J. Phys. Chem. C 2007, 111, 5977-5981
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Observation of the Surface and Volume Nucleation Phenomena in Undercooled Sucrose Solution Droplets J. P. Hindmarsh,*† A. B. Russell,‡ and X. D. Chen§ Department of Chemical and Materials Engineering, The UniVersity of Auckland, PriVate Bag 92019, Auckland, New Zealand ReceiVed: October 17, 2006; In Final Form: February 28, 2007
We present the direct observation of surface-activated ice nucleation in undercooled sucrose solution droplets. Video images of freezing sucrose solution droplets while suspended at the junction of a thermocouple show two distinctive nucleation mechanisms for a droplet. These are at the surface and in the volume of the droplet. Analysis of the temperature-dependent nucleation data support the conclusion that they are separate nucleation mechanisms. Increased sucrose concentration caused surface nucleation to become less favorable. The results are not entirely described by either the two-dimensional or the capillary theories of surface nucleation but do suggest that surface-activated nucleation is a pseudo-heterogeneous process.
1. Introduction Conventional wisdom for the freezing of droplets is that nucleation will occur within the droplet volume. Classical theory models the homogeneous nucleation rate on nucleation initiated in the volume of supercooled droplets. However, a substantial number of researchers have presented theoretical and laboratory evidence of the existence of nucleation occurring at the surface of droplets.1-12 This is where freezing initiates at the surface of a supercooled droplet at the liquid-vapor interface rather than in the bulk volume. Djikaev et al.1 described this phenomenon as “pseudo-heterogeneous” nucleation where the liquid-vapor interface acted as the heterogeneous substrate for the formation of a crystal nuclei. Recently, Kay et al.7 reviewed the theoretical and laboratory evidence available on the phenomena. They concluded that surface nucleation of droplets could not be confirmed or disregarded. Surface nucleation could not be supported as there was no direct observation of surface nucleation, the thermodynamic criteria did not demonstrate a preference for surface nucleation, and nucleation rate measurements to directly test this hypothesis were not available. In this work we present direct observation of both the surface and volume nucleation phenomenon within droplets of sucrose solution. From temperaturedependent nucleation data, we are able to derive nucleation rate parameters to obtain some insight into how the two nucleation mechanisms differ. 2. Materials and Method 2.1. Solution Preparation. Crystalline sucrose (99.5%) from BDLT Laboratory Supplies was dissolved in distilled water to prepare the sucrose solutions of varying concentrations (5, 15, 20, or 30 wt %). The solutions were shaken in a bottle and * Corresponding author. E-mail:
[email protected]. Tel.: +64 6 350 5856. Fax: +64 6 350 5655. † Current address: Riddet Centre, Massey University, Private Bag 11 222, Palmerston North, New Zealand. ‡ Current address: Unilever R&D Colworth, Sharnbrook, Bedford MK44 ILQ, UK. § Current address: Faculty of Engineering, Monash University Victoria, Australia.
were left to dissolve overnight. Each concentration was confirmed by measuring its refractive index. 2.2. Droplet Freezing. Described simply, the experimental apparatus is a droplet suspended on the junction of a thermocouple in a cold air stream while the temperature at the thermocouple tip was recorded and the droplet freezing was monitored with video camera. A schematic diagram of the experimental rig is shown in Figure 1. The droplet was suspended on a 25.4 µm diameter T-type copper-constantan thermocouple (Omega Inc, UK). The air stream temperature was monitored with a 1 mm diameter T-type thermocouple (Omega Inc, UK). All thermocouples were sampled at 50 Hz. A twin-fluid nozzle was used to mix liquid nitrogen with dry air to produce a cold air stream. This was then passed through a heat exchanger to cool another air stream. Care was taken in the experiments to avoid artificial nucleation of the droplet with the most likely source being airborne particles colliding with the droplet (such as ice crystals and dust). Special care was taken to remove all moisture and dust from the air stream. A series of three 5 µm fiber microfilters and silicon gel moisture strippers was used to remove the moisture and dust from the air flow. A video camera fitted with macro lenses (magnification of 280 ×) recorded the freezing of the droplet. All of the thermocouples were calibrated at the freezing point of distilled water to ( 0.2 oC. The air temperature was controlled to within 0.5 oC. The air velocity was calibrated with a hotwire anemometer to 0.02 m/s. The microsyringe had a droplet size deviation of 0.01 µL. The maximum experimental error for the experimental conditions was calculated as (4%. For each experiment, a droplet of 2 µL was placed at the junction of the thermocouple with a 5 µL microsyringe. The droplet was then exposed to the airflow. The droplet temperature was recorded until the droplet was observed to nucleate. The nucleation temperature Tn was taken from the time-temperature profile of the freezing droplet. Figure 2 shows a typical profile. The arrow indicates the point from which the nucleation temperature Tn was taken. This is the lowest temperature of the cooling period before the droplet temperature rises rapidly due to recalescence. Experimental measurements and numerical models have shown that for the conditions (droplet size and air-cooling
10.1021/jp0668302 CCC: $37.00 © 2007 American Chemical Society Published on Web 04/03/2007
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Figure 1. Schematic diagram of experimental rig.
