A genetic algorithm-based approach for numerical solution of droplet status after Coulomb fission using the energy

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Tafresh University, Tafresh 39518-79611, Iran

2 Department of Mechanical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran

10.22059/jcamech.2020.304872.523

Abstract

As a droplet moves, due to evaporation at the surface, the droplet size is gradually reduced. Due to decreasing the size of the droplets moving in the spray core, the surface charges become closer and the repulsive force between the charges increases. When the Coulombic force overcomes the surface tension force (Rayleigh instability) the droplet breaks into smaller droplets (Coulomb fission). The present study predicts droplet Coulomb fission and droplets trajectories of steady spray plume in a monodisperse Electrohydrodynamics (EHD) spray within a Lagrangian framework. Droplet fission is simulated based on the principle of minimum free energy using the Genetic Algorithm (GA) and droplet trajectories are predicted using the Lagrangian single-droplet dynamic tracking method. The numerical model is validated by comparing the model predictions with the experimental and previous modeling results. In the current method, an optimization method for minimizing the energy in the minimum energy principle is utilized to avoid any simplifying assumptions, such as number of sibling droplets and charge distribution on their surfaces which may affect the physics of the problem. According to the process of the present solutions and results, it is clearly seen that the developed method has sufficient accuracy and precision.

Keywords

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[2] J. B. Fenn, Electrospray wings for molecular elephants (Nobel lecture), Angewandte Chemie International Edition, Vol. 42, No. 33, pp. 3871-3894, 2003.
[3] X. Hou, K.-L. Choy, Synthesis and characteristics of CuInS2 films for photovoltaic application, Thin Solid Films, Vol. 480, pp. 13-18, 2005.
[4] R. Y. Hsu, J. H. Liao, H. W. Tien, G. R. Her, Gas chromatography electrospray ionization mass spectrometry analysis of trimethylsilyl derivatives, Journal of Mass Spectrometry, Vol. 51, No. 10, pp. 883-888, 2016.
[5] M. K. I. Khan, A. Nazir, A. A. Maan, Electrospraying: a novel technique for efficient coating of foods, Food Engineering Reviews, Vol. 9, No. 2, pp. 112-119, 2017.
[6] S. Martin, P. Garcia-Ybarra, J. Castillo, Electrospray deposition of catalyst layers with ultra-low Pt loadings for PEM fuel cells cathodes, Journal of Power Sources, Vol. 195, No. 9, pp. 2443-2449, 2010.
[7] K. Mohammadi, M. R. Movahhedy, S. Khodaygan, A multiphysics model for analysis of droplet formation in electrohydrodynamic 3D printing process, Journal of Aerosol Science, Vol. 135, pp. 72-85, 2019.
[8] A. M. Gañán-Calvo, J. M. López-Herrera, N. Rebollo-Muñoz, J. Montanero, The onset of electrospray: the universal scaling laws of the first ejection, Scientific reports, Vol. 6, pp. 32357, 2016.
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[10] J.-P. Borra, Review on water electro-sprays and applications of charged drops with focus on the corona-assisted cone-jet mode for High Efficiency Air Filtration by wet electro-scrubbing of aerosols, Journal of Aerosol Science, Vol. 125, pp. 208-236, 2018.
[11] A. Ganan-Calvo, J. Lasheras, J. Dávila, A. Barrero, The electrostatic spray emitted from an electrified conical meniscus, Journal of aerosol science, Vol. 25, No. 6, pp. 1121-1142, 1994.
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[13] H. Oh, K. Kim, S. Kim, Characterization of deposition patterns produced by twin-nozzle electrospray, Journal of Aerosol Science, Vol. 39, No. 9, pp. 801-813, 2008.
[14] J. H. Jung, H. Oh, S. S. Kim, Numerical simulation of the deposition pattern in multiple electrohydrodynamic spraying, Powder Technology, Vol. 198, No. 3, pp. 439-444, 2010.
[15] W. Yang, B. Lojewski, Y. Wei, W. Deng, Interactions and deposition patterns of multiplexed electrosprays, Journal of Aerosol Science, Vol. 46, pp. 20-33, 2012.
[16] Z. Jiang, Y. Gan, Y. Shi, An improved model for prediction of the cone-jet formation in electrospray with the effect of space charge, Journal of Aerosol Science, Vol. 139, pp. 105463, 2020.
[17] J. Grifoll, J. Rosell-Llompart, Efficient Lagrangian simulation of electrospray droplets dynamics, Journal of aerosol science, Vol. 47, pp. 78-93, 2012.
