Numerical simulations and experimental verifications at micro-, meso-, andmacroscales of droplet evaporation: A comprehensive review with special focus on saline droplets

Abstract

Evaporation of saline droplets significantly impacts industrial processes such as water and gas treatment. Simulations, with advantages in describing temperature, concentration, and velocity distribution inside the droplet, receive increasing attentions. This paper summarized research on numerical simulations of droplet evaporation atmicro-, meso-, and macroscales, emphasizing saline or multicomponent droplets. Accurate description of physics at phase interfaces andwithin proves to be critical for modeling. While recent studies have investigated on interface motion and temperature distribution, the coupling effect of internal concentration and flow distribution is still rarely considered. Among numerical methods, the lattice Boltzmann method is suitable for droplet scale due to its ability to handle non-continuum behavior. Bridging multiscale models remains a challenge, particularly in describing Marangoni and capillary flows. Experimental approaches to the effects of external physical fields (electric, magnetic, convection, and laser) and substrate properties on evaporation were also reviewed. Visualizing evaporation under various conditions can validate macroscopic models, while experiments with different substrates can validate molecular scale simulations, as substrate properties primarily affect evaporation by affecting capillary flow at the droplet bottom. This paper comprehensively reviewed numerical research on droplet evaporation, and analyzed the advantages, limitations, and development directions of various numericalmethods.

References

[1] Yang K, Sun J, Lu H, McColl CA, Jiang Y, He Q. Enhanced surface water-energy coupling on the Tibetan Plateau over the past six decades (1960-2020). Fundam Res. 2024, in press.

[2] Zhu L, Li X, Feng B, Liu F. Evaluation of transmission risk of respiratory particles under different ventilation strategies in an elevator. Build Simul. 2024;17:771-784.

[3] Chen Q, Thu K, Bui TD, Li Y, Ng KC, Chua KJ. Development of a model for spray evaporation based on droplet analysis. Desalination. 2016;399:69-77.

[4] Chen Q, Li Y, Chua KJ. Experimental and mathematical study of the spray flash evaporation phenomena. Appl Therm Eng. 2018;130:598-610.

[5] Dong C, Huang Y, Zhang L. Slug flow-enhanced vacuum membrane distillation for seawater desalination: flux improvement and anti-fouling effect. Sep Purif Technol. 2023;320:124178.

[6] Li A, He M, Zheng M, et al. Bioinspired multi-scale core-spun yarn-based solar evaporator for ultra-efficient and durable high-salinity brine desalination. Fundam Res. 2023, in press.

[7] Zhou Z, Cao C, Cao L, et al. Effect of surfactant concentration on the evaporation of droplets on cotton (Gossypium hirsutum L.) leaves. Colloids Surf B. 2018;167:206-212.

[8] Gao K, Haddad S, Paolini R, et al. The use of green infrastructure and irrigation in the mitigation of urban heat in a desert city. Build Simul. 2024;17:679-694.

[9] Zhou Z, Cao C, Cao L, et al. Evaporation kinetics of surfactant solution droplets on rice (Oryza sativa) leaves. PLoS One. 2017;12:e0176870.

[10] Deng B, De Ruiter J, Schroën K. Application of microfluidics in the production and analysis of food foams. Foods. 2019;8:476.

[11] Duverge JJ, Rajagopalan P. Assessment of factors influencing the energy and water performance of aquatic centres. Build Simul. 2020;13:771-786.

[12] Wang Y, Zou Y, Yang Y, Wu S, Zhang X, Ren X. Movement and control of evaporating droplets released from an open surface tank in the push-pull ventilation system. Build Simul. 2016;9:443-457.

[13] Pandya B, Modi N, Upadhyai R, Patel J. Thermodynamic performance and comparison of solar assisted double effect absorption cooling system with LiCl-H2O and LiBr-H2O working fluid. Build Simul. 2019;12:1063-1075.