Figure 4. Video frames showing random nucleation on the surface of a sucrose droplet; conditions: 15 wt %, 2 µL droplet nucleating at -17.6 oC, time period between frames 0.04 s. White bar is 1 mm.
TABLE 1: Percentage of Observed Nucleation Locations for Sucrose Concentrations for a Population of 50 for Each Concentration, 2 µL Droplets Cooled in an Air Stream of -25 °C, and 0.42 m s-1. composition (wt %)
Figure 2. Temperature profile of freezing 20 wt % sucrose, 2 µL droplet in an air stream of -25 oC and 0.42 m/s. Arrow indicates point from which the nucleation temperature is taken.
Figure 3. Video frames showing random nucleation within the volume of a sucrose droplet; conditions: 20 wt %, 2 µL droplet nucleating at -20.1 oC, time period between frames 0.04 s. White bar is 1 mm.
conditions) the droplet internal temperature gradient is negligible (less than 0.2 oC from surface to center of droplet).13,14 As such, the droplet temperature can be assumed to be uniform. 3. Results and Discussion The monitoring of the nucleation of sucrose solution droplets resulted in the observation of three distinct nucleation events within the suspended droplet: nucleation located in the internal volume of the droplet, at the droplet surface, and at the thermocouple. Figure 3 shows a series of video frames that demonstrate a typical volume nucleation for a 15 wt % sucrose droplet. A volume nucleation is characterized by the initial nuclei appearing as a small opaque white spherulite suspended in the volume of the droplet, which grows radially until it fills the volume of the droplet. Figure 4 shows a typical surface nucleation for a 15 wt % sucrose droplet. A surface nucleation is distinctive as ice appears as a small disc on the surface of
5 15 20 30
thermocouple
nucleation location volume
surface
55% 39% 27% 20%
10% 46% 63% 72%
35% 15% 10% 8%
the droplet, and it grows radially across the surface as a thin sheet until it covers the entire external droplet surface or, in some cases, penetrates into the volume of the droplet. It is quite common to observe the ice shell formed on the surface that is moving while growing and generally rising to the top of the droplet. The movement is likely to be a combination of convection produced by the air flow around the droplet (bottom to top) and the density difference between the ice and liquid. Thermocouple nucleation appeared at either the point where the thermocouple wire entered the top of the droplet or at the tip of the thermocouple. Table 1 shows the frequency of occurrence of nucleation at each location for the range of sucrose concentrations used. It can be observed that as the sucrose concentration increased, volume nucleations became more predominant, the proportion of surface nucleations decreased, and the proportion of nucleations initiated by the thermocouple also decreased. It is well documented that sucrose is an ice nucleation inhibitor.15-17 This is why the mean nucleation temperature decreases with increasing sucrose solution. Charoenrein and Reid15 and Muhr et. al.17 both observed that the heterogeneous nucleation potential appeared to decrease at a greater rate than that of homogeneous nucleation for increasing sucrose concentration (nucleation was observed to occur less frequently on the container walls with large sucrose concentrations). With the frequency of surface nucleations also decreasing, the result lends some support to the theory that droplet surface nucleation is a pseudoheterogeneous process. Table 2 shows the mean temperatures for the surface and volume nucleation. The mean nucleation temperatures for both locations decrease for increasing sucrose concentration. Significantly, while there is a slight decrease in the difference between the means, the surface nucleation temperatures are consistently lower than those for the volume nucleation but the frequency of surface nucleation decreases with increasing sucrose concentration (see Table 1).