[18] J. Grifoll, J. Rosell-Llompart, Continuous droplets' charge method for the Lagrangian simulation of electrostatic sprays, Journal of Electrostatics, Vol. 72, No. 5, pp. 357-364, 2014.
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[35] R. B. Cole, 2011, Electrospray and MALDI mass spectrometry: fundamentals, instrumentation, practicalities, and biological applications, John Wiley & Sons,
[36] P. Kebarle, M. Peschke, On the mechanisms by which the charged droplets produced by electrospray lead to gas phase ions, Analytica Chimica Acta, Vol. 406, No. 1, pp. 11-35, 2000.
[37] S. Banerjee, S. Mazumdar, Electrospray ionization mass spectrometry: a technique to access the information beyond the molecular weight of the analyte, International journal of analytical chemistry, Vol. 2012, 2012.
[38] Q. He, D. Fu, The improvement of genetic algorithm and its applications for the inversion of orthorhombic anisotropic media, in: SEG Technical Program Expanded Abstracts 1999, Eds., pp. 1791-1792: Society of Exploration Geophysicists, 1999.
[39] H. C. Hunter III, Studies Related to Coulombic Fissions of Charged Droplets and Hygroscopic Behavior of Mixed Particles, 2011.
[40] P. Kebarle, U. H. Verkerk, Electrospray: from ions in solution to ions in the gas phase, what we know now, Mass spectrometry reviews, Vol. 28, No. 6, pp. 898-917, 2009.
[1]           S. Boehringer, P. Ruzgys, L. Tamò, S. Šatkauskas, T. Geiser, A. Gazdhar, D. Hradetzky, A new electrospray method for targeted gene delivery, Scientific reports, Vol. 8, No. 1, pp. 1-12, 2018.
[2]           J. B. Fenn, Electrospray wings for molecular elephants (Nobel lecture), Angewandte Chemie International Edition, Vol. 42, No. 33, pp. 3871-3894, 2003.
[3]           X. Hou, K.-L. Choy, Synthesis and characteristics of CuInS2 films for photovoltaic application, Thin Solid Films, Vol. 480, pp. 13-18, 2005.
[4]           R. Y. Hsu, J. H. Liao, H. W. Tien, G. R. Her, Gas chromatography electrospray ionization mass spectrometry analysis of trimethylsilyl derivatives, Journal of Mass Spectrometry, Vol. 51, No. 10, pp. 883-888, 2016.
[5]           M. K. I. Khan, A. Nazir, A. A. Maan, Electrospraying: a novel technique for efficient coating of foods, Food Engineering Reviews, Vol. 9, No. 2, pp. 112-119, 2017.
[6]           S. Martin, P. Garcia-Ybarra, J. Castillo, Electrospray deposition of catalyst layers with ultra-low Pt loadings for PEM fuel cells cathodes, Journal of Power Sources, Vol. 195, No. 9, pp. 2443-2449, 2010.
[7]           K. Mohammadi, M. R. Movahhedy, S. Khodaygan, A multiphysics model for analysis of droplet formation in electrohydrodynamic 3D printing process, Journal of Aerosol Science, Vol. 135, pp. 72-85, 2019.
[8]           A. M. Gañán-Calvo, J. M. López-Herrera, N. Rebollo-Muñoz, J. Montanero, The onset of electrospray: the universal scaling laws of the first ejection, Scientific reports, Vol. 6, pp. 32357, 2016.
[9]           M. Cloupeau, B. Prunet-Foch, Electrohydrodynamic spraying functioning modes: a critical review, Journal of Aerosol Science, Vol. 25, No. 6, pp. 1021-1036, 1994.
[10]         J.-P. Borra, Review on water electro-sprays and applications of charged drops with focus on the corona-assisted cone-jet mode for High Efficiency Air Filtration by wet electro-scrubbing of aerosols, Journal of Aerosol Science, Vol. 125, pp. 208-236, 2018.
[11]         A. Ganan-Calvo, J. Lasheras, J. Dávila, A. Barrero, The electrostatic spray emitted from an electrified conical meniscus, Journal of aerosol science, Vol. 25, No. 6, pp. 1121-1142, 1994.
[12]         O. Wilhelm, L. Mädler, S. E. Pratsinis, Electrospray evaporation and deposition, Journal of Aerosol Science, Vol. 34, No. 7, pp. 815-836, 2003.
[13]         H. Oh, K. Kim, S. Kim, Characterization of deposition patterns produced by twin-nozzle electrospray, Journal of Aerosol Science, Vol. 39, No. 9, pp. 801-813, 2008.
[14]         J. H. Jung, H. Oh, S. S. Kim, Numerical simulation of the deposition pattern in multiple electrohydrodynamic spraying, Powder Technology, Vol. 198, No. 3, pp. 439-444, 2010.
[15]         W. Yang, B. Lojewski, Y. Wei, W. Deng, Interactions and deposition patterns of multiplexed electrosprays, Journal of Aerosol Science, Vol. 46, pp. 20-33, 2012.
[16]         Z. Jiang, Y. Gan, Y. Shi, An improved model for prediction of the cone-jet formation in electrospray with the effect of space charge, Journal of Aerosol Science, Vol. 139, pp. 105463, 2020.