[14] Yue J, Li Y, Luo Z, Huang X, Kong Q, Wang Z. Study on deterioration law and mechanism of gray brick due to salt crystallization. Materials. 2022;15:2936.

[15] Granneman SJC, Lubelli B, van Hees RPJ. Mitigating salt damage in building materials by the use of crystallization modifiers-a review and outlook. J Cult Herit. 2019;40:183-194.

[16] Ates C, Karwan F, Okraschevski M, Koch R, Bauer H. Conditional generative adversarial networks for modelling fuel sprays. Energy AI. 2023;12:100216.

[17] Honzawa T, Kai R, Hori K, Seino M, Nishiie T, Kurose R. Experimental and numerical study of water sprayed turbulent combustion: proposal of a neural network modeling for five-dimensional flamelet approach. Energy AI. 2021;5:100076.

[18] Maxwell JC. VIII. A dynamical theory of the electromagnetic field. Philosophical transactions of the Royal Society of London. 1865;155:459-512.

[19] Langmuir I. The evaporation of small spheres. Phys Rev. 1918;12:368.

[20] Fuchs N. Concerning the Velocity of Evaporation of Small Droplets in a Gas Atmosphere. Physikalische Zeitschrift der Sowjetunion. 1947;6:NACA-TM-1160.

[21] Wang W, Huang X, Wang L, et al. Study on the mechanism of sessile droplets evaporation enhanced by the electric field. Chem Eng Sci. 2024;288:119768.

[22] Guo P, Zhang B, Li T, Xu B, Li J. An experimental and numerical study on the brine droplet evaporation considering salt precipitation. Appl Therm Eng. 2023;234:121312.

[23] Zhang B, Niu Y, Guo P. Establishment of reaction engineering approach for saline droplet and its application in spray evaporation simulation. Desalination. 2024;575:117330.

[24] Cedeno R, Grossier R, Tishkova V, Candoni N, Flood A, Veesler S. Evaporation dynamics of sessile saline microdroplets in oil. Langmuir. 2022;38:9686-9696.

[25] Guo G, Deng H, Zhu C, Ji Z. Spatially dependent salinity effect in actively vacuumed spray flash desalination. Desalination. 2022;537:115868.

[26] van Gaalen RT, Diddens C, Wijshoff HMA, Kuerten JGM. Marangoni circulation in evaporating droplets in the presence of soluble surfactants. J Colloid Interface Sci. 2021;584:622-633.

[27] Ljung AL, Lundström TS. Heat and mass transfer boundary conditions at the surface of a heated sessile droplet. Heat Mass Transfer. 2017;53:3581-3591.

[28] Al-Rawi O, Wilson M. Influence of forced convection on the evaporation and internal dynamics inside of an array of salt solution droplets. MATEC Web of Conference. 2018;240:01002.

[29] Muramatsu H, Pillai AL, Kitada K, Kurose R. Numerical simulation of bi-component fuel droplet evaporation using Level Set method. Fuel. 2022;318:123331.

[30] Yang K, Hong F, Cheng P. A fully coupled numerical simulation of sessile droplet evaporation using arbitrary Lagrangian-Eulerian formulation. Int J Heat Mass Transfer. 2014;70:409-420.

[31] Jiang Y, Chi F, Chen Q, Zhou X. Effect of substrate microstructure on thermocapillary flow and heat transfer of nanofluid droplet on heated wall. Microgravity Sci Technol. 2021;33:37.

[32] Li H, Anglart H. Prediction of dryout and post-dryout heat transfer using a two-phase CFD model. Int J Heat Mass Transfer. 2016;99:839-850.

[33] Ljung AL, Lundström TS. Evaporation of a sessile water droplet subjected to forced convection in humid environment. Drying Technol. 2019;37:129-138.

[34] Nguyen TAH, Biggs S, Doi A, Nguyen A. A new way of assessing droplet evaporation independently of the substrate hydrophobicity and contact line mode: a case study of sessile droplets with surfactants. Colloids Surf A. 2019;577:396-404.

