# Molecular Dynamics Simulations on Evaporation of Droplets with Dissolved Salts

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{+}-water has the strongest interaction and hydration effect, so LiCl aqueous droplets evaporate the slowest, then NaCl and KCl. Higher salt concentration also enhances the ion-water interaction and hydration effect, and hence corresponds to a slower evaporation. In the last stage of evaporation, only a small amount of water molecules are left in the droplet, leading to a significant increase in ion-water interactions, so that the evaporation becomes slower compared to that in the second stage.

## 1. Introduction

^{2}law [5,6,9]. The D

^{2}law was derived based on the droplet evaporation in an infinite space [15], and predicts that the derivative of the square of the droplet diameter with respect to time is constant, or dD

^{2}/dt = ‒K, where K is the evaporation constant. However, Semenov et al. [16] presented that for the evaporation of sessile drops on hydrophobic substrates, the evaporation rate is proportional to the radius of the three phase line instead of being proportional to the area of the surface of the droplet. Semenov et al. [17] also investigated the effect of the influence of kinetic effects on evaporation of pinned sessile water droplets of submicrometer size placed on a heat conductive substrate. Their computer simulation model took into account the following phenomena: influence of curvature of the droplet’s surface on the saturated vapor pressure above the surface (Kelvin’s equation), the effect of latent heat of vaporization, thermal Marangoni convection, and Stefan flow inside an air domain above the droplet.

^{−}, H

_{2}PO

_{4}

^{−}, Na

^{+}or NH

_{4}

^{+}(N = 0, 4 and 8) under a vacuum, and their results showed a somewhat slower evaporation rate for clusters with Cl

^{−}and Na

^{+}than those with H

_{2}PO

_{4}

^{−}and NH

_{4}

^{+}. Daub and Cann [27] studied evaporation and condensation of a small cluster (N = 10, 20, 30 and 40) of water or methanol containing one single Ca

^{2+}, Na

^{+}or Cl

^{−}ion in either a vacuum or under argon gas. Daub and Cann [19] also studied the evaporation of a water cluster (N = 10, 15 or 20) containing one Na

^{+}ion or one Ca

^{2+}ion under the action of an electric field. Daub and Cann’s results demonstrated that the interaction between ions and water molecules affects the evaporation of the cluster [19,27]. Kӧhler [21] investigated the process of formation of liquid cloud drops based on equilibrium thermodynamics, where water vapor condensed with existence of nucleus (solutes), and proposed the well-known Kӧhler theory expressed as:

_{w}is the water vapor pressure outside the droplet, p° is the corresponding saturation vapor pressure over a flat surface, σ

_{w}is the droplet surface tension, ρ

_{w}is the density of pure water, n

_{s}is the moles of solute, M

_{w}is the molecular weight of water, and D is the droplet diameter. According to Kӧhler’s theory, the droplet diameter, water surface tension, and molar concentration of the solute significantly affect the water vapor pressure and hence the droplet evaporation rate.

## 2. Molecular Dynamics Simulations

#### 2.1. Interatomic Potential and Initial Configuration

^{+}, Na

^{+}, K

^{+}, and Cl

^{−}ions, the long-range Coulombic force between ions must be considered. Thus, a combined potential model of Lennard-Jones 12-6 potential and Coulombic potential is adopted here, which can be expressed as [29,30]:

Particle | σ (Å) | ε (KJ mol^{−}^{1}) | q (e) |
---|---|---|---|

O | 3.169 | 0.6502 | −0.8476 |

H | 0.000 | 0.0000 | +0.4238 |

Na^{+} | 2.583 | 0.4184 | +1.0000 |

Li^{+} | 1.505 | 0.6904 | +1.0000 |

K^{+} | 3.331 | 0.4184 | +1.0000 |

Cl^{−} | 4.400 | 0.4184 | −1.0000 |

N | 3.710 | 0.6990 | +0.0000 |

^{−}

^{3}gas density. The number of salt molecules is assumed to be 0, 40, 80, and 120, respectively, to analyze the effect of salt concentration on droplet evaporation. It is noted that the maximum salt mole concentration is 9.7%, which is less than its saturation concentration, and hence salt crystallization cannot occur. The droplet radius is fixed to 2 nm for all cases. This value corresponds to a density of 1 g·cm

^{−}

^{3}as the droplet is composed of pure water.

**Figure 1.**Initial configuration of system: green balls are N, white balls are H, red balls are O, blue balls are positive ions, and purple balls are chloride ions.

