Abstract
The wide range of applications of particulate materials in the modern industry, as well as growing concerns about their potential risks to human health and the environment, has boosted studies related to the production, control, and classification of nanoparticles. Differential mobility analyzers (DMAs) are one of the main technologies used to characterize the size distribution of nanoparticles in aerosols. However, the high price and complexity of this equipment have been limiting factors for its use. Thus, the purpose of this study was to evaluate the performance of a Long-DMA, designed and built with its own technology and to propose and solve an inverse problem to determine the monodisperse aerosol concentration distribution. The polydisperse aerosols were generated by atomization of NaCl solutions with 0.1, 0.5, and 1.0 g L−1 concentrations. In order to estimate the theoretical nanoparticle size distributions of monodisperse aerosols, a new mobility balance was proposed. This was based on the Wiedensohler charge distribution associated with a loss parameter, obtained considering a formulation and solution of an optimization problem by using the differential evolution algorithm. The Long-DMA was able to produce monodisperse aerosols for all the saline concentrations evaluated, showing evidence of its potential for classifying nanoparticles. Comparisons between the experimental and theoretical results showed that the proposed mobility balance was able to satisfactorily describe the distributions related to monodisperse aerosols. The proposed methodology was able to estimate the monodisperse aerosol distribution in intermediate solution concentration using only the data about the highest and lowest concentrations. It is worth mentioning that the cost of the designed equipment was approximately 10% of the commercial equipment value.



















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Alonso M, Kousaka Y, Nomura T, Hashimoto N, Hashimoto T (1997) Bipolar charging and neutralization of nanometer-sized aerosol particles. J Aerosol Sci 28:1479–1490. https://doi.org/10.1016/S0021-8502(97)00036-0
Anh HPH, Son NN, Van Kien C, Ho-Huu V (2018) Parameter identification using adaptive differential evolution algorithm applied to robust control of uncertain nonlinear systems. Appl Soft Comput J 71:672–684. https://doi.org/10.1016/j.asoc.2018.07.015
Asbach C, Kaminski H, Fissan H, Monz C, Dahmann D, Mülhopt S, Paur HR, Kiesling HJ, Herrmann F, Voetz M, Kuhlbusch TAJ (2009) Comparison of four mobility particle sizers with different time resolution for stationary exposure measurements. J Nanopart Res 11:1593–1609. https://doi.org/10.1007/s11051-009-9679-x
Awad NH, Ali MZ, Duwairi RM (2017) Multi-objective differential evolution based on normalization and improved mutation strategy. Nat Comput 16:661–675. https://doi.org/10.1007/s11047-016-9585-y
Baron PA, Willeke K (2001) Aerosol measurement: principles, techniques, and applications, 2nd edn. Wiley, New York
Biskos G (2004) Description and theoretical analysis of a differential mobility spectrometer. Ph.d. thesis, University of Cambridge, UK
Cai R, Chen DR, Hao J, Jiang J (2017) A miniature cylindrical differential mobility analyzer for sub-3 nm particle sizing. J Aerosol Sci 106:111–119. https://doi.org/10.1016/j.jaerosci.2017.01.004
Chen DR, Pui DYH, Hummes D, Fissan H, Quant FR, Sem GJ (1998) Design and evaluation of a nanometer aerosol differential mobility analyzer (Nano-DMA). J Aerosol Sci 29:497–509. https://doi.org/10.1016/S0021-8502(97)10018-0
Cho K, Hogan CJ, Biswas P (2007) Study of the mobility, surface area, and sintering behavior of agglomerates in the transition regime by tandem differential mobility analysis. J Nanopart Res 9:1003–1012. https://doi.org/10.1007/s11051-007-9243-5
Colbeck I, Lazaridis M (2014) Aerosol science: Technology and applications, 1st edn. Wiley, Chichester
Collins DR, Cocker DR, Flagan RC, Seinfeld JH (2004) The scanning DMA transfer function. Aerosol Sci Technol 38:833–850. https://doi.org/10.1080/027868290503082