[35] Saufi AE, Frassoldati A, Faravelli T, Cuoci A. DropletSMOKE++: a comprehensive multiphase CFD framework for the evaporation of multidimensional fuel droplets. Int J Heat Mass Transfer. 2019;131:836-853.

[36] Gaballa H, Jafari S, Habchi C, Hemptinne JC. Numerical investigation of droplet evaporation in high-pressure dual-fuel conditions using a tabulated real-fluid model. Int J Heat Mass Transfer. 2022;189:122671.

[37] Strotos G, Malgarinos I, Nikolopoulos N, Gavaises M. Predicting the evaporation rate of stationary droplets with the VOF methodology for a wide range of ambient temperature conditions. Int J Therm Sci. 2016;109:253-262.

[38] Reutzsch J, Kieffer-Roth C, Weigand B. A consistent method for direct numerical simulation of droplet evaporation. J Comput Phys. 2020;413:109455.

[39] Li J, Zhang J. A theoretical study of the spheroidal droplet evaporation in forced convection. Phys Lett. 2014;378:3537-3543.

[40] Rybdylova O, Poulton L, Al Qubeissi M, et al. A model for multi-component droplet heating and evaporation and its implementation into ANSYS fluent. Int Commun Heat Mass Transfer. 2018;90:29-33.

[41] Saufi AE, Calabria R, Chiariello F, et al. An experimental and CFD modeling study of suspended droplets evaporation in buoyancy driven convection. Chem Eng J. 2019;375:122006.

[42] Säckel W, Nieken U. Simulation of morphology evolution in spray drying of suspensions by a meshfree approach. Chem Ing Tech. 2022;94:340-347.

[43] Hou D, Wang G, Gao J, Luo KH. Molecular dynamics study on evaporation of metal nitrate-containing nanodroplets in flame spray pyrolysis. Nanoscale. 2023;15:5877-5890.

[44] Zhang Y, Jia M, Yi P, Chang Y, He Z, Wang Q. A molecular dynamics study of binary-component n-alkane fuel vaporization characteristics at sub/supercritical nitrogen environments. Proc Combust Inst. 2021;38:3303-3312.

[45] Ren J, Crivoi A, Duan F. Dendritic nanoparticle self-assembly from drying a sessile nanofluid droplet. Phys Chem Chem Phys. 2021;23:15774-15783.

[46] Zolotarev PA, Kolegov KS. Monte Carlo simulation of particle size separation in evaporating bi-dispersed colloidal droplets on hydrophilic substrates. Phys Fluids. 2022;34:017107.

[47] Zhang T, Xu H, Wu T, Li B, Wang J. Numerical simulation of evaporation and internal flow of substrate droplet under electric field. Chem Ind Eng Prog. 2022;41:609-618.

[48] Yao J, Wang J, Dong Q, et al. Lattice Boltzmann study of droplet evaporation on a heated substrate under a uniform electric field. Appl Therm Eng. 2022;211:118517.

[49] Wang B, Wang X, Duan Y, Chen M. Molecular dynamics simulation on evaporation of water and aqueous droplets in the presence of electric field. Int J Heat Mass Transfer. 2014;73:533-541.

[50] Ren G, Wang YT. Saturated sodium chloride solution under an external static electric field: a molecular dynamics study. Chin Phys B. 2015;24:126402.

[51] Hens A, Biswas G, De S. Evaporation of water droplets on Pt-surface in presence of external electric field-a molecular dynamics study. J Chem Phys. 2015;143:094702.

[52] Chatterjee S, Hens A, Ghanta KC, Biswas G. Molecular dynamics study of sessile ionic nanodroplet under external electric field. Chem Eng Sci. 2021;229:116143.

