Formation of Polycrystalline Microparticles from Evaporating Fine Droplets of Aqueous NaCl Solution

Abstract

An experimental setup has been developed that enables the conversion of a complex stream of polydisperse droplets generated by an ultrasonic dispenser into a stream of nearly identical droplets falling through a vertical channel. The fall of droplets of an aqueous NaCl solution in this channel, filled with heated dry air, is studied. Water from the droplets evaporates quickly, and crystals of a solid salt crust form on their surface. At a later stage of the process, the remaining solution is removed from the droplet using a jet of water vapor that passes through the pores of the polycrystalline crust. It was first observed that some of the drying droplets suddenly shifted to one side under the influence of the reactive force generated by the vapor jet. Images obtained using a scanning electron microscope show that the salt particles formed have a diameter of around 25 µm, are slightly porous, and consist of numerous crystals. It has been proven that these particles do not have a central cavity. The use of seawater and the role of salt particles in protecting against thermal radiation from fires are briefly discussed. Calculations based on Mie theory have shown that the contribution of light scattering by thin-walled hollow sea salt particles formed above the ocean surface during relatively slow evaporation of seawater droplets can be significant to the ocean’s heat balance.

1. Introduction

The study of the evaporation of small droplets of aqueous solutions of nonvolatile substances is of interest for solving a wide variety of problems. For example, such droplets are used in the pharmaceutical industry to produce medicinal powders [1,2,3,4,5,6,7,8,9] and in seawater desalination [10,11,12,13]. Mist curtains containing seawater droplets are used to protect against the thermal radiation of fires [14,15]. The evaporation of pesticide droplets on plants’ roots or leaves will affect their insecticidal effect [16,17,18,19,20]. Controlling the evaporation of saline droplets is important for indoor air quality and reducing energy consumption in buildings [21,22]. The evaporation of seawater droplets above the sea surface affects the interaction between the ocean and the lower atmosphere [23,24,25,26,27].

The presence of a nonvolatile substance in a water droplet significantly complicates the physical picture of droplet evaporation. Due to the slow diffusion of the dissolved substance, water evaporation increases the concentration of that substance near the droplet surface, and the subsequent formation of a solid crust further hinders evaporation. As a result of the increase in pressure, water vapor can penetrate the structure of the polycrystalline shell, and the remaining solution is jetted out of the particle. Interestingly, the resulting solid particles may have a complex crystalline structure that depends on the temperature and relative humidity of the surrounding air.

The process described above is known. References to relevant studies can be found in both review articles [1,28,29,30,31,32,33] and regular papers [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]. The papers [34,39,40,46,47,48] examine the evaporation of water droplets containing dissolved sodium chloride. These publications are most relevant to the present study. As usual, the low diffusivity of sodium chloride in water [49,50,51] leads to an increase in salt concentration at the evaporation surface and a significant decrease in the evaporation rate of the aqueous solution [52,53].

This study continues the laboratory investigations into the formation of crystalline sodium chloride microparticles from droplets of saline water surrounded by heated dry air. Based on the observed sharp decrease in the falling speed of the evaporating droplet and the deviation of its trajectory from the vertical, the escape of water vapor and the remaining concentrated salt solution through a side opening in the polycrystalline shell was detected. It has been established that this effect occurs just before the formation of a rather dense polycrystalline particle.

It should be noted that this experimental study specifically examines conditions under which evaporating droplets suspended in still air remain spherical, and the small equilibrium falling velocity of the droplets in a vertical channel decreases only slowly as the water evaporates. Physical estimates confirming the appropriate choice of experimental conditions are presented in Section 3 before the discussion of the results obtained.

2. Laboratory Setup and Experimental Procedure

The experiments were conducted using droplets of an aqueous sodium chloride solution. The concentration of the solution was equal to $c_{\mathrm{salt}}=35\pm 0.5$ g/L, which corresponds to the average concentration of salts in seawater. As in a recent article [54], a complex stream of polydisperse droplets generated by a dispenser was converted into a flow of falling droplets with diameters of 90–100 μm in the air-filled vertical channel. This was achieved using the design shown in Figure 1, where “1” denotes a cylindrical plastic housing containing an ultrasonic dispenser from Altrasonic (Hangzhou, China). This housing, with an internal diameter of 38 mm, is connected to a vertical channel “2”, with a square cross-section of 20 mm × 20 mm. The vertical channel acts as a simple and effective filter, retaining only drops of nearly identical, specified size from the polydisperse droplets generated by the dispenser, which have a wide size distribution.