Undercooled Sucrose Solution Droplets
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TABLE 2: Nucleation Events versus Sucrose Concentration for a Sample Size of 30 Surface or Volume Nucleations in 2 µL Droplets in an Air Stream at a Temperature of -25 oC and a Velocity of 0.42 ms-1 location
mean nucleation temperature
sucrose (wt %)
surface
volume
surface (oC)
volume (oC)
difference (oC)
5 15 20 30
23 16 5 4
7 14 25 26
-17.3 -18.1 -18.9 -20.7
-19.6 -20.1 -20.8 -22.4
2.3 2.0 1.9 1.7
According to the classical nucleation theory, a first-order representation of the temperature-dependent nucleation rate J(T) is given by8,9
(
J(T) ) J0 exp -
)
(
∆G * Γ ) J0 exp kT T∆T2
)
(1)
where
J0 ) Anw
kT ∆g exp h kT
(
)
(2)
and
Γ)
16πγ3slυ2i T2mf
(3)
3kq2
The exponential factor ∆G* describes the thermodynamics of nucleus formation and the prefactor J0 describes the kinetics of nucleus growth. The temperature-dependent free energy of formation for a critical cluster ∆G* can be redefined with the formation factor Γ where γsl is the solid liquid interfacial energy, υi is the specific volume of the ice phase, ∆T ) T - Tm is the undercooling, which is the difference between the temperature T and the melting temperature Tm, q is the latent heat of fusion, and k is Boltzmann’s constant. The factor f accounts for the catalytic role of an ice-forming nucleus, which presumably depends on the water, ice, and substrate interfacial free energies. The prefactor J0 is certainly temperature dependent but its dependency is generally negligible when compared to that of the Boltzmann factor for ∆G* in eq 1.8,10 The classical nucleation theory relates the prefactor J0 to the surface density of water molecules, nw, the surface area of ice-forming nucleus, A, and the activation energy for self-diffusion, ∆g. If it is assumed that the temperature-dependent droplet nucleation is a stochastic process, the probability of a droplet nucleating P at a given temperature T while undergoing cooling can be given by9
P≡
Nf ) 1 - exp(- β-1 N0
∫TT J(T)dT)
(4)
and Γ to eqs 1 and 4. The results are summarized in Table 3. The plots of the nucleation rate parameters J0 and Γ versus sucrose concentration are shown in Figure 6. The trends of the volume nucleation rate parameters are consistent with those with homogeneous nucleation in sucrose solutions.15 This is where the growth factor J0 decreases and the formation factor Γ remains reasonably constant for increasing sucrose concentration. The growth factor J0 decreases as a consequence of the decrease in the concentration of water molecules and in the nucleus growth kinetics. The kinetics of ice growth decline due to the reduced diffusivity of water in higher sucrose concentrations. This also results in a decrease in the linear growth velocity, which was observed from measuring the linear ice growth from the volume nucleations (Table 3). Figure 6 shows that for the surface nucleation, the J0 and Γ parameters increased with increasing sucrose concentration. This has previously been observed with heterogeneous nucleation of sucrose solutions by the bacterial ice nucleant Pseudomonas syringae.15 This adds support to the theory that surface nucleation is a pseudo-heterogeneous process at the liquidvapor interface. Shaw et al.9 also found that the growth factor J0 increased with surface-stimulated nucleation of water droplets. The increased nucleation growth factor did not coincide with an increase in the linear growth velocity of the ice from surface nucleation. Table 3 shows that there was no significant difference between the linear growth velocities for the surface and volume nucleation. Applying the classical nucleation theory (eqs 1 to 3), any increase in the nucleation growth factor there would have to be a corresponding increase in either or both the surface density of water molecules, nw, and the surface area of ice-forming nucleus A. The two main surface nucleation theories are that surface/ volume nucleation of a droplet is governed by a capillary-wetting criterion, or alternatively that it is essentially a two-dimensional (2D) process at the liquid/air interface.7 The 2D nucleation theory suggests that reduced dimensionality leads to greater growth kinetics and reduced energy of formation of the nucleus. This suggests that surface nucleation would have a higher growth factor J0 and lower formation factor Γ irrespective of the sucrose concentration. As a consequence, surface nucleation would be assumed to be dominant for all conditions, which was not observed. Our results therefore suggest that reduced dimensionality cannot describe the surface nucleation mechanism observed in these experiments. Djikaev et. al.,18 applying a capillarity approximation, derived a criterion for surface nucleation to be more thermodynamically favorable than that within the droplet volume if