[53] Zhang J, Borg MK, Ritos K, Reese JM. Electrowetting controls the deposit patterns of evaporated salt water nanodroplets. Langmuir. 2016;32:1542-1549.

[54] Zhan L, Chen H, Zhou H, et al. Molecular dynamics study on evaporation of high-salinity wastewater droplet. Appl Therm Eng. 2022;213:118752.

[55] Wen Y, Liu Y. On-demand evaporation mode of sessile droplet by designing substrate surface wettability patterns. Phys Fluids. 2021;33:122015.

[56] Huang Y, Zhang C, Meng S. Molecular origin of fast evaporation at the solid-water-vapor line in a sessile droplet. Nanoscale. 2022;14:2729-2734.

[57] Wu M, Di Y, Man X, Doi M. Drying droplets with soluble surfactants. Langmuir. 2019;35:14734-14741.

[58] Zhang J, Borg MK, Sefiane K, Reese JM. Wetting and evaporation of salt-water nanodroplets: a molecular dynamics investigation. Phys Rev E. 2015;92:052403.

[59] Savenko VS, Verbinska GM, Bulavin LA. Computer simulation of evaporation process of NaCl aqueous solution. Ukr J Phys. 2016;61:812-812.

[60] Wu S, Yu X, Qiu L, Zhu Y, Wu Z. Molecular dynamics simulation and analysis on evaporation of high-salt solution. J Therm Sci Technol. 2023;22:38-46.

[61] Liu L, Han Y, Wang Q, Fu Q. Evaporation of supercritical droplets in an electric field using molecular dynamics simulation. AIP Adv. 2022;12:045021.

[62] Kumar VA, Sajith V, Sathian SP. Influence of nanoparticles on the evaporation of a nanodroplet from solid substrates: an experimental and molecular dynamics investigation. Colloids Surf A. 2021;615:126227.

[63] Sun Y, Huang T, Zhao J, Chen Y. Evaporation of a nanodroplet on a rough substrate. Front Phys. 2017;12:126401.

[64] Gao Y, Liu J. Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations. Phys D. 2021;428:133067.

[65] Datadien KPN, Di Staso G, Diddens C, Wijshoff HMA, Toschi F. Comparison of lattice Boltzmann, finite element and volume of fluid multicomponent methods for microfluidic flow problems and the jetting of microdroplets. Commun Comput Phys. 2023;33:912-936.

[66] Gunstensen AK, Rothman DH, Zaleski S, Zanetti G. Lattice Boltzmann model of immiscible fluids. Phys Rev A. 1991;43:4320.

[67] Rothman DH, Keller JM. Immiscible cellular-automaton fluids. J Stat Phys. 1988;52:1119-1127.

[68] Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E. 1993;47:1815.

[69] Shan X, Chen H. Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Phys Rev E. 1994;49:2941.

[70] Shan X, Doolen G. Multicomponent lattice-Boltzmann model with interparticle interaction. J Stat Phys. 1995;81:379-393.

[71] Shan X, Doolen G. Diffusion in a multicomponent lattice Boltzmann equation model. Phys Rev E. 1996;54:3614.

[72] Swift MR, Orlandini E, Osborn WR, Yeomans JM. Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys Rev E. 1996;54:5041.

[73] He X, Shan X, Doolen GD. Discrete Boltzmann equation model for nonideal gases. Phys Rev E. 1998;57:R13.

[74] Ziegler DP. Boundary conditions for lattice Boltzmann simulations. J Stat Phys. 1993;71:1171-1177.

[75] Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. 1997;9:1591-1598.

[76] Guo Z, Zheng C, Shi B. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin Phys. 2002;11:366.

[77] Shao JY, Shu C, Wu J, Chew YT. A stencil adaptive phase-field lattice Boltzmann method for two dimensional incompressible multiphase flows. Int J Numer Methods Fluids. 2013;72:671-696.