#### 2.2. Preparation of Initial Equilibrium State

_{neighbor}≥ 9, in the vapor phase if n

_{neighbor}≤ 1, or in interface region if 2 ≤ n

_{neighbor}≤ 8. The interface is ignored in the present work, so n

_{neighbor}≥ 4 is used as a threshold value to determine the droplets.

**Figure 2.**Snapshots of the simulation boxes and corresponding number densities of water molecules, Na

^{+}and Cl

^{¯}ions at different evaporation instants: (

**a**) t=0 ps; (

**b**) t=500 ps; (

**c**) t=1,000 ps; (

**d**) t=1,600 ps.

#### 2.3. Droplet Evaporation

^{+}and Cl

^{−}ions at different evaporation instants. It can be seen that the droplets deviate from the initial spherical shape and their volume gradually decreases with time, however, Na

^{+}and Cl

^{−}ions cannot escape from the droplet and finally crystallize as the droplet evaporates completely.

## 3. Results and Discussion

#### 3.1. Effect of Salt Concentration

^{+}and Cl

^{−}have not yet affected the evaporation. Later, the evaporation rates increase because more heat is transferred to the droplet and the difference between four droplets occurs, the water droplet evaporates faster than three aqueous droplets and vanishes about at t = 1,150 ps. The aqueous droplet with high LiCl concentration has a lower evaporation rate than that with low LiCl concentration. In the last stage of evaporation (at about t > 1,200 ps), the evaporation rates for aqueous droplets decrease compared to that in the second stage.

**Figure 3.**Temporal evolution of the water molecule number in the droplet with various salt concentrations.

^{+}-O, Cl

^{−}-O for the aqueous droplet with 80 LiCl molecules at different evaporation instants are shown in Figure 4. The hydration number in the present work is defined as the average number of water molecules around an ion in the first solvation shell, and can be expressed as:

_{ion}is the number density of ions (Li

^{+}or Cl

^{−}), g

_{ion-O}(r) is the radial distribution function, and r

_{sol}is the radius of the first solvation shell. Figure 4 shows that the first peak values of g

_{Li}

^{+}

_{-O}(r) and g

_{Cl}

^{−}

_{-O}(r) occur at r = 1.95 Å and 3.25 Å, and the first valley values at 2.85 Å and 4.15 Å at t < 600 ps, which implies that the water molecules located at a distance r < 2.85 from Li

^{+}and 4.15 Å from Cl

^{−}are attracted strongly by the ions, thus, 2.85 Å and 4.15 Å can be regarded as the radius of the first solvation shell for Li

^{+}and Cl

^{−}, respectively.

**Figure 4.**Radial distribution functions and hydration numbers at various evaporation instants for aqueous droplet with 80 LiCl molecules: (a) g

_{Li}

^{+}

_{-O}(r) and N

_{Li}

^{+}

_{-O}(r); (b) g

_{Cl}

^{−}

_{-O}(r) and N

_{Cl}

^{−}

_{-O}(r).

^{+}is 3.80 at t = 0 ps, 3.71 at t = 200 ps, 3.45 at t = 400 ps, as well as 3.34 at t = 600 ps, with only 9.2% decrease from t = 0 ps to t = 600 ps; however, hydration number of Cl

^{−}is 8.70 at t = 0 ps, 8.68 at t = 200 ps, 8.67 at t = 400 ps, and 8.65 at t = 600 ps. Therefore, only 52 and four water molecules escape the confinement of Li

^{+}and Cl

^{−}, respectively. At the same period, about 270 water molecules escape from the droplet due to evaporation (Figure 3). The results above demonstrates that the free water molecules with a weak interaction with ions made the biggest contribution to evaporation rate at the beginning of evaporation, and hence no visible difference is observed for pure water and aqueous solution with various LiCl concentrations.

^{+}and Cl

^{−}at t = 600 ps for aqueous droplets with 40, 80, and 120 LiCl molecules are listed in Table 2. Although high LiCl concentration leads to a small hydration number, the hydration effect is enhanced because the total number of water molecules bounded by Li

^{+}and Cl

^{−}is increased. The addition of Li

^{+}and Cl

^{−}into the water droplet also affects the interaction between water molecules. Table 3 lists the coordination number of water molecular at t = 0 ps, which is defined as the average number of water molecules in a sphere with 0.35 nm radius around a water molecule. The value of 0.35 nm chosen here is based on the fact that it is a standard length to determine the formation of hydrogen bonds between water molecules [26]. Table 3 shows that the coordination number of water molecular is reduced for high LiCl concentration, thus, the interaction between water molecules becomes less with increased LiCl concentration. The average interaction energies between water molecules and ions (Li

^{+}and Cl

^{−}) for various LiCl concentrations are calculated by Equation (2) and shown in Figure 5. The negative value means that water molecules are attracted by ions. The interaction energy is stronger for high LiCl concentration at t < 1,200 ps. Based on results above, the low evaporation rate of the droplet with high LiCl concentration can be attributed to stronger hydration effect and stronger attractive force to water imposed by Li

^{+}and Cl

^{−}as compared to that with low LiCl concentration.