Figure 1. The image of the experimental setup.

In [48], the calculations of the droplets’ trajectories were carried out to determine the required distance between the dispenser and the axis of the long vertical channel. The viscous drag force stabilizes the droplet fall velocity. This velocity changes only because of the droplet’s gradual evaporation. Note that the vertical channel used in the present paper is much longer than that in [54] because we were going to obtain hollow or dense crystalline particles from the droplets of aqueous solution of sodium chloride. To promote the droplets’ evaporation, the air in the vertical channel was heated using a heat gun R858D (REXANT, Moscow, Russia) “3”. To monitor air temperature and humidity in the experiment, the digital thermometer HI98501 (HANNA Instruments, Vöhringen, Germany) and the thermohygrometer IVTM-7 M K (Exis, Saint Petersburg, Russia) were used. The following values for air temperature and relative humidity were selected as the operating conditions: $T=60\pm 1 °\mathrm{C}$ and $\phi =30\pm 1\%$. Measurements showed that the air temperature and humidity remained constant throughout the entire channel during the experiment. These conditions, as in [43,44,47], allow the setup to be relatively compact but lead to more rapid water evaporation from the droplets and the formation of a polycrystalline salt crust on the surface of small droplets containing a more concentrated solution. At the bottom of the vertical channel, there were glass windows (w) measuring 20 mm × 60 mm, which allowed the falling particles to be illuminated and observed. The channel ended with a removable plug “4”, into which a glass plate was placed during the experiment. Salt particles that fell onto the plate were examined using scanning electron microscopy (SEM) after the experiment. An LED light source “5” (Logocam, LED BM-50 V 3200/5600, Jaffa, Israel) was used for video recording by a high-speed camera “6” (Photron FASTCAM NOVA, Tokyo, Japan) equipped with a lens AF-S VR Micro-NIKKOR 105 mm f/2.8 G (Nikon, Tokyo, Japan). The length of the evaporating droplet’s trajectory in the channel to the upper edge of the camera’s field of view was approximately 46 cm. This study focuses on the final stage of water evaporation, when a solid crystalline particle is forming.

High-speed (5000 fps) photography of falling particles was performed at the final part of the trajectory, approximately 3 cm from the surface of the glass plate. Under these conditions, the microdroplets had time to dry during their fall and landed on the plate surface as salt particles. The microsphere samples were examined using a MIRA3 scanning electron microscope (TESCAN, Brno, Czech Republic). Before this procedure, the samples on a glass substrate were coated with a 20 nm thick gold layer using a Q150R S automatic magnetron sputtering system (Quorum Technologies, Lewes, UK).

3. Experimental Results

To interpret the experimental results, it is necessary to understand the main features of the interaction between falling evaporating droplets and the surrounding air. Let us first assess the validity of the natural assumption that small water droplets falling through immovable air under the influence of gravity are spherical. The deformation of the droplet reaches its maximum value at the start of this process, when the viscosity of the air has not yet reduced the dynamic imbalance between the droplet and the surrounding air. The Bond number $\mathrm{B}\mathrm{o}={\rho }_{\mathrm{w}}{gd}^2/\gamma$, where ${\rho }_{\mathrm{w}}$ is the water density, g is the acceleration of gravity, $d$ is the droplet diameter, and γ is the surface tension of water, can be used to estimate the droplet deformation. Even for a relatively large droplet with a diameter of 0.1 mm, we obtain $\mathrm{B}\mathrm{o}=1.3·{10}^{-3}\ll 1$. This means that the droplets in our experiment are perfect spheres. Following the above estimate, the considered droplets of saline water are assumed to be spherical.

