Chemical Engineering Science 61 (2006) 6029 – 6034 www.elsevier.com/locate/ces

Evaporative cooling of micron-sized droplets in a low-pressure aerosol reactor Sergey P. Fisenko a , Wei-Ning Wang b , I. Wuled Lenggoro b , Kikuo Okyuama b,∗ a A.V. Luikov Heat & Mass Transfer Institute of National Academy of Sciences, Minsk, Belarus b Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, Higashi Hiroshima, 739-8527, Japan

Received 2 December 2005; received in revised form 17 May 2006; accepted 23 May 2006 Available online 27 May 2006

Abstract The results of experimental and computational investigation of evaporative cooling of micron-sized droplets in a low-pressure aerosol reactor (LPAR) are reported. The cooling rate of the aerosol was found to be about 2 × 103 K/s. A constant low pressure, the flow rates of the carrier gas and solution are major factors that affect droplet cooling. A higher total pressure accelerated the change in droplet radius. For some regimes it was predicted that an aerosol undergoes freezing and then melting. The characteristic time required for evaporative cooling is about 1 ms. The agreement between experimental results and calculated values, based on the free molecular approximation of heat and mass transfer processes, is reasonably good. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Aerosol; Evaporation; Freezing; Heat transfer; Mass transfer; Spray pyrolysis

1. Introduction One of the promising methods for producing particles with a controlled size, morphology, and composition is spray pyrolysis (SP), which is based on solution droplet-to-particle conversion (Kodas and Hampden-Smith, 1999; Lenggoro et al., 2000; Messing et al., 1993; Okuyama and Lenggoro, 2003). Inside the spray chamber (e.g., an aerosol reactor), each droplet has the same composition and, as a result, the desired particles can be readily pyrolyzed by controlling the composition of the starting solutions. However, only submicron to micron size particles can be produced via spray pyrolysis under atmospheric conditions, due to the limited generation of small droplets (below 1
m) based on the one-droplet-to-one-particle (ODOP) principle. A modified spray pyrolysis method for the production of nanoparticles, namely, the so-called low-pressure spray pyrolysis (LPSP), was recently developed and introduced by Kang and Park (1995), in which a glass filter is used as the droplet generator. The low-pressure spray route is unique, because by starting

∗ Corresponding author. Tel.: +81 82 424 7716; fax: +81 82 424 5494.

E-mail address: [email protected] (K. Okyuama). 0009-2509/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.05.028

from a micron droplet, it is possible to produce nanoparticles with particle sizes in the order of several tens of nanometers. However, to date, for low-pressure spray pyrolysis systems, no systematic investigation of the relationship between operation parameters and particle size/morphology has been reported. It is likely that droplet evaporation plays significant role at this process. The optimization and further development of a low-pressure spray system (Lenggoro et al., 2004; Wang et al., 2004, 2005a,b, 2006) revealed some problems, related to heat and mass transfer in aerosol droplets during evaporation. In such a low-pressure system, the evaporative cooling of a droplet becomes a particularly interesting issue, because the solution will exist in a strong non-equilibrium supersaturated state during the chilling process. There is currently a strong motivation for using of small droplets for evaporative cooling in a variety of engineering applications (Francois and Shyy, 2002). It is noteworthy that the evaporative cooling of millimeter-sized droplets under atmospheric pressure, which has vast industrial applications, is still under development (Fisenko et al., 2004). The evaporation cooling of millimeter-sized droplets of aqueous solutions (e.g. ammonia chloride), which has unique features, was also