Case | Hydration number of Li^{+} | Hydration number of Cl^{−} |
---|---|---|

40 LiCl | 3.76 | 9.02 |

80 LiCl | 3.34 | 8.65 |

120 LiCl | 3.06 | 8.16 |

Case | 0 LiCl | 40 LiCl | 80 LiCl | 120 LiCl |
---|---|---|---|---|

Hydration number | 4.97 | 4.79 | 4.67 | 4.42 |

**Figure 5.**Average interaction energies between water molecules and ions (Li

^{+}and Cl

^{−}) for various LiCl concentrations.

#### 3.2. Effect of Salt Category

^{+}, Na

^{+}, and K

^{+}at evaporation instants of 0, 300, and 1,000 ps. Oxygen atoms are closer to cations than hydrogen atoms due to attracted Coulombic interaction. The number of water molecules around Li

^{+}, Na

^{+}, and K

^{+}differs significantly, more water molecules occur around Li

^{+}, then Na

^{+}and K

^{+}. As the droplet evaporates, the water molecules around cations are gradually reduced.

**Figure 7.**Snapshots of local distribution of water molecules around cations at different evaporation instants for various salts: (

**a1**), (

**a2**) and (

**a3**) KCl at 0, 300, and 1,000 ps; (

**b1**), (

**b2**) and (

**b3**) NaCl at 0, 300, and 1,000 ps; (

**c1**), (

**c2**) and (

**c3**) LiCl at 0, 300, and 1,000 ps. (White balls: H, red balls: O, purple balls: Cl

^{−}blue ball: K

^{+}, Na

^{+}or Li

^{+}).

_{Cation-Cl}

^{−}, g(r)

_{Cation-O}, g(r)

_{Cl}

^{−}

_{-O}for LiCl, NaCl, and KCl aqueous droplets at various evaporation instants of 0, 600, 1,300, and 1,600 ps are show in Figure 8, where the subscript "Cation" denotes K

^{+}, Na

^{+}, or Li

^{+}, respectively. The positions of first peak of g(r)

_{Cation-Cl}

^{−}are 0.24 nm, 0.27 nm and 0.33 nm for LiCl, NaCl, and KCl aqueous droplets (Figure 8a), and the positions are almost unchanged throughout the evaporation process. However, the peak values of g(r)

_{Cation-Cl}

^{−}are elevated with the time, which means that more and more cations and chloride ions aggregate together. Eventually, a crystal will form when all water molecules in the droplet evaporate completely. The peak values of g(r)

_{Cation-O}(Figure 8b) and g(r)

_{Cl}

^{−}

_{-O}(Figure 8c) for LiCl aqueous droplet are the largest throughout the evaporation process, then for NaCl and the smallest for KCl. Thus, the strongest hydration effect occurs for LiCl aqueous droplet according to Equation (4).

_{Cation-O}for three aqueous droplets is more significant than that of g(r)

_{Cl}

^{−}

_{-O}. Therefore, only the average interaction energy between water molecules and cations (K

^{+}, Na

^{+}, or Li

^{+}) is calculated by Equation (2) and is plotted in Figure 9. The attractive force between water molecules and Li

^{+}is the strongest, while the weakest is for K

^{+}. The results confirm again that the strong hydration effect and attractive force are responsible for the slow evaporation. The results can also be connected to the Hoffmeister series effect [33] in term of structure breakers or structure enhancer cations. Hofmeister series is a classification of ions in order of their ability to salt out. The order of cations is usually given as: K

^{+}> Na

^{+}> Li

^{+}in Hofmeister series, therefore, the present results are in good agreement with the Hofmeister series effects.

**Figure 8.**The radial distribution functions at different evaporation instants: (

**a**) g(r)

_{Cation-Cl}

^{−}; (

**b**) g(r)

_{Cation-O}; (

**c**) g(r)

_{Cl}

^{−}

_{-O}. (cation denotes K

^{+}, Na

^{+}, or Li

^{+}).

^{+}has weaker hydration effect and smaller attractive force towards water molecules than Li

^{+}.

**Figure 9.**Average interaction energies between water molecules and ions (Li

^{+}and Cl

^{−}) for various salts.