Ealias AM, Saravanakumar MP (2017) A review on the classification, characterisation, synthesis of nanoparticles and their application. IOP Conf Ser Mater Sci Eng. https://doi.org/10.1088/1757-899X/263/3/032019
Flagan RC (2008) Differential mobility analysis of aerosols: a tutorial. KONA Powder Part J 26:254–268. https://doi.org/10.14356/kona.2008023
Friedlander SK, Pui DYH (2004) Emerging issues in nanoparticle aerosol science and technology experimental methods and instrumentation. J Nanopart Res 6:313–320. https://doi.org/10.1023/B:NANO.0000034725.89027.6b
Fuchs NA (1963) On the stationary charge distribution on aerosol particles in a bipolar ionic atmosphere. Geofis Pura e Appl 56:185–193. https://doi.org/10.1007/BF01993343
Hagwood C, Sivathanu Y, Mulholland G (1999) The DMA transfer function with brownian motion a trajectory/Monte-Carlo approach. Aerosol Sci Technol 30:40–61. https://doi.org/10.1080/027868299304877
Han HS, Chen DR, Pui DYH, Anderson BE (2000) A nanometer aerosol size analyzer (nASA) for rapid measurement of high-concentration size distributions. J Nanopart Res 2:43–52. https://doi.org/10.1023/A:1010014109495
Han JW, Li QX, Wu HR, Zhu HJ, Song YL (2019) Prediction of cooling efficiency of forced-air precooling systems based on optimized differential evolution and improved BP neural network. Appl Soft Comput J. https://doi.org/10.1016/j.asoc.2019.105733
Hernandez-Sierra A, Alguacil FJ, Alonso M (2003) Unipolar charging of nanometer aerosol particles in a corona ionizer. J Aerosol Sci 34:733–745. https://doi.org/10.1016/S0021-8502(03)00033-8
Hinds WC (1999) Aerosol technology: properties, behavior and measurement of airborne particles, 2nd edn. Wiley, New York
Intra P, Tippayawong N (2008) An overview of differential mobility analyzers for size classification of nanometer-sized aerosol particles. Songklanakarin J Sci Technol 30:243–256
Jana ND, Sil J (2016) Levy distributed parameter control in differential evolution for numerical optimization. Nat Comput 15:371–384. https://doi.org/10.1007/s11047-015-9488-3
Jiang J, Attoui M, Heim M, Brunelli NA, McMurry PH, Kasper G, Flagan RC, Giapis K, Mouret G (2011) Transfer functions and penetrations of five differential mobility analyzers for sub-2 nm particle classification. Aerosol Sci Technol 45:480–492. https://doi.org/10.1080/02786826.2010.546819
Kamarulzaman NA, Lee KE, Siow KS, Mokhtar M (2019) Psychological and sociological perspectives for good governance of sustainable nanotechnology development in Malaysia. J Nanopart Res. https://doi.org/10.1007/s11051-019-4583-5
Karlsson MNA, Martinsson BG (2003) Methods to measure and predict the transfer function size dependence of individual DMAs. J Aerosol Sci 34:603–625. https://doi.org/10.1016/S0021-8502(03)00020-X
Knutson EO, Whitby KT (1975) Accurate measurement of aerosol electric mobility moments. J Aerosol Sci 6:453–460. https://doi.org/10.1016/0021-8502(75)90061-0
Knutson EO, Whitby KT (1975) Aerosol classification by electric mobility: apparatus, theory, and applications. J Aerosol Sci 6:443–451. https://doi.org/10.1016/0021-8502(75)90060-9
Krames J, Büttner H, Ebert F (1991) Submicron particle generation by evaporation of water droplets. J Aerosol Sci 22:15–18. https://doi.org/10.1016/S0021-8502(05)80023-0
Larsson S, Jansson M, Boholm Å (2019) Expert stakeholders’ perception of nanotechnology: risk, benefit, knowledge, and regulation. J Nanopart Res. https://doi.org/10.1007/s11051-019-4498-1
Navrotsky A (2000) Nanomaterials in the environment, agriculture, and technology (NEAT). J Nanopart Res 2:321–323. https://doi.org/10.1023/A:1010007023813
Oberdörster G, Oberdörster E, Oberdörster J (2005) Review nanotoxicology: an emerging discipline evolving from studies of ultrafine particles. Environ Health Perspect 113:823–839. https://doi.org/10.1289/ehp.7339
Pui DYH, Brock JR, Chen DR, Fissan H, Frisbie CD, Lyman CE, Miller JC, Mulholland GW, Pecora R, Preining O, Vo-Dinh T (2000) Instrumentation and measurement issues for nanometer particles: workshop summary. J Nanopart Res 2:103–112. https://doi.org/10.1023/A:1010025905861
Purohit R, Mittal A, Dalela S, Warudkar V, Purohit K, Purohit S (2017) Social, environmental and ethical impacts of nanotechnology. Mater Today Proc 4:5461–5467. https://doi.org/10.1016/j.matpr.2017.05.058