[78] Zhang C, Zhang H, Zhang X, Yang C, Cheng P. Evaporation of a sessile droplet on flat surfaces: an axisymmetric lattice Boltzmann model with consideration of contact angle hysteresis. Int J Heat Mass Transfer. 2021;178:121577.

[79] Srivastava S, Perlekar P, ten Thije Boonkkamp JHM, Verma N, Toschi F. Axisymmetric multiphase lattice Boltzmann method. Phys Rev E. 2013;88:013309.

[80] Kazemian BB, Cheng P. Simulations of contact angle hysteresis effects in droplet sliding on inclined isothermal surfaces and droplet evaporating on heated horizontal surfaces by a lattice Boltzmann method with a variable solid-fluid interaction strength scheme. Int J Heat Mass Transfer. 2022;186:122454.

[81] Albernaz D, Do-Quang M, Amberg G. Multirelaxation-time lattice Boltzmann model for droplet heating and evaporation under forced convection. Phys Rev E. 2015;91:043012.

[82] Wang D, Cheng P. Nanoparticles deposition patterns in evaporating nanofluid droplets on smooth heated hydrophilic substrates: a 2D immersed boundary-lattice Boltzmann simulation. Int J Heat Mass Transfer. 2021;168:120868.

[83] Xie C, Zhang J, Bertola V, Wang M. Droplet evaporation on a horizontal substrate under gravity field by mesoscopic modeling. J Colloid Interface Sci. 2016;463:317-323.

[84] Zarghami A, Van den Akker HEA. Thermohydrodynamics of an evaporating droplet studied using a multiphase lattice Boltzmann method. Phys Rev E. 2017;95:043310.

[85] Farhadi J, Bazargan V. Marangoni flow and surfactant transport in evaporating sessile droplets: a lattice Boltzmann study. Phys Fluids. 2022;34:032115.

[86] Yang W, Li H, Alhosani MH, Zhang T. Prediction of thin liquid film evaporation characteristics with a thermal lattice Boltzmann method. 2016 15th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM). 2016:1240-1247.

[87] Sugimoto M, Sawada Y, Kaneda M, Suga K. Consistent evaporation formulation for the phase-field lattice Boltzmann method. Phys Rev E. 2021;103:053307.

[88] Lee T. Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids. Comput Math Appl. 2009;58:987-994.

[89] Safari H, Rahimian MH, Krafczyk M. Consistent simulation of droplet evaporation based on the phase-field multiphase lattice Boltzmann method. Phys Rev E. 2014;90:033305.

[90] Hu Y. A diffuse interface-lattice Boltzmann model for surfactant transport on an interface. Appl Math Lett. 2021;111:106614.

[91] Saroj SK, Panigrahi PK. Magnetic suppression of the coffee ring effect. J Magn Magn Mater. 2020;513:167199.

[92] Chattopadhyay A, Dwivedi RK, Harikrishnan AR, Dhar P. Ferro-advection aided evaporation kinetics of ferrofluid droplets in magnetic field ambience. Phys Fluids. 2020;32:082001.

[93] Zaibudeen AW, Bandyopadhyay R. DC field coupled evaporation of a sessile gold nanofluid droplet. Soft Matter. 2021;17:10294-10300.

[94] Xu H, Wang J, Tian J, et al. Evaporation characteristics and heat transfer enhancement of sessile droplets under non-uniform electric field. Exp Therm Fluid Sci. 2021;126:110378.

[95] Liu Z, Zhou J, Li Y, Zhuo X, Shi X, Jing D. Evaporation and drying characteristics of the sessile ferrofluid droplet under a horizontal magnetic field. Fundam Res. 2022;2:222-229.

[96] Shyam S, Mondal PK, Mehta B. Field driven evaporation kinetics of a sessile ferrofluid droplet on a soft substrate. Soft Matter. 2020;16:6619-6632.

[97] Jaiswal V, Dhar P. Interplay of electro-thermo-solutal advection and internal electrohydrodynamics governed enhanced evaporation of droplets. Proc Royal Soc A. 2019;475:20190046.