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experimentally and theoretically investigated recently (Shabunya et al., 2003). The evaporative cooling effect becomes stronger if we deal with smaller droplets. The reason is not only the smaller storage of heat energy in these smaller droplets, but because of the Kelvin effect (Defay et al., 1966; Kubo, 1968; Hinds, 1999). For pure liquids, this effect is described by the Kelvin equation pR /ps = exp(2
v/kT R), where pR and ps are partial pressure and saturated pressure of droplet vapor, respectively,
the surface tension, v the volume per molecule at liquid phase, k the Boltzmann constant, T the temperature and R the droplet radius. The Kelvin equation describes the fact that the actual vapor pressure at the interface is a function of the curvature. As from the above equation, for the same temperature the vapor pressure is an exponential function of the inverse of the droplet diameter. For water droplets at 20 ◦ C, however, this Kelvin effect is significant only for particles less than 100 nm. At present work, the Kelvin effect is negligible, because the droplet size is relatively large (in micron order). Thus, the following equations will not include this effect. For pressures of about 10–40 Torr the evaporation of micronsized water droplets extends practically to the free molecular regime (Fuchs, 1959). For example, for a pressure of 20 Torr, the mean free path of water molecule w in the mixture is about 4
m, and the mean droplet radius R in our experiments is about 1
m. It has been established (Fisenko et al., 2004) that, for evaporative cooling, there is a very important parameter: the ratio of mass flow rates of the cooled liquid Qw and air, Qa . For our LPSP experiments, this ratio, Qw /Qa , is in the range of 0.17–2.2. The objective of this work is to investigate the evaporative cooling effect of micron-sized water droplets in a low-pressure aerosol reactor (LPAR), which is important for the successful development of LPSP, suitable for commercial applications. 2. Mathematical model of evaporative cooling For the free molecular regime of droplet evaporation a system of equations thatat describe heat and mass transfer between a droplet cloud and a gaseous co-flow is available. The average distance between droplets is much larger than their radius. Therefore, the evaporation of a single droplet is considered. The first equation, which describes the change in droplet radius R(z) (Fuchs, 1959), is
 dR(z) m pv (Tm ) ps (Td ) = , (1) −√ √ dz ul 2mkT m 2mkT d where u the co-flow velocity, l the liquid density, m the mass of vapor molecule, pv the partial water vapor pressure, ps (T ) the saturated vapor pressure, Tm the mixture temperature, and z the spatial variable. The equation for the change in droplet temperature, Td (z), is (Fuchs, 1959) dTd (z) 3 3Td dRd (z) = , {A} − √ dz Rd dz ul cl R(z) 2k

(2)

where the explicit expression for A is
pv (Tm )(cT m + U + 0.5kT m ) A= √ mT m  ps (Td )(cT d + U + 0.5kT d ) − √ mT d   (cg Tm + 0.5kT m ) (cg Td + 0.5kT d ) , + p(Tm ) −   mg Tm mg Td where cl is the specific heat capacity of the liquid, U and c the latent heat of phase transitions and the heat capacity per one vapor molecule, p the carrier gas pressure, cg and mg are, correspondingly, the heat capacity per molecule and the mass of a carrier gas molecule. It should be emphasized that the evaporative cooling rate is inversely proportional to the droplet radius. The number density of droplets, Nd , affects the intensity of heat and mass transfer between a droplet cloud and the gaseous mixture because it has an effect on interfacial surface. Below we consider evaporative cooling under a constant pressure. Thus, only one more equation for the water vapor density or the temperature of the mixture is needed. These variables characterize the state of the mixture. We use the equation for the temperature Tm of the mixture um cm

dTm (z) = −4Rd2 Nd [A]. dz

(3)

If the droplets temperature is lower than or equal to 0 ◦ C, U includes the latent heat of melting plus the latent heat of the evaporation. It should be noted that Eq. (3) does not include effects related to the wall of the low-pressure chamber. The initial conditions for the system (1)–(3) are as follows: droplet radii R(0)=R0 , temperatures of droplets and gaseous mixture are equal T (0)=T0 . The total pressure Pt , Pt = (n + nv )kT m

(4)

is constant during the entire evaporation process. As the temperature of the gaseous mixture drops during chilling the number density of the vapor molecules increase, because the number density of the carrier gas molecules is constant. This decreases the cooling rate of droplets during evaporation and even slightly restores the droplet temperature. In our experiments, the low pressure was obtained by means of a vacuum pump, a pressure-pump sensor with a special controller (ACX2200, Mykrolis Co., USA). As a result, the experiments actually run at the non-steady-state regime with small fluctuations in total and partial pressures. Nevertheless, for simplicity of calculation the steady-state approximation is used below, as follows from Eqs. (1)–(3). At the beginning of the simulation we assume, that partial pressure of the water vapor maintains the same ratio of the total pressure as for the gas flow, passing through water solution. In this case, the partial pressure of the water vapor is equal to the saturated water pressure for the solution temperature.