Ramechecandane S, Beghein C, Allard F, Bombardier P (2011) Modelling ultrafine/nano particle dispersion in two differential mobility analyzers (M-DMA and L-DMA). Build Environ 46:2255–2266. https://doi.org/10.1016/j.buildenv.2011.05.005
Renn O, Roco MC (2006) Nanotechnology and the need for risk governance. J Nanopart Res 8:153–191. https://doi.org/10.1007/s11051-006-9092-7
Said MI, Harbrecht B (2019) Size-controlled synthesis of Mn3O4 nanoparticles: characterization and defect chemistry. J Nanopart Res 21:1–15. https://doi.org/10.1007/s11051-019-4502-9
Seol KS, Yabumoto J, Takeuchi K (2002) A differential mobility analyzer with adjustable column length for wide particle-size-range measurements. J Aerosol Sci 33:1481–1492. https://doi.org/10.1016/S0021-8502(02)00094-0
Song DK, Lee HM, Chang H, Kim SS, Shimada M, Okuyama K (2006) Performance evaluation of long differential mobility analyzer (LDMA) in measurements of nanoparticles. J Aerosol Sci 37:598–615. https://doi.org/10.1016/j.jaerosci.2005.06.003
Soysal U, Géhin E, Algré E, Berthelot B, Da G, Robine E (2017) Aerosol mass concentration measurements: recent advancements of real-time nano/micro systems. J Aerosol Sci 114:42–54. https://doi.org/10.1016/j.jaerosci.2017.09.008
Stolzenburg D, Steiner G, Winkler PM (2017) A DMA-train for precision measurement of sub-10 nm aerosol dynamics. Atmos Meas Tech 10:1639–1651. https://doi.org/10.5194/amt-10-1639-2017
Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. J Glob Optim 23:1–12
Tigges L, Wiedensohler A, Weinhold K, Gandhi J, Schmid H (2015) Bipolar charge distribution of a soft X-ray diffusion charger. J Aerosol Sci 90:77–86. https://doi.org/10.1016/j.jaerosci.2015.07.002
Vafashoar R, Meybodi MR (2020) A multi-population differential evolution algorithm based on cellular learning automata and evolutionary context information for optimization in dynamic environments. Appl Soft Comput J 8:8. https://doi.org/10.1016/j.asoc.2019.106009
Vo-Dinh T, Griffin GD, Alarie JP, Cullum B, Sumpter B, Noid D (2000) Development of nanosensors and bioprobes. J Nanopart Res 2:17–27. https://doi.org/10.1023/A:1010005908586
Wang SC, Flagan RC (1990) Scanning electrical mobility spectrometer. Aerosol Sci Technol 13:230–240. https://doi.org/10.1016/j.buildenv.2011.05.00510.1080/02786829008959441
Wang C, Friedlander SK, Mädler L (2005) Nanoparticle aerosol science and technology: an overview. China Particuol 3:243–254. https://doi.org/10.1016/S1672-2515(07)60196-1
Wang S, Li Y, Yang H (2019) Self-adaptive mutation differential evolution algorithm based on particle swarm optimization. Appl Soft Comput J. https://doi.org/10.1016/j.asoc.2019.105496
Wiedensohler A (1988) An approximation of the bipolar charge distribution for particles in the submicron size range. J Aerosol Sci 19:387–389. https://doi.org/10.1016/0021-8502(88)90278-9
Wiedensohler A, Fissan HJ (1991) Bipolar charge distributions of aerosol particles in high-purity argon and nitrogen. Aerosol Sci Technol 14:358–364. https://doi.org/10.1080/02786829108959498
Wiedensohler A, Birmili W, Nowak A, Sonntag A, Weinhold K, Merkel M, Wehner B, Tuch T, Pfeifer S (2012) Mobility particle size spectrometers: harmonization of technical standards and data structure to facilitate high quality long-term observations of atmospheric particle number size distributions. Atmosp Meas Tech. https://doi.org/10.5194/amt-5-657-2012
Zhang W (2003) Nanoscale iron particles for environmental remediation: an overview. J Nanoparticle Res 5:323–332. https://doi.org/10.1023/A:1025520116015
Zhu L, Ma Y, Bai Y (2020) A self-adaptive multi-population differential evolution algorithm. Nat Comput 19:211–235. https://doi.org/10.1007/s11047-019-09757-3
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Gomes, T.L.C., Lobato, F.S., Borges, L.C. et al. Mathematical modeling of monodisperse nanoparticle production in aerosols using separation in an electric field. Soft Comput 25, 11347–11362 (2021). https://doi.org/10.1007/s00500-021-05931-x
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DOI: https://doi.org/10.1007/s00500-021-05931-x