[98] Kaushal A, Mehandia V, Dhar P. Regulating complex fluid sessile droplet evaporation kinetics by suppression of internal electro-convection. Colloids Surf A. 2022;653:130010.

[99] Almada LFA, Fontes KES, Vitoriano JO, Melo VRM, Fraga FEN. Applying pulsed corona discharge in hypersaline droplets. J Phys D: Appl Phys. 2020;54:055202.

[100] Wang J, Zhao T, Tian J, et al. Oscillating evaporation of pendant droplets under the action of ionic wind. Colloids Surf A. 2022;650:129579.

[101] Gibbons MJ, Garivalis AI, O’Shaughnessy S, Di Marco P, Robinson AJ. Evaporating hydrophilic and superhydrophobic droplets in electric fields. Int J Heat Mass Transfer. 2021;164:120539.

[102] Starinskaya E, Miskiv NB, Nazarov AD, Terekhov VV, Terekhov VI. Experimental study of evaporating droplets suspended ethanol-water solution under conditions of forced convection. Interfacial Phenom Heat Transfer. 2018;6:115-127.

[103] Bochkareva EM, Miskiv NB, Nazarov AD. Features of heat transfer during the evaporation of a drop of nanofluid. J Phys: Conf Ser. 2019;1382:012105.

[104] Misyura SY. Evaporation and heat and mass transfer of a sessile drop of aqueous salt solution on heated wall. Int J Heat Mass Transfer. 2018;116:667-674.

[105] Misyura SY, Kuznetsov GV, Volkov RS, Lezhnin SI, Morozov VS. The effect of impurity particles on the forced convection velocity in a drop. Powder Technol. 2020;362:341-349.

[106] Li D, Jiao L, Chen R, et al. Controllable light-induced droplet evaporative crystallization. Soft Matter. 2021;17:8730-8741.

[107] Liu Z, Yan Y, Wang X, Chen X. Droplet deposition pattern affected by different heating directions. J Bionic Eng. 2020;17:795-801.

[108] Basu N, Mukherjee R. Morphology modulation in evaporative drying mediated crystallization of sodium chloride solution droplet with surfactant. Soft Matter. 2018;14:7883-7893.

[109] Dewangan JK, Basu N, Chowdhury M. Cationic surfactant-directed structural control of NaCl crystals from evaporating sessile droplets. Soft Matter. 2022;18:62-79.

[110] Shao X, Hou Y, Zhong X. Modulation of evaporation-affected crystal motion in a drying droplet by saline and surfactant concentrations. Colloids Surf A. 2021;623:126701.

[111] Ghafouri A, Zhao M, Singler TJ, Yong X, Chiarot PR. Interfacial targeting of sessile droplets using electrospray. Langmuir. 2018;34:7445-7454.

[112] Zhong X, Ren J, Duan F. Wettability effect on evaporation dynamics and crystalline patterns of sessile saline droplets. J Phys Chem B. 2017;121:7924-7933.

[113] Guo D, Li X, Zhang H, et al. Experimental study on the characteristics of temperature dependent surface/interfacial properties of a non-ionic surfactant aqueous solution at quasi-thermal equilibrium condition. Int J Heat Mass Transfer. 2022;182:122003.

[114] Qazi MJ, Liefferink RW, Schlegel SJ, Backus EHG, Bonn D, Shahidzadeh N. Influence of surfactants on sodium chloride crystallization in confinement. Langmuir. 2017;33:4260-4268.

[115] Zhang Y, Ye F, Dai J, He B, Zang D. Influence of nano-scaled roughness on evaporation patterns of colloidal droplets. Acta Phys Sin. 2017;66:177-183.

[116] Wang X, Liu Z, Wang L, Yan Y. Investigation of droplet evaporation on copper substrate with different roughness. J Bionic Eng. 2020;17:835-842.

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