## 4. Conclusions

^{2}law, which was regarded as a good description of evaporation of micro- and milli-scale droplets. Therefore, it is worth studying further that whether the present results may extend to micro- and milli-scale droplets.

## Acknowledgment

## References

- Semenov, S.; Starov, V.M.; Velarde, M.G.; Rubio, R.G. Droplets evaporation: Problems and solutions. Eur. Phys. J.-Spec. Top.
**2011**, 197, 265–278. [Google Scholar] [CrossRef] - Starov, V.M.; Churaev, N.V. Crystal groth at the end of a capillary on solution evaporation. J. Eng. Phys.
**1988**, 54, 443–446. [Google Scholar] [CrossRef] - Sone, Y.; Sugimoto, H. Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum. Phys. Fluids.
**1993**, 5, 1491–1511. [Google Scholar] [CrossRef] - Sumardiono, S.; Fischer, J. Molecular simulations of droplet evaporation by heat transfer. Microfluid. Nanofluid.
**2007**, 3, 127–140. [Google Scholar] [CrossRef] - Landry, E.S.; Mikkilineni, S.; Paharia, M.; McGaughey, A.J.H. Droplet evaporation: A molecular dynamics investigation. J. Appl. Phys.
**2007**, 102, 124301. [Google Scholar] [CrossRef] - Long, L.N.; Micci, M.M.; Wong, B.C. Molecular dynamics investigation of droplet evaporation. Comput. Phys. Commun.
**1996**, 96, 167–172. [Google Scholar] [CrossRef] - Mason, P.E. Molecular dynamics study on the microscopic details of the evaporation of water. J. Phys. Chem. A
**2011**, 115, 6054–6058. [Google Scholar] [CrossRef] [PubMed] - Consolini, L.; Aggarwal, S.K.; Murad, S. A molecular dynamics simulation of droplet evaporation. Int. J. Heat Mass Tran.
**2003**, 46, 3179–3188. [Google Scholar] [CrossRef] - Walther, J.H.; Koumoutsakos, P. Molecular dynamics simulation of nanodroplet evaporation. J. Heat Tran.
**2001**, 123, 741–748. [Google Scholar] [CrossRef] - Kaltz, T.L.; Long, L.N.; Micci, M.M. Supercritical vaporization of liquid oxygen droplets using molecular dynamics. Combust. Sci. Technol.
**1998**, 136, 279–301. [Google Scholar] [CrossRef] - Bhansali, A.P.; Bayazitoglu, Y.; Maruyama, S.; Little, J.K. Molecular dynamics simulation of an evaporating sodium droplet. Int. J. Therm. Sci.
**1999**, 38, 66–74. [Google Scholar] [CrossRef] - Wang, Z.J.; Chen, M.; Guo, Z.Y.; Yang, C. Molecular dynamics study on the liquid vapor interfacial profiles. Fluid Phase Equilibr.
**2001**, 183, 321–329. [Google Scholar] [CrossRef] - Carey, V.P.; Wemhoff, A.P. Disjoining pressure effects in ultra-thin liquid films in micropassages-comparison of thermodynamic theory with predictions of molecular dynamics simulations. J. Heat Transfer
**2006**, 128, 1276–1284. [Google Scholar] [CrossRef] - Yu, J.P.; Wang, H. A molecular dynamics investigation on evaporation of thin liquid films. Int. J. Heat Mass Transfer
**2012**, 55, 1218–1225. [Google Scholar] [CrossRef] - Faeth, G.M. Current status of droplet and liquid combustion. Prog. Energy Combust. Sci.
**1977**, 3, 191–224. [Google Scholar] [CrossRef] - Semenov, S.; Starov, V.M.; Rubio, R.G.; Agogo, H.; Velarde, M.G. Evaporation of sessile water droplets: Universal behaviour in presence of contact angle hysteresis. Colloid. Surface. A
**2011**, 391, 135–144. [Google Scholar] [CrossRef] - Semenov, S.; Starov, V.M.; Rubio, R.G.; Velarde, M.G. Computer simulations of evaporation of pinned sessile droplets: influence of kinetic effects. Langmuir
**2012**, 28, 15203–15211. [Google Scholar] [CrossRef] [PubMed] - Mucha, M.; Jungwirth, P. Salt crystallization from an evaporating aqueous solution by molecular dynamics simulations. J. Phys. Chem. B
**2003**, 107, 8271–8274. [Google Scholar] [CrossRef] - Daub, C.D.; Cann, N.M. How are completely desolvated ions produced in electrospray ionization: Insights from molecular dynamics simulations. Anal. Chem.