γsl + γlv - γsv > 0
(5)
m
where N0 is the total number of sampled droplets, Nf is the number of observed nucleated droplets in the temperature internal from the equilibrium melting temperature Tm to T, and β is the cooling rate. The temperature-dependent nucleation rate parameters J0 and Γ can be calculated from the experimentally obtainable P ≡ Nf/N0 by fitting eqs 1 and 4. Because the droplets were not cooled at a constant cooling rate, β was taken as the slope of the temperature transition at the nucleation temperature for each droplet. Figure 5 shows the probability distributions for the surface and volume at each sucrose concentration. The solid lines are the resulting linear least-squares fit of parameters J0
where γlv and γsv are the liquid-vapor and the solid-vapor interfacial tensions, respectively. The criterion coincides with the partial wettability of the solid nucleus. It is well documented that the liquid-vapor interfacial tensions of sucrose solutions increase with increasing sucrose concentration.19 As a consequence, for volume nucleation to become more favorable with increasing sucrose concentration (experimentally observed), there must be a proportionally greater increase in the solidliquid interfacial tension γsl or a decrease in the γsv solidvapor interfacial tensions. There is no data available for either interfacial tensions so it is not possible to comment on the applicability of the wetting criterion. Kay7 was sceptical of the wetting criterion because it is probable that a critical nucleus is
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Figure 5. Probability distributions P versus undercooling ∆T for 5, 15, 20, and 30 wt % sucrose solution droplets; 2 µL droplets freezing in -25 oC, 0.42 m/s air. Observed location of nucleation indicated, and solid lines are the best fits for eq 4.
TABLE 3: Temperature-Dependent Nucleation Rate Parameters Extracted from the Best-Fit of Eqs 4 and 1 in Figure 5 and the Linear Ice Crystal Growth Velocities for Each Nucleation Event in Sucrose Solution Droplets surface sucrose log(J0) (wt %) (s-1) 5 15 20 30
4.6 6.6 11.1 12.5
volume
Γ (K3)
log(J0) (s-1)
Γ (K3)
0.8 × 106 1.4 × 106 2.1 × 106 2.7 × 106
9.1 7.1 7.0 6.8
2.0 × 106 1.4 × 106 1.6 × 106 1.7 × 106
growth velocity surface volume (mm/s) (mm/s) 6.7 4.0 3.9 2.2
6.5 4.1 4.0 1.9
a strong nonequilibrium object so it would not form a equilibrium shape such as a lenticular lens. One speculation on a possible reason for the effect of sucrose on the surface nucleation parameters could be that sucrose solutions are known to form a depletion layer largely devoid of sucrose molecules near the water-air interface.20 Sucrose is a hydrophilic solute that is repelled by the water-air interface, and although sucrose molecules homogeneously pervade the whole volume of the droplet, they are only present in lower concentrations in the depletion layer, which is approximately 0.6 nm.20 With increased sucrose concentration, the depleted layer becomes more defined, which implies that the droplet surface would have a greater surface density of water molecules and a greater kinetic growth rate than the bulk sucrose solution. This would manifest as a larger nucleation growth factor J0. But this does not explain the observed increase in the formation factor Γ with increasing sucrose concentration. It is likely that the surface nucleation mechanism is more complex than or does not conform to the simple single-exponential nucleation rate model in eq 1. Another unsubstantiated theory is that surface nucleation occurs because of the barrier effect of the droplet liquid-vapor interface. As the droplet is cooled, through the action of
Figure 6. Plots of fitted nucleation rate parameters versus sucrose concentration for surface and volume nucleation events; (a) prefactor J0 and (b) exponential factor Γ. Lines are the linear trends for reference only.