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Before the numerical simulation it is useful to make some analytical estimates. According to expression (3), the decrease in the temperature in a vapor–gas mixture depends on the droplet number concentration and total pressure of the mixture. A simple estimation shows that characteristic time, , for the relaxation field of the temperature in the droplet is ∼

R2 2 a

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Water & air Qw/ Qa

0 cm

Glass filter

,

where a is the water heat diffusivity; numerically, for a droplet with a radius of 1
m ∼10−7 s (Fisenko et al., 2004). It is clear that the approximation of the average temperature can be used to describe the evaporative cooling, which has duration several milliseconds at our case. If we neglect the cooling of the gaseous mixture due to evaporative cooling, the minimally possible droplet temperature, Tf , can be easily estimated from algebraic Eq. (5), which follows from the right-hand side of Eq. (1):  ps (T0 )Pt ≈ ps (Tf ) T0 /Tf , Pa

(5)

where Pa is the atmospheric pressure. In particular, according to (5), for a total pressure of 40 Torr and an initial temperature of 20 ◦ C, Tf will be about −15 ◦ C. The detailed calculations, presented below, give the value for the temperature, which is close to this estimation. The left-hand side of Eq. (5) is an estimation of the partial pressure of water vapor after filtration through at LPSP device. There are also additional important conclusions from expression (5). The first is that the larger is the total pressure the higher is the final droplet temperature. The second is that if we increase the initial temperature T0 we also significantly increase the final temperature due to exponential dependence of saturation pressure on temperature. The mass flow rate of water, Qw , is expressed by means of our variables as Qw = Nd ul 4R 3 /3, and gaseous mixture flow Qa is Qa = m u. We accept that, for micrometer size droplets, the velocities of the gas and disperse phase are practically equal to each other, therefore the ratio Qw /Qa does not depend on the velocities of co-flows. 3. Experimental procedure and results A schematic diagram of a typical LPSP process as shown in Fig. 1 and was used in our previous research (Wang et al., 2004, 2005b, 2006). It is composed of an atomizer system, a tubular ceramic reactor, a particle collector, and a pressure control system. The atomizer system is composed of a two-fluid nozzle and a glass filter. The precursor, e.g. water in this study, is supplied by a peristaltic pump through the two-fluid nozzle, at feeding rates ranging from 40 to 200 mL/h, to the glass filter surface, which has an average pore size of 5.5
m and a surface

3 cm

B

10 cm Droplet

P

Vacuum pump

A

>> <<

Thermal couple Fig. 1. Schematic diagram of a filter type atomizer and its temperature measurement.