Let us now estimate how quickly the heat conduction in water can equalize the temperature throughout the droplet. An important thermal criterion is the Fourier number, $\mathrm{F}\mathrm{o}=\alpha t/a^2$, where $\alpha =0.14·{10}^{-6}$ m²/s is the thermal diffusivity of water, $t$ is the time, and $a$ is the droplet radius. Assuming $\mathrm{F}\mathrm{o}=1$, we can estimate the relaxation time of temperature in a droplet of water. For a droplet with radius of $a=50$ µm, a small value $t=a^2/\alpha =18$ ms is obtained. This time is considerably shorter than the typical time taken for a droplet to fall and evaporate. Therefore, such a droplet can be considered isothermal.

It should be noted that more complex sessile droplets not only have a shape that differs from a sphere, but are generally not isothermal. Furthermore, such droplets exhibit rather complex convection, which requires a specific analysis [55,56,57,58,59,60]. The above physical estimates indicate that this problem does not arise for the equilibrium falling droplets under consideration.

It is also interesting to estimate the diffusion relaxation time for the dissolved NaCl concentration, $t_D=\mathrm{L}\mathrm{e}\times t$, where $\mathrm{L}\mathrm{e}=\alpha /D$ is the Lewis number. With diffusion coefficient of NaCl in water $D=2·{10}^{-9}$ m²/s we have $\mathrm{L}\mathrm{e}=70$. It turns out that a uniform concentration of salt even in such a small droplet of water occurs in the time $t_D=1.3$ s. It is important that $t_D\gg t$. This result is a physical explanation for the solid crust formation on the surface of an evaporating saline water droplet.

Note that at the top of the vertical channel, the droplet’s falling velocity is far from its equilibrium value. The dynamic relaxation of the droplet takes some time. At the end of the non-equilibrium section of the channel, the droplet falls at a speed at which the force of gravity acting on it is balanced by the viscous drag of the gas. The dynamic relaxation time of a small droplet can be estimated using the well-known formula:

$$t_{\mathrm{rel}}={\displaystyle \frac{2}{9}}{\displaystyle \frac{{\rho }_{\mathrm{w}}{a}^2}{{\eta }_{\mathrm{air}}}}$$

(1)

where ${\rho }_{\mathrm{w}}={10}^3$ kg/m³ is the density of water, $a$ is the droplet radius, and ${\eta }_{\mathrm{air}}=1.97·{10}^{-5}$ Pa s is the dynamic viscosity of surrounding air. For droplet radius of $a=50$ µm, Equation (1) yields a value $t_{\mathrm{rel}}=28$ ms, which is several orders of magnitude smaller than the fall time of an evaporating droplet in the vertical channel. This result implies that the falling velocity of the droplet and the salt particle formed from it is determined entirely by the equilibrium between the force of gravity and the viscous drag of the air.

To calculate the evaporation of a water droplet containing dissolved salt, one can use the complete kinetic evaporation model employed in [14,53] or the simplified model proposed in [61]. However, such a calculation is not relevant to this study, which focuses on the formation of polycrystalline salt particles. Unfortunately, the processes occurring after the formation of a solid salt crust on the droplet surface are difficult to describe theoretically. Therefore, in this experimental study, only theoretical estimates of the settling velocity of falling solid particles are used, assuming that the shape of these particles differs only slightly from spherical.

Most of the evaporating and partially solidified droplets, whose trajectories are recorded using a high-speed camera, move downwards. Since the size of these particles is approximately half that of the droplets of aqueous solutions whose fall was considered in [54], the viscous drag force of air is well described by Stokes’ law. This statement is confirmed by the typical value of the Reynolds number for a spherical particle with a diameter $d$ falling in an immovable gas at a certain velocity $v_{\mathrm{p}}$:

$${\mathrm{Re}}_{\mathrm{p}}={\rho }_{\mathrm{air}}{v}_{\mathrm{p}}d/{\eta }_{\mathrm{air}}$$