Undercooled Sucrose Solution Droplets Brownian motion partially formed nuclei (assembling or disassembling groups of water molecules) will accumulate at or near the droplet surface due to liquid-vapor interface being a barrier. This leads to a higher probably of a group of partially formed nuclei colliding to form a complete nuclei at or nearer the surface than in the bulk of the droplet. As the solution diffusivity is reduced (sucrose concentration is increased) this effect becomes less significant as there is less total redistribution of molecules during the droplet-cooling period. 4. Conclusions Video images paired with measured nucleation temperatures prove that there are indeed two distinctive nucleation mechanisms with sucrose solution droplets. The nucleation rate analysis suggests that the surface nucleation mechanism is a pseudo-heterogeneous process but none of the current theories for surface nucleation can fully describe the phenomena. A far larger sample population is required before an accurate analysis of the surface nucleation mechanism can be undertaken. A more accurate and automated experimental apparatus than the apparatus that was used in the current study is required to undertake this. References and Notes (1) Djikaev, Y.; Tabazadeh, A.; Hamill, P.; Reiss, H. J. Phys. Chem. A. 2002, 106, 10247-10253.
J. Phys. Chem. C, Vol. 111, No. 16, 2007 5981 (2) Gao, W.; Smith, D.; Segob, D. Cold Reg. Sci. Technol. 1999, 29, 121-133. (3) Grange, G.; Le´vis, A.; Mutaftschiev, B. J. Colloid Interface Sci. 1986, 109, 543-551. (4) Kashchiev, D. Nucleation: Basic Theory with Applications; Butterworths Heinemann: Oxford, UK, 2000. (5) Tolbert, M.; Middlebrook, A. J. Geophys. Res. 1990, 95, 2242322431. (6) Molina, M.; Zhang, R.; Wooldridge, P.; McMahon, J.; Kim, J.; Chang, H.; Beyer, K. Science 1993, 261, 1418-1423. (7) Kay, J.; Tsemekhman, V.; Larson, B.; Baker, M.; Swanson, B. Atmos. Chem. Phys. 2003, 3, 1439-1443. (8) Seeley, L.; Seidler, G. Phys. ReV. Lett. 2001, 87, 055702. (9) Shaw, R.; Durant, A.; Mi, Y. J. Phys. Chem. B. 2005, 109, 98659868. (10) Tabazadeh, A.; Djikaev, Y.; Hamill, P.; Reiss, H. J. Phys. Chem. A. 2002, 106, 10238-10246. (11) Turner, G.; Bartell, L. J. Phys. Chem. A. 2005, 109, 6877-6879. (12) Xu, Q.; Lavernia, E. Acta Metall. 2001, 49, 3849-3861. (13) Hindmarsh, J.; Russell, A.; Chen, X. Int. J. Heat. Mass Transfer 2003, 46, 1199-1213. (14) Lin, X. Drying of single milk droplet. Ph. D. Thesis, The University of Auckland, New Zealand, 2004. (15) Charoenrein, S.; Reid, D. Thermochim. Acta 1989, 156, 373-381. (16) Miyata, K.; Kanno, H. J. Mol. Liq. 2005, 119, 189-193. (17) Muhr, A.; Blanshard, J.; Sheard, S. J. Food. Technol. 1986, 21, 587-603. (18) Djikaev, Y.; Tabazadeh, A.; Reiss, H. J. Chem. Phys. 2003, 118, 6572-6581. (19) Bubnik, Z.; Kadlek, P.; Urban, D.; Bruhns, M. Sugar Technologists Manual : Chemical and Physical Data for Sugar Manufactures and Users; Bartens: Berlin, Germany, 1995. (20) Docoslisa, A.; Gieseb, R.; van Ossa, C. Colloids Surf., B 2000, 19, 147-162.
