A distributed parameter model for the solvent evaporation from a saline droplet including internal solute diffusion and heat conduction

References

• Abdullahi, H., C. L. Burcham, and T. Vetter. 2020. A mechanistic model to predict droplet drying history and particle shell formation in multicomponent systems. Chem. Eng. Sci. 224:115713. doi:10.1016/j.ces.2020.115713.
   Web of Science ®Google Scholar
• Abramzon, B., and W. A. Sirignano. 1989. Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Transf. 32 (9):1605–18. doi:10.1016/0017-9310(89)90043-4.
   Web of Science ®Google Scholar
• Adhikari, B., T. Howes, and B. R. Bhandari. 2007. Use of solute fixed coordinate system and method of lines for prediction of drying kinetics and surface stickiness of single droplet during convective drying. Chem. Eng. Process 46 (5):405–19. doi:10.1016/j.cep.2006.06.018.
   Web of Science ®Google Scholar
• Ali, M., T. Mahmud, P. J. Heggs, and A. E. Bayly. 2017. Modelling drying and crystallisation in a single droplet. EuroDrying’2017 – 6th European Drying Conference.
   Google Scholar
• Anderson, E. L., P. Turnham, J. R. Griffin, and C. C. Clarke. 2020. Consideration of the aerosol transmission for COVID-19 and public health. Risk Anal. 40 (5):902–7. doi:10.1111/risa.13500.
   PubMed Web of Science ®Google Scholar
• Asadi, S., N. Bouvier, A. S. Wexler, and W. D. Ristenpart. 2020. The coronavirus pandemic and aerosols: Does COVID-19 transmit via expiratory particles? In. Aerosol Sci. Technol. 1 (2):1–4. doi:10.1080/02786826.2020.1749229.
   Google Scholar
• Bridgeman, O. C., and E. W. Aldrich. 1964. Vapor pressure tables for water. Journal of Heat Transfer 86 (2):279–86. doi:10.1115/1.3687121.
   Google Scholar
• Brokaw, R. S. 2002. Predicting transport properties of dilute gases. Ind. Eng. Chem. Proc. Des. Dev. 8 (2):240–53. doi:10.1021/i260030a015.
   Google Scholar
• Clift, R., J. R. Grace, and M. E. Weber. 1978. Bubbles, drops and particles. New York: Academic Press Inc.
   Google Scholar
• Crowe, C. T., J. D. Schwarzkopf, M. Sommerfeld, and Y. Tsuji. 2011. Multiphase flows with droplets and particles. 2nd ed. Boca Raton: CRC Press.
   Google Scholar
• De Oliveira, P. M., L. C. C. Mesquita, S. Gkantonas, A. Giusti, and E. Mastorakos. 2021. Evolution of spray and aerosol from respiratory releases: Theoretical estimates for insight on viral transmission. Proc. Math. Phys. Eng. Sci. 477 (2245):20200584. doi:10.1098/rspa.2020.0584.
   PubMed Web of Science ®Google Scholar
• de Souza Lima, R., M. I. Ré, and P. Arlabosse. 2020. Drying droplet as a template for solid formation: A review. In. Powder Technol. 359:161–71. doi:10.1016/j.powtec.2019.09.052.
   Web of Science ®Google Scholar
• Dormand, J. R., and P. J. Prince. 1980. A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6 (1):19–26. doi:10.1016/0771-050X(80)90013-3.
   Google Scholar
• Fuchs, N. A. 1959. Evaporation and droplet growth in gaseous media. Oxford: Pergamon Press. doi:10.1016/c2013-0-08145-5.
   Google Scholar
• Fuchs, N., and A. Sutugin. 1971. High-dispersed aerosols. In Topics in current aerosol research, eds. G. M. Hidy and J. R. Brock, 1. Oxford: Pergamon. doi:10.1016/b978-0-08-016674-2.50006-6.
   Google Scholar
• Gregson, F. K. A. 2020. Evaporation kinetics and particle formation from aerosol solution microdroplets. PhD thesis, University of Bristol.
   Google Scholar
• Gregson, F. K. A., J. F. Robinson, R. E. H. Miles, C. P. Royall, and J. P. Reid. 2019. Drying kinetics of salt solution droplets: Water evaporation rates and crystallization. J. Phys. Chem. B 123 (1):266–76. doi:10.1021/acs.jpcb.8b09584.