(2)

where ${\rho }_{\mathrm{air}}=1.06$ kg/m³ is the density of air. Assuming $d=25$ µm for the experimental conditions, with a typical equilibrium particle fall velocity $v_{\mathrm{p}}=60$ mm/s (upper estimate), we obtain ${\mathrm{Re}}_{\mathrm{p}}\approx 0.08$. Such a low Reynolds number means that Stokes’ formula for the drag coefficient $C_D=24/{\mathrm{Re}}_{\mathrm{p}}$ is applicable for spherical particles [62,63]. The condition of equilibrium between gravitational force and drag force leads to the following equation for the equilibrium velocity of a spherical salt particle with a conventional porosity $p$, which may be a real porosity or a relative volume of the central cavity (in the case of hollow particle with a dense salt shell):

$$v_{\mathrm{p}}={\displaystyle \frac{{\rho }_{\mathrm{salt}}\left(1-p\right)}{18{\eta }_{\mathrm{air}}}}{gd}^2$$

(3)

where ${\rho }_{\mathrm{salt}}=2173$ kg/m³ is the density of salt crystals. One might decide that the value of $p$ can be determined from Equation (3). However, it will be shown below that this is not the case due to the very low porosity and slightly non-spherical shape of many particles. Unfortunately, Formula (3) provides only a rough estimate of the settling velocity of polycrystalline salt particles (even those that are nearly spherical but consist of large salt crystals). Therefore, the measured values of the salt particle velocity are used only for a qualitative analysis of the problem, whilst the actual sizes and shapes of the resulting polycrystalline particles are determined from SEM images of the particles deposited on a glass plate.

As the depth of field of the high-speed camera’s lens is quite shallow, only a few particles are clearly visible over a significant part of the trajectory. The observed tracks of most of these particles are strictly vertical. This result can be regarded as indirect evidence that the shape of the solidifying particles is close to spherical. Indeed, if the particles’ shape differed significantly from a sphere, their motion would be more complex.

Before proceeding to the analysis of the experimental data, we shall consider the errors in measuring the coordinates of the falling particles, which are linked to the limited resolution of the high-speed camera used. The resulting image of the particle consists of a small number of pixels and, naturally, does not allow us to determine the shape of the particle. Furthermore, the coordinates of the particle’s center are determined with a known error, which for the conditions under consideration is ±9 µm. During the observation period, the particle travels approximately 15–20 mm vertically. Obviously, the measurements of the coordinates, for example, of the leading edge of the particle’s image, allow its vertical trajectory to be determined with sufficient accuracy. At the same time, when observing a possible slight displacement of the particle in the horizontal direction, the aforementioned error must be taken into account, which was done when interpreting the measurements discussed below.

It is interesting to note those particles whose trajectories deviate slightly from the vertical for a brief moment. Most likely, these deviations are due to the escape of vapor and solution residues through the pores in the polycrystalline salt structure. One of these successful observations of a particle, whose trajectory deviates from the vertical, is shown in Figure 2. Of course, we cannot directly visualize the jetting, the presence of which is confirmed by the particle’s dynamics. It should be noted that this sudden deviation is observed in only one of the particles in the group. The other particles nearby continue to fall strictly vertically. This means that the change in the particle’s trajectory in question cannot be explained by a disturbance in the air flow, which would inevitably have affected the entire group of nearby particles.

Figure 2. (a) Downward motion of the particle: A—with a velocity $v_{\mathrm{p}1}$ before the lateral force is applied; B—with a velocity $v_{\mathrm{p}2}<v_{\mathrm{p}1}$ after this force is applied. (b) Lateral motion of the particle.

A small but sharp decrease in the particle’s falling speed at a conventional moment in time $t_{\ast }=0.08-0.09$ s is shown in Figure 2a. The vertical component of the particle velocity (in direction of z-axis) is constant for both ${t<t}_{\ast }$ and ${t>t}_{\ast }$, but the velocity value changes from $v_{\mathrm{p}1}=56$ mm/s to $v_{\mathrm{p}2}=53$ mm/s for ${t>t}_{\ast }$. As noted above, the error in measuring the particle’s vertical coordinate is negligible. Therefore, the stated values for the particle’s velocity are sufficiently accurate. The decrease in the particle falling velocity is due to mass losses after the remaining concentrated solution has escaped from the particle along with the vapor.

