Article pubs.acs.org/JPCA
Observation of the Binary Coalescence and Equilibration of Micrometer-Sized Droplets of Aqueous Aerosol in a Single-Beam Gradient-Force Optical Trap R. Power,† J. P. Reid,† S. Anand,‡ D. McGloin,‡ A. Almohamedi,§ N. S. Mistry,⊥ and A. J. Hudson*,⊥ †
School of Chemistry, University of Bristol, Cantock’s Close, Bristol, BS8 1TS, United Kingdom Electronic Engineering and Physics Division, University of Dundee, Dundee, DD1 4HN, United Kingdom § Department of Physics, University of Leicester, Leicester, LE1 7RH, United Kingdom ⊥ Department of Chemistry, University of Leicester, Leicester, LE1 7RH, United Kingdom ‡
ABSTRACT: The binary coalescence of aqueous droplets has been observed in a single-beam gradient-force optical trap. By measuring the time-dependent intensity for elastic scattering of light from the trapping laser, the dynamics of binary coalescence have been examined and the time scale for equilibration of a composite droplet to ambient conditions has been determined. These data are required for modeling the agglomeration of aqueous droplets in dense sprays and atmospheric aerosol. Elastic-light scattering from optically trapped particles has not been used previously to study the time-resolved dynamics of mixing. It is shown to offer a unique opportunity to characterize the binary coalescence of aqueous droplets with radii from 1 to 6 μm. The study of this size regime, which cannot be achieved by conventional imaging methods, is critical for understanding the interactions of droplets in the environment of dense sprays.
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INTRODUCTION The coalescence and agglomeration of aqueous droplets in dense sprays is relevant to intranasal drug delivery, fuel injection systems, and the industrial process of spray drying. Coalescence is also a critical process in governing the mixing state and lifetime of aerosol particles in the atmosphere. However, as a fundamental process it remains to be fully characterized and understood. The development of experimental techniques to provide quantitative information under controlled conditions on interparticle interactions and the binary coalescence and mixing of particles is of crucial importance for modeling the complex dynamics that occur in dense sprays and aerosols. Physical models have already been described in the literature for simulating the coalescence dynamics of microdroplets suspended in an immiscible continuous phase, either gas1−6 or liquid.7,8 The main focus for many of these models is in quantifying the time elapsed between the initial contact of a pair of isolated droplets and the full recovery of a spherical geometry in the composite droplet; this is referred to as the binary coalescence time. However, the dynamics of coalescence can be more complex; for example, the distortion of the liquid− air interface (or the interface between immiscible liquids) from a spherical geometry following the impact of a pair of droplets leads to a transient increase in the surface tension, which can result in oscillations in the shape of the composite droplet prior to the recovery of a spherical geometry. The theoretical modeling of aerosols is further complicated by the dependence of coalescence dynamics on the composition and size distribution of droplets and the nonideal properties of liquid phases due to high concentrations of dissolved salts. This © 2012 American Chemical Society
makes it imperative to test and refine theories against experimental data obtained for binary events recorded under controlled conditions with a range of relevant particle sizes. The coalescence dynamics for aqueous droplets, with radii in excess of 100 μm, has been studied experimentally on microfluidic platforms,9−12 and the coalescence of a droplet of oil suspended in water with a phase-separated layer of oil has been visualized using bright field microscopy.13 There have been similar high frame rate imaging studies on the coalescence of aerosol droplets, with particle radii in excess of 100 μm,14−17 but the limitations of optical imaging have meant that detailed data have not been obtained for smaller particle sizes, 0 s, reflected in the data shown in Figure 4b, is a consequence of the kinetic energy gained by the incoming particle as it is accelerated to the waist of the laser. There is a fairly regular separation of about 400 μs between the intensity
Figure 9. The elastic scattering of light measured in the backward direction during the binary coalescence of droplets in a 1070 nm optical trap. The initially trapped droplet was formed by nebulizing an aqueous solution containing 40 g L−1 of NaCl. The incoming droplet was formed by nebulizing pure water. 8882
dx.doi.org/10.1021/jp304929t | J. Phys. Chem. A 2012, 116, 8873−8884
The Journal of Physical Chemistry A
Article
video recording, at a perpendicular angle of orientation to the trapping laser, will be applied to estimate the velocity of the incoming droplet. A technique used to measure the axial displacement of aerosol droplets, under equilibrium conditions, by side imaging at 90° to the trapping-laser beam has been described in a previous publication.39 This can be adapted to enable time-resolved measurements. These measurements will provide comprehensive data on the binary coalescence of aqueous droplets with radii in the range of 1 to 4 μm that can be used to test and refine the models for agglomeration of droplets in dense sprays.
representative example of case C. The mass loading of salt in the trapped droplet is not altered following the coalescence event between a salt-doped droplet and a pure water droