications. Current state of understanding on this phenomenon can be summarised as follows [6,7,14,17,25–27]:
Fig. 2. Efficiency curve of cement classified in a dynamic separator. The method of characterisation of particle size distributions is not specified (Guizani et al. [4]).
470
K. Nageswararao / Powder Technology 286 (2015) 468–470
• it is reasonable to accept that all reported occurrences of fish hook are repeatable. However, the conditions under which it is reproducible have not been stated so that they could be corroborated by independent investigators. As such, it cannot be described as a scientifically significant physical effect (Popper [28]); and • the passive acceptance of this phenomenon is attributable to the indiscriminate use of repeatability and reproducibility in fish hook literature.
3. Summary and conclusions Results and conclusions based on size distribution data from laser diffractometry are as reliable as the data inputs, namely, the refractive index, imaginary refractive index of the test material and the refractive index of the dispersing medium. Assumed values of these optical parameters could result in particle size distributions of unknown accuracy and precision. The errors are compounded when such data are used for calculation of classifier efficiency curves. The observations of Abdiollahzadeh et al. [1], Alves et al. [2] and Altun and Benzer [3] on fish hook are subject to this limitation and should be treated with caution. The fish hook in efficiency curves reported by Eswaraiah et al. [5] in the sub sieve range based on characterisation of particle size by sieving technique too is subject to the limitation regarding the reliability of their base data. Due to lack of knowledge on the method of characterisation of particle size, fish hook in efficiency curves reported by Guizani et al. [4] too is subject to the limitation of uncertainty. Acknowledgements I am highly obliged to Sri Satya Simha, now with Mawarid Mining LLC, Oman for introducing the Works of Sri Aurobindo on Nature, which have a profound influence on my understanding of particulate systems. Lengthy discussions with Dr K Badarinath, Assistant Professor, Department of Mechanical and Aerospace Engineering, Indian Institute of Technology, Hyderabad were particularly useful. References [1] L. Abdollahzadeh, M. Habibian, R. Etezazian, S. Naseri, Study of particle's shape factor, inlet velocity and feed concentration on mini-hydrocyclone classification and fishhook effect, Powder Technol. 285 (2015) 294–301. [2] A. Alves, J. Pava, R. Salcedo, Cyclone optimization including particle clustering, Powder Technol. 272 (2015) 14–22. [3] O. Altun, H. Benzer, Selection and mathematical modelling of high efficiency air classifiers, Powder Technol. 264 (2014) 1–8. [4] R. Guizani, I. Mokni, H. Mhiri, P. Bournot, CFD modeling and analysis of the fish-hook effect on the rotor separator's efficiency, Powder Technol. 264 (2014) 149–157. [5] C. Eswaraiah, S.I. Angadi, B.K. Mishra, Mechanism of particle separation and analysis of fish-hook phenomenon in a circulating air classifier, Powder Technol. 218 (2012) 57–63.
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