   PubMed Web of Science ®Google Scholar
• Hairer, E., and G. Wanner. 1991. Solving ordinary differential equations II: Stiff and differential - algebraic problems. 1st ed. Berlin, Heidelberg: Springer-Verlag. doi:10.1007/978-3-662-09947-6.
   Google Scholar
• Handscomb, C. S., M. Kraft, and A. E. Bayly. 2009. A new model for the drying of droplets containing suspended solids. Chem. Eng. Sci. 64 (4):628–37. doi:10.1016/j.ces.2008.04.051.
   Web of Science ®Google Scholar
• Hardy, D. A., J. F. Robinson, T. G. Hilditch, E. Neal, P. Lemaitre, J. S. Walker, and J. P. Reid. 2023. Accurate measurements and simulations of the evaporation and trajectories of individual solution droplets. J. Phys. Chem. B 127 (15):3416–30. doi:10.1021/acs.jpcb.2c08909.
   PubMed Web of Science ®Google Scholar
• Kukkonen, J., T. Vesala, and M. Kulmala. 1989. The interdependence of evaporation and settling for airborne freely falling droplets. J. Aerosol Sci. 20 (7):749–63. doi:10.1016/0021-8502(89)90087-6.
   Web of Science ®Google Scholar
• Langmuir, I. 1918. The evaporation of small spheres. Physical Review 12 (5):368. doi:10.1103/PhysRev.12.368.
   Google Scholar
• Lindfield, G., and J. Penny. 2018. Numerical methods: Using MATLAB. 4th ed. London: Academic Press. doi:10.1016/C2016-0-00395-9.
   Google Scholar
• Liu, L., J. Wei, Y. Li, and A. Ooi. 2017. Evaporation and dispersion of respiratory droplets from coughing. Indoor Air. 27 (1):179–90. doi:10.1111/ina.12297.
   PubMed Web of Science ®Google Scholar
• Mao, N., C. K. An, L. Y. Guo, M. Wang, L. Guo, S. R. Guo, and E. S. Long. 2020. Transmission risk of infectious droplets in physical spreading process at different times: A review. In. Build. Environ. 185:107307. doi:10.1016/j.buildenv.2020.107307.
   PubMed Web of Science ®Google Scholar
• Morawska, L., and J. Cao. 2020. Airborne transmission of SARS-CoV-2: The world should face the reality. Environ. Int. 139:105730. doi:10.1016/J.ENVINT.2020.105730.
   PubMed Web of Science ®Google Scholar
• Parienta, D., L. Morawska, G. R. Johnson, Z. D. Ristovski, M. Hargreaves, K. Mengersen, S. Corbett, C. Y. H. Chao, Y. Li, and D. Katoshevski. 2011. Theoretical analysis of the motion and evaporation of exhaled respiratory droplets of mixed composition. J. Aerosol Sci. 42 (1):1–10. doi:10.1016/j.jaerosci.2010.10.005.
   Web of Science ®Google Scholar
• Perry, R. H., and D. W. Green. 1997. Perry's chemical Engineers’ handbook. 7th ed. New York: McGraw-Hill Education.
   Google Scholar
• Pitzer, K. S. 1973. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 77 (2):268–77. doi:10.1021/j100621a026.
   Web of Science ®Google Scholar
• Poozesh, S., F. Algasem, M. A. Azad, and P. J. Marsac. 2022. Multicomponent droplet drying modeling based on conservation and population balance equations. Pharm. Res. 39 (9):2033–47. doi:10.1007/s11095-022-03248-4.
   PubMed Web of Science ®Google Scholar
• Pourfattah, F., L. P. Wang, W. Deng, Y. F. Ma, L. Hu, and B. Yang. 2021. Challenges in simulating and modeling the airborne virus transmission: A state-of-the-art review. In. Phys. Fluids (1994) 33 (10):101302. doi:10.1063/5.0061469.
   PubMed Web of Science ®Google Scholar
• Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. 1992. Numerical recipes in C: The art of scientific computing. 2nd ed. Cambridge: Cambridge University Press.
   Google Scholar
• Ranz, W. E., and W. R. Marshall. 1952a. Evaporation from drops - Part 1. In. Chem. Eng. Prog. (48:141–6.
   Web of Science ®Google Scholar
• Ranz, W. E., and W. R. Marshall. 1952b. Evaporation from drops part II. Chem. Eng. Prog. 48 (4):173–80.
   Web of Science ®Google Scholar
• Redrow, J., S. Mao, I. Celik, J. A. Posada, and Z. g Feng. 2011. Modeling the evaporation and dispersion of airborne sputum droplets expelled from a human cough. Build. Environ. 46 (10):2042–51. doi:10.1016/j.buildenv.2011.04.011.
   Web of Science ®Google Scholar
• Rezaei, M., and R. R. Netz. 2021. Water evaporation from solute-containing aerosol droplets: Effects of internal concentration and diffusivity profiles and onset of crust formation. Phys. Fluids (1994) 33 (9):091901. doi:10.1063/5.0060080.
   PubMed Web of Science ®Google Scholar
• Robinson, R. A., and R. H. Stokes. 2012. Electrolyte solutions: Second revised edition. Mineola, NY: Dover Publications.
   Google Scholar
• Rogers, R. R., and M. K. Yau. 1989. A short course in cloud physics. 3rd ed. Oxford: Butterworth-Heinemann.
   Google Scholar
• Rosenbrock, H. H. 1963. Some general implicit processes for the numerical solution of differential equations. The Computer Journal 5 (4):329–30. doi:10.1093/comjnl/5.4.329.
   Web of Science ®Google Scholar
• Sadafi, M. H., I. Jahn, A. B. Stilgoe, and K. Hooman. 2014. Theoretical and experimental studies on a solid containing water droplet. Int. J. Heat Mass Transf. 78:25–33. doi:10.1016/j.ijheatmasstransfer.2014.06.064.
   Web of Science ®Google Scholar
• Sazhin, S. S. 2006. Advanced models of fuel droplet heating and evaporation. Prog. Energy Combust. Sci. 32 (2):162–214. doi:10.1016/j.pecs.2005.11.001.
   Web of Science ®Google Scholar
• Schiesser, W. E., and G. W. Griffiths. 2009. A compendium of partial differential equation models: Method of lines analysis with matlab. New York: Cambridge University Press. doi:10.1017/CBO9780511576270.
   Google Scholar
• Schiller, L., and A. Naumann. 1935. A drag coefficient correlation. VDI Zeitung. 77:318–320.
   Google Scholar
• Seinfeld, J. H., and S. N. Pandis. 2016. Atmospheric chemistry and physics: From air pollution to climate change. 3rd ed. Hoboken, NJ: Wiley-Blackwell.
   Google Scholar
• Seydel, P., J. Blömer, and J. Bertling. 2006. Modeling particle formation at spray drying using population balances. Drying Technol. 24 (2):137–46. doi:10.1080/07373930600558912.
   Web of Science ®Google Scholar
• Tang, I. N. 1996. Chemical and size effects of hygroscopic aerosols on light scattering coefficients. J. Geophys. Res. 101 (D14):19245–50. doi:10.1029/96JD03003.
   Web of Science ®Google Scholar
• van der Lijn, J. 1976. The “constant rate period” during the drying of shrinking spheres. Chem. Eng. Sci. 31 (10):929–35. doi:10.1016/0009-2509(76)87043-1.
   Web of Science ®Google Scholar
• Vehring, R. 2008. Pharmaceutical particle engineering via spray drying. In. Pharm. Res. 25 (5):999–1022. doi:10.1007/s11095-007-9475-1.
   PubMed Web of Science ®Google Scholar
• Vejerano, E. P., and L. C. Marr. 2018. Physico-chemical characteristics of evaporating respiratory fluid droplets. J. R Soc. Interface 15 (139):20170939. doi:10.1098/rsif.2017.0939.
   PubMed Web of Science ®Google Scholar
• Wells, W. F. 1934. On air-borne infection: Study II. Droplets and droplet nuclei. Am. J. Epidemiol. 20 (3):619–27. doi:10.1093/oxfordjournals.aje.a118097.
   Google Scholar
• Xie, X., Y. Li, A. T. Y. Chwang, P. L. Ho, and W. H. Seto. 2007. How far droplets can move in indoor environments - revisiting the Wells evaporation-falling curve. Indoor Air 17 (3):211–25. doi:10.1111/j.1600-0668.2007.00469.x.
   PubMed Web of Science ®Google Scholar
• Yarin, A. L., G. Brenn, O. Kastner, D. Rensink, and C. Tropea. 1999. Evaporation of acoustically levitated droplets. J. Fluid Mech. 399:151–204. doi:10.1017/S0022112099006266.
   Web of Science ®Google Scholar