The horizontal motion of the particle at ${t>t}_{\ast }$ is shown in Figure 2b. The vertical bars, rather than dots, indicate measurement errors caused by the relatively large pixels in the image captured by a digital camera. As shown in Figure 2b, the horizontal velocity $u_{\mathrm{p}}$ of the particle is equal to zero during the initial time interval of $∆t\approx 0.1$ s. After that, the velocity first increases, but then decreases and remains almost constant, at least for 0.3 s. This result can be explained by the fact that the mass flow rate of steam with solution residues continues throughout this time.

In view of the observed momentary deviation in the trajectory of the falling particle, it should be noted that studies [29,34,37] have reported the existence of numerous hollow spherical particles formed by evaporation of droplets containing a nonvolatile substance. Many of the solid shells collected after the experiment have a small orifice. The images of such particles leave no doubt that the momentary exit of a vapor jet and the solution entrained by it from the central zone of the particle is a fairly common phenomenon accompanying the evaporation of droplets containing a nonvolatile substance. In this study, there were no specific holes in the massive solid particles, but the effect of the escaping vapor jet on the trajectory of the evaporating particle was observed.

Several SEM images of the obtained salt particles were taken. All particles consisted of nearly identical large sodium chloride crystals. Two of these images are shown in Figure 3. The shape of the particle in Figure 3a appears to be the closest to spherical. For Figure 3b, a particle was selected whose shape differed most significantly from a sphere. Nevertheless, the asymmetry of even this second particle does not appear to be significant. This means that the drag force for an asymmetric particle differs only slightly from that for a spherical particle. The shape of the small salt particles cannot change when they settle on the glass substrate. This happened whilst the particles were falling.

Figure 3. SEM images of salt particles: (a) almost spherical particle, (b) asymmetric particle. Sodium chloride crystals and some gaps between them are visible. “TюмГУ” is the University of Tyumen.

Returning to the relationship between salt particle size and their falling velocity, we can substitute several particle diameter values into Equation (2), assuming that the particles are non-porous. Simple calculations give $v_{\mathrm{p}}=37.5$ mm/s at $d=25$ μm and $v_{\mathrm{p}}=54$ mm/s at $d=30$ μm. Based on a comparison of these results and the measured values $v_{\mathrm{p}1}=56$ mm/s and $v_{\mathrm{p}2}=53$ mm/s, two important conclusions can be drawn: (1) the drag coefficient of salt particles is greater than that of a smooth sphere, and (2) the particles have no central hole, and the conventional volumetric porosity of salt particles is negligibly small. The last statement is convincingly supported by the physical estimates given above. This enables us to obtain the initial diameter of droplets in the cross-section of the inlet of the vertical channel:

$$d_0=d/\sqrt[3]{c_{\mathrm{salt}}}$$

(4)

Equation (4) gives $d_0=94$ µm at $d=30$ µm. This is consistent with the values for the initial diameter, approximately 90–100 µm, reported in [54]. This implies that evaporation of the droplet before it reaches the vertical channel is negligible, even in the heated air.

It should be noted that the experimental results of this work were obtained at unusually high temperatures and low relative humidity of the surrounding air. Such conditions are rare in nature and technology. As a rule, droplets of aqueous sodium chloride solution or seawater do not evaporate so quickly. In this case, thin-walled hollow salt particles are indeed formed, the size of which is not much smaller than the size of the initial solution droplets [29,32,33,34,35,36,37,38,39,40,41,42,45,46].

4. Some Applications

The formation of solid hollow particles during the evaporation of droplets of aqueous solutions of nonvolatile substances is not only of academic interest. Such particles, formed from seawater droplets in water mist curtains, are used to shield against thermal radiation of large flames during fires [14,15]. Unfortunately, in some coastal regions, as well as on seagoing ships and oil platforms, there is no access to fresh water. Therefore, in [14,15], a study was conducted on the possible use of seawater. It was shown that the infrared optical properties of hollow salt shells, which are formed from seawater droplets in the lower part of a mist curtain, contribute sufficiently to the attenuation of the infrared radiation of real large fires.