area of 1.77 × 10−2 m2 (Shibata Scientific Technology Ltd., Tokyo). The carrier gas flows in the same direction as the water through the two-fluid nozzle. Air was used as the carrier gas in this study, and the total carrier gas flow rate to the glass filter was controlled at 2.0 L/min by a volume flow meter under 0.1 MPa and room temperature. Thus, the ratio of mass flow rates Qw /Qa was in the range of 0.33–1.67. In this work, the temperature of the droplets/carrier gas under the low-pressure system was measured in order to check the evaporative cooling effect, which is schematically shown in Fig. 1. A K-type thermal couple (Hayashi Denko, Co., Tokyo), with a measuring range of −40 to 375 ◦ C, was used for the temperature measurements. As mentioned above, Eq. (3) does not describe the interaction of the gas flow with the chamber wall. For a correct comparison between the calculated results and the experimental data, temperature measurements must be done near the inlet of aerosol generator (namely, the glass filter in this work). Therefore, during the measurement, the thermal couple was located at two places near the inlet of chamber, i.e., distances of 3 cm (A) and 10 cm (B) from the lower side of the glass filter (Fig. 1). Due to the difficulty in collecting pure water droplets for temperature measurement in the low-pressure system, we were only able to in situ measure the temperature of the droplets/carrier gas mixture. It is also noteworthy that due to some heat transfer from the surrounding air (room temperature) to the glass filter, the experimental data would be expected to be slightly different from the simulation results. The effects of operating pressure change and the ratio of mass flow rates Qw /Qa were investigated systematically. The data are shown in Figs. 2 and 3. From Fig. 2, it can be seen that the temperature of the mixture increases with the increasing of operating pressures. According to the above-developed theory, the heat capacity of gas flow is increased with increasing total pressure and, in addition, an increase in the partial pressure of water vapor in the mixture. The latter parameter strongly decreases on evaporation cooling of droplets, and thereby, chilling of the gas flow occurs. This result is also in agreement with the important conclusion derived from Eq. (5) as stated above. The measured temperatures at a distance of 10 cm from glass filter are slightly higher those at 3 cm. This relates to increasing the external heat transfer of

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1.00

15 Dimensionless droplet radius [R /R0]

Temperature of Mixture [°C]

Troom = 19 °C; Qw /Qa = 0.33

3 cm from the filter 10 cm from the filter

12

9

6

3

0 20

30

40 50 60 Operating Pressure [ Torr]

70

0.95 2 0.90

0.85

1

80 0.80 1

10

Fig. 2. Temperature of droplets/gas mixture versus operating pressure.

100

1000

Dimensionless distance [z /R0] Fig. 4. Droplet radii versus dimensionless distance; Curve 1 for 60 Torr, Curve 2 for 20 Torr, Nd = 1.1 × 1010 droplet/m3 , Qw /Qa ≈ 0.03.

15

12

20 Torr 40 Torr 20

9

6

3

0 0.4

0.8

1.2

1.6

Droplet temperature [°C]

Temperature of Mixture [°C]

Troom = 22°C

15 10 5 1 0 -5

2

Qw /Qa [-] -10 Fig. 3. Temperature of droplets/gas mixture versus water flow rate at a distance of 3 cm downward from the glass filter.

-15 0.1

the chamber wall. The calculated temperatures of pure droplets and carrier gas will be shown in the section dealing with simulation results. As seen in Fig. 3, when the dimensionless parameter Qw /Qa is increased, the gas temperature increases correspondingly. This is due to the increasing total interfacial surface per unit of volume; droplets evaporate less in order to reach a steadycondition (Fisenko et al., 2004). The lower is the total pressure the higher is the rate of evaporative cooling of droplets and the chilling effects on gas flow, which has been found and explained in the above (Fig. 2). 4. Simulation results The results of a numerical solution for a system of ordinary differential equations (1)–(4) are presented below. The change in droplet radius due to evaporative cooling is shown in Fig. 4. It was a gratifying that the calculated results for all

1

10

100

1000

Dimensionless distance [z /R0] Fig. 5. Droplet temperatures versus dimensionless distance; Curve 1 for 60 Torr, Curve 2 for 20 Torr, Nd = 1.1 × 1010 droplet/m3 , Qw /Qa ≈ 0.03.

droplet sizes in dimensionless units lie on the same curve. Thus, only the total pressure determines the change in droplet size in co-flows, the parameter Qw /Qa is smaller than that in the majority of the experiments. As can be seen in Fig. 4, the final droplet radius is reached as 3 × 103 R0 is approached. The droplet temperature behavior is more complicated, and is shown in Fig. 5. The findings indicate that a rapid change in droplet temperature occurs. At the beginning of the process, the temperature drops very fast, and after the fraction of water vapor increase, the temperature arises. As 2 × 103 R0 is approached, the temperature drops to the final temperature. Again it can be seen that the most important parameter is the total pressure. Droplet radius affects only