[17]         J. Grifoll, J. Rosell-Llompart, Efficient Lagrangian simulation of electrospray droplets dynamics, Journal of aerosol science, Vol. 47, pp. 78-93, 2012.
[18]         J. Grifoll, J. Rosell-Llompart, Continuous droplets' charge method for the Lagrangian simulation of electrostatic sprays, Journal of Electrostatics, Vol. 72, No. 5, pp. 357-364, 2014.
[19]         A. M. Gañán-Calvo, N. Rebollo-Muñoz, J. Montanero, The minimum or natural rate of flow and droplet size ejected by Taylor cone–jets: physical symmetries and scaling laws, New Journal of Physics, Vol. 15, No. 3, pp. 033035, 2013.
[20]         D. C. Taflin, T. L. Ward, E. J. Davis, Electrified droplet fission and the Rayleigh limit, Langmuir, Vol. 5, No. 2, pp. 376-384, 1989.
[21]         W. Gu, P. E. Heil, H. Choi, K. Kim, Comprehensive model for fine Coulomb fission of liquid droplets charged to Rayleigh limit, Applied physics letters, Vol. 91, No. 6, pp. 064104, 2007.
[22]         L. Rayleigh, XX. On the equilibrium of liquid conducting masses charged with electricity, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 14, No. 87, pp. 184-186, 1882.
[23]         A. Gomez, K. Tang, Charge and fission of droplets in electrostatic sprays, Physics of Fluids, Vol. 6, No. 1, pp. 404-414, 1994.
[24]         J. Shrimpton, Dielectric charged drop break-up at sub-Rayleigh limit conditions, IEEE Transactions on Dielectrics and Electrical insulation, Vol. 12, No. 3, pp. 573-578, 2005.
[25]         J. Shrimpton, Modeling dielectric charged drop break up using an energy conservation method, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 15, No. 5, pp. 1471-1477, 2008.
[26]         D. G. Roth, A. J. Kelly, Analysis of the disruption of evaporating charged droplets, IEEE transactions on industry applications, No. 5, pp. 771-775, 1983.
[27]         R. Clift, J. R. Grace, M. E. Weber, 2005, Bubbles, drops, and particles, Courier Corporation,
[28]         M. Rahmanpour, R. Ebrahimi, Numerical Simulation of Heat and Mass Transfer and Fission of Charged Droplets in an Electrohydrodynamic spray, Thesis, K. N. Toosi University of Technology, Iran, 2017.
[29]         A. H. Lefebvre, V. G. McDonell, 2017, Atomization and sprays, CRC press,
[30]         Y. Mori, K. Hijikata, T. Nagasaki, Electrostatic atomization for small droplets of uniform diameter, Trans. Jpn. Soc. Mech. Eng. Ser. B, Vol. 47, pp. 1881-1890, 1981.
[31]         H. Liu, M. Altan, Science and engineering of droplets: fundamentals and applications, Appl. Mech. Rev., Vol. 55, No. 1, pp. B16-B17, 2002.
[32]         S. R. Turns, 1996, Introduction to combustion, McGraw-Hill Companies,
[33]         M. Rahmanpour, R. Ebrahimi, Numerical simulation of electrohydrodynamic spray with stable Taylor cone–jet, Heat and Mass Transfer, Vol. 52, No. 8, pp. 1595-1603, 2016.
[34]         J. B. Fenn, Ion formation from charged droplets: roles of geometry, energy, and time, Journal of the American Society for Mass Spectrometry, Vol. 4, No. 7, pp. 524-535, 1993.
[35]         R. B. Cole, 2011, Electrospray and MALDI mass spectrometry: fundamentals, instrumentation, practicalities, and biological applications, John Wiley & Sons,
[36]         P. Kebarle, M. Peschke, On the mechanisms by which the charged droplets produced by electrospray lead to gas phase ions, Analytica Chimica Acta, Vol. 406, No. 1, pp. 11-35, 2000.
[37]         S. Banerjee, S. Mazumdar, Electrospray ionization mass spectrometry: a technique to access the information beyond the molecular weight of the analyte, International journal of analytical chemistry, Vol. 2012, 2012.
[38]         Q. He, D. Fu, The improvement of genetic algorithm and its applications for the inversion of orthorhombic anisotropic media,  in: SEG Technical Program Expanded Abstracts 1999, Eds., pp. 1791-1792: Society of Exploration Geophysicists, 1999.
[39]         H. C. Hunter III, Studies Related to Coulombic Fissions of Charged Droplets and Hygroscopic Behavior of Mixed Particles, 2011.
[40]      P. Kebarle, U. H. Verkerk, Electrospray: from ions in solution to ions in the gas phase, what we know now, Mass spectrometry reviews, Vol. 28, No. 6, pp. 898-917, 2009.

Volume 51, Issue 2
December 2020
Pages 454-463
  • Receive Date: 21 June 2020
  • Revise Date: 23 August 2020
  • Accept Date: 01 September 2020