Studies [29,34,37] have shown that hollow particles can form from saltwater droplets even without the significant heat input observed in water mist curtains illuminated by the thermal radiation of fires. Such milder conditions also occur in atmospheric air over the ocean surface. It turns out that the optical properties of hollow salt particles in the visible and near-infrared spectral ranges are also favorable for the thermal regime of the ocean. These particles formed from water sprays can protect the ocean from excessive heating by solar radiation. To justify this statement, let us compare the calculated values of the transport efficiency factor of scattering $Q_{\mathrm{s}}^{\mathrm{tr}}=Q_{\mathrm{s}}\times \left(1-\overline{\mu }\right)$, where $Q_{\mathrm{s}}$ is the ordinary efficiency factor of scattering and $\overline{\mu }$ is the asymmetry factor of scattering [64,65,66,67], for the seawater droplet and the corresponding hollow sea salt particle. The transport approximation allows for a fairly accurate calculation of radiation transport in media with multiple scattering [67,68]. This approach to accounting for anisotropic scattering is used in solving a wide range of physical problems [69,70,71,72].

If the spectral optical properties of the materials are known, calculations can be performed using the Mie theory for homogeneous and hollow spherical particles, as described in [67]. The optical constants of water in the visible and near-infrared ranges were taken from the classic work [73]. The optical constants of solid NaCl were calculated using the approximation suggested in [14] to approximate experimental data reported in [74,75]. The independent scattering hypothesis can be applied to these randomly distributed droplets and particles, as their sizes and the distances between them are generally much greater than the wavelength of solar radiation [76,77,78].

Of course, the evaporation of sea water droplets in the air near the ocean surface occurs much more slowly than in the laboratory setup described above, where the air is preheated. Therefore, the evaporation of water results in hollow salt particles that are much smaller than the original seawater droplets. The results of the calculations for a droplet with a radius of 50 µm and two hollow spherical sea salt particles of equal mass of salt are shown in Figure 4. The first hollow particle has a shell thickness of $\delta =2$ µm (particle 1 in Figure 4); the corresponding parameter for the second particle is $\delta =1.5$ µm.

Figure 4. Transport efficiency coefficient for the seawater droplet (blue line) and two hollow salt particles with the same salt mass: 1—the shell thickness $\delta =2$ µm; 2—the shell thickness $\delta =1.5$ µm.

The calculations were carried out for the most interesting spectral range, encompassing the visible range and a short-wavelength part of the near-infrared range. It is clear that hollow salt particles scatter radiation from the solar spectrum by an order of magnitude more effectively than the seawater droplets from which such solid particles are formed during evaporation. This means that a horizontal curtain of hollow sea salt particles can make a considerable contribution to the attenuation of solar radiation reaching the sea surface. The effect described should be taken into account when calculating the heat balance of the ocean and atmosphere.

5. Conclusions

The use of a specially designed laboratory setup allowed us to convert a complex stream of polydisperse droplets generated by an ultrasonic dispenser into a stream of nearly identical droplets falling through a vertical channel. Physical estimates showed that the equilibrium between the force of gravity and the drag force of the surrounding air determines the fall of evaporating saline water droplets and the resulting salt particles. This simplifies the analysis of the optical measurements of the particle fall parameters.

The initial salt concentration in the droplets is close to typical seawater values. The air in the vertical channel was heated before the experiment. At an ambient air temperature of around 60 °C, the water evaporates rapidly, and salt crystals begin to form on the droplet surface. At a later stage of the process, due to the water vapor pressure, the remaining solution is removed through the pores of the solidifying polycrystalline salt particle. The main features of this process have been described in the cited literature. In this paper, we observed the effect of the escaping jet on the dynamics of the solidifying particle.

This study was the first to observe that some saline water particles, as they dried, suddenly began to shift sideways under the action of a reactive force generated by the vapor jet. The prolonged vertical fall of such particles slows down due to the loss of a small part of their mass. The resulting solid salt particles are slightly porous and consist of many large crystals. This is clearly visible in the SEM images of the particles and is consistent with measurements of the particle fall velocity.

Some applications of hollow salt particles obtained by less intense heating are discussed. It was noted that such particles are formed when seawater droplets evaporate; this seawater is used to create mist curtains that shield the intense thermal radiation in the event of unexpected fires. There are also geophysical problems associated with the formation of hollow particles of sea salt. Calculations based on Mie theory have shown that the contribution of light scattering by hollow sea salt particles forming above the ocean surface may be considerable in the ocean’s heat balance.