S. P. Fisenko et al. / Chemical Engineering Science 61 (2006) 6029 – 6034

6033

24 Final relative droplet radius [R/R0]

20

Gas temperature [°C]

16 12 8 1 4 0

2

-4

100

0.88

0.84

0.80

0.76 20

-8 10

0.92

1000

40

Dimensionless distance [z / R0]

60

80

Total pressure [ Torr]

Fig. 6. Gaseous mixture temperature versus dimensionless distance; Curve 1 for 60 Torr, Curve 2 for 20 Torr, Nd =1.1×1010 droplet/m3 , Qw /Qa ≈ 0.03.

Fig. 8. Final relative droplet radius versus total pressure, Qw /Qa ≈ 0.03.

4

0.990

0.988 Droplet radius [R /R0]

Final droplet temperature [°C]

0.989 2

0

-2

-4

0.987 0.986 0.985 0.984 0.983

-6

0.982

-8

0.981 20 20

30

40

50

60

70

80

30

40

50

60

70

80

70

80

Total pressure [ Torr]

(a)

Total pressure [ Torr] 4

the route for reaching the final temperature. The rate of temperature change is high, about 2 × 103 K/s. As seen in Figs. 4–8 the number droplet Nd , remains constant, meaning that, when the total pressure is increased, the ratio Qw /Qa decreases. Note that for a better understanding of LPSP performance the existence of a freezing zone, where the droplet temperature is below 0 ◦ C, is extremely important. In Fig. 6 the monotonous dependence of the temperature of a gaseous mixture versus distance in the chamber is shown. The final temperature is reached as 2 × 103 R0 is approached and is practically equal to the droplet temperature. These calculations were made using a mono-disperse approximation. For a ratio of Qw /Qa of about 0.03, the dependence of the final droplet temperature on the total pressure is presented in Fig. 7. If the pressure is lower than 50 Torr, we see that the

Final droplet temperature [°C]

Fig. 7. Final droplet temperatures versus total pressure, Qw /Qa ≈ 0.03.

2 0 -2 -4 -6 -8 20

(b)

30

40

50

60

Total pressure [Torr]

Fig. 9. (a) Final droplet size versus total pressure for a constant Qw /Qa =0.33. (b) Final droplet temperature for a constant Qw /Qa = 0.33.

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final temperature of the droplet is below zero. For a pressure of 20 Torr the result of the numerical calculation differs from analytical estimation by more than 8◦ . It is clear from data in Fig. 5, that the analytical estimation gives the value for the minimal droplet temperature during evaporative cooling. At first glance, the results displayed in Fig. 8 are surprising. The findings show that increasing the total pressure in the chamber increases the evaporation rate. The explanation of this result is again the exponential dependence of saturated vapor pressure on temperature. As the result of the very fast cooling the droplets practically stop evaporating because of the equilibrium between the outgoing and falling flows of vapor molecules. Using the parameter Qw /Qa , we can say that by increasing the pressure, we decrease this parameter and create better conditions for the evaporation of water molecules. It is noteworthy that only in the case of relatively larger final radius at dimensionless units of about 0.8; the droplet has lost about half its mass. In Fig. 9a the dependence of final droplet radius is shown for significantly larger mass flow rates of water for Qw /Qa =0.33. As this ratio increases, the droplet radius becomes smaller. The calculated final droplet temperature is plotted in Fig. 9b for the same value for Qw /Qa . Interestingly, the results do not depend on the mass flow rate ratio or droplet radius. A comparison of Figs. 9b and 7 confirms this conclusion. 5. Conclusions The evaporative cooling of micron-sized droplets was investigated theoretically and experimentally for condition of coflows in a low-pressure aerosol reactor. Such conditions occur during LPSP process. The calculations are made for the free molecular regime of evaporation. In our experiments, the main factor that affects the final parameters of the system is the total pressure. The total pressure was maintained by a vacuum pump and a special controller. The rate of cooling of micron size droplets is about 2 × 103 K/s. Of interest is the fact that fast freezing and subsequent melting of droplets was discovered during evaporative cooling. The droplet radius and temperature change, and the duration of these processes determine many features associated with LPSP, in particular, the formation of a supersaturated solution inside the droplets during rapid cooling. Acknowledgments Financial support of Japan Society for the Promotion of Science (JSPS) for Dr. S. Fisenko (as a visiting fellow) and Dr. W.N. Wang (as a postdoctoral fellow) is greatly