**2011**, 83, 8372–8376. [Google Scholar] [CrossRef] [PubMed] - Theron, S.A.; Zussman, E.; Yarin, A.L. Experimental investigation of the governing parameters in the electrospinning of polymer solution. Polymer
**2004**, 45, 2017–2030. [Google Scholar] [CrossRef] - Kӧhler, H. The nucleus in and the crowth of hygroscopic droplets. Transactions of the Faraday Society.
**1936**, 32, 1152–1161. [Google Scholar] [CrossRef] - Jungwirth, P.; Tobias, D.J. Molecular stucture of salt solution: A new view of the interface with implications for heterogeneous atmospheric chemistry. J. Phys. Chem. B
**2001**, 105, 10468–10472. [Google Scholar] [CrossRef] - Jungwirth, P.; Tobias, D.J. Ions at the air/water interface. J. Phys. Chem. B
**2002**, 106, 6361–6373. [Google Scholar] [CrossRef] - Li, X.; Hede, T.; Tu, Y.Q.; Leck, C.; Ågren, H. Surface-active cis-pinonic acid in atmopheric droplet: A molecular dynamics study. J. Phys. Chem. Lett.
**2010**, 1, 769–773. [Google Scholar] [CrossRef] - Sun, L.; Li, X.; Hede, T.; Tu, Y.Q.; Leck, C.; Ågren, H. Molecular dynamics simulations of the surface tension and structure of salt solution and clusters. J. Phys. Chem. B
**2012**, 116, 3198–3204. [Google Scholar] [CrossRef] [PubMed] - Caleman, C.; Spoel, D.V.D. Evaporation from water clusters containing singly charged ions. Phys. Chem. Chem. Phys.
**2007**, 9, 5105–5111. [Google Scholar] [CrossRef] [PubMed] - Daub, C.D.; Cann, N.M. Molecular dynamics simulations to examine structure, energetics, and evaporation/condensation dynamics in small charged clusters of water or methanol containing a single monatomic ion. J. Phys. Chem. A
**2012**, 116, 10488–10495. [Google Scholar] [CrossRef] [PubMed] - Znamenskiy, V.; Marginean, I.; Vertes, A. Solvated ion evaporation from charged water nanodroplets. J. Phys. Chem. A
**2003**, 107, 7406–7412. [Google Scholar] [CrossRef] - Bouazizi, S.; Nasr, S. Local order in aqueous lithium chloride solutions as studied by X-ray scattering and molecular dynamics simulations. J. Mol. Struct.
**2007**, 837, 206–213. [Google Scholar] [CrossRef] - Chowdhuri, S.; Chandra, A. Molecular dynamics simulations of aqueous NaCl and KCl solutions: Effects of ion concentration on the single-particle, pair, and collective dynamical properties of ions and water molecules. J. Phys. Chem.
**2001**, 115, 3732–3741. [Google Scholar] [CrossRef] - Beckers, J.V.L.; Lowe, C.P.; Leeuw, S.W.D. An iterative PPPM method for simulating coulombic systems on distributed memory parallel computers. Mol. Simulat.
**1998**, 3, 369–383. [Google Scholar] [CrossRef] - Shigeo, M.A.; Sohei, M.; Akihiro, O. Surface phenomena of molecular clusters by molecular dynamics method. Therm. Sci. Eng.
**1994**, 2, 77–84. [Google Scholar] - Zhang, Y.J.; Cremer, P.S. Interactions between macromolecules and ions: the Hofmeister series. Curr. Opin. Chem. Biol.
**2006**, 10, 658–663. [Google Scholar] [CrossRef] [PubMed]

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**MDPI and ACS Style**

Wang, B.-B.; Wang, X.-D.; Chen, M.; Xu, J.-L.
Molecular Dynamics Simulations on Evaporation of Droplets with Dissolved Salts. *Entropy* **2013**, *15*, 1232-1246.
https://doi.org/10.3390/e15041232

**AMA Style**

Wang B-B, Wang X-D, Chen M, Xu J-L.
Molecular Dynamics Simulations on Evaporation of Droplets with Dissolved Salts. *Entropy*. 2013; 15(4):1232-1246.
https://doi.org/10.3390/e15041232

**Chicago/Turabian Style**

Wang, Bing-Bing, Xiao-Dong Wang, Min Chen, and Jin-Liang Xu.
2013. "Molecular Dynamics Simulations on Evaporation of Droplets with Dissolved Salts" *Entropy* 15, no. 4: 1232-1246.
https://doi.org/10.3390/e15041232