acknowledged. This work was also supported in part by NEDO’s Nano-technology Particle Project funded by the Ministry of Economy, Trade, and Industry (METI), and Grants-inAid from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. References Defay, R., Prigogine, I., Bellemans, A., Everett, D.H., 1966. Surface Tension and Adsorption. Longmans, London 218–222–226–237. Fisenko, S.P., Brin, A.A., Petruchik, A.I., 2004. Evaporative cooling of water in a mechanical draft cooling tower. International Journal of Heat & Mass Transfer 47 (1), 165–177. Francois, M., Shyy, W., 2002. Micro-scale drop dynamics for heat transfer enhancement. Progress in Aerospace Sciences 38, 275–304. Fuchs, N.A., 1959. Evaporation and Droplet Growth in Gaseous Media. Pergamon Press, New York. Hinds, W.C., 1999. Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles, second ed. Wiley, Inc., New York, pp. 281–283. Kang, Y.C., Park, S.B., 1995. A high-volume spray aerosol generator producing small droplets for low pressure applications. Journal of Aerosol Science 26 (7), 1131–1138. Kodas, T.T., Hampden-Smith, M.J., 1999. Aerosols Processing of Materials. Wiley, New York. Kubo, R., 1968. Thermodynamics: An Advanced Course with Problems and Solutions. North Holland Pub. Co., Amsterdam. Lenggoro, I.W., Hata, T., Iskandar, F., Lunden, M.M., Okuyama, K., 2000. An experimental and modeling investigation of particle production by spray pyrolysis using a laminar flow aerosol reactor. Journal of Materials Research 15, 733–743. Lenggoro, I.W., Itoh, Y., Okuyama, K., Kim, T.O., 2004. Nanoparticles of a doped oxide phosphor prepared by direct spray pyrolysis. Journal of Materials Research 19 (12), 3534–3539. Messing, G.L., Zhang, S.C., Jayanthi, G.V., 1993. Ceramic powder synthesis by spray pyrolysis. Journal of the American Ceramic Society 76 (11), 2707–2726. Okuyama, K., Lenggoro, I.W., 2003. Preparation of nanoparticle via spray route. Chemical Engineering Science 58 (3–6), 537–547. Shabunya, S.I., Wende, B., Fisenko, S.P., Schaber, K., 2003. Simulations and experiments on the formation of ammonium chloride particles in wet scrubbers. Chemical Engineering and Processing 42 (10), 789–800. Wang, W.N., Itoh, Y., Lenggoro, I.W., Okuyama, K., 2004. Nickel and nickel oxide nanoparticles prepared from nickel nitrate hexahydrate by a low pressure spray pyrolysis. Materials Science and Engineering B 111 (1), 69–76. Wang, W.N., Lenggoro, I.W., Okuyama, K., 2005a. Dispersion and aggregation of nanoparticle derived from colloidal droplets under low-pressure conditions. Journal of Colloid and Interface Science 288 (2), 423–431. Wang, W.N., Lenggoro, I.W., Terashi, Y., Wang, Y.C., Okuyama, K., 2005b. Direct synthesis of barium titanate nanoparticles via a low pressure spray pyrolysis method. Journal of Materials Research 20 (10), 2873–2882. Wang, W.N., Lenggoro, I.W., Okuyama, K., Terashi, Y., Wang, Y.C., 2006. Effects of ethanol addition and Ba/Ti ratios on preparation of barium titanate nanocrystals via a spray pyrolysis method. Journal of the American Ceramic Society 89 (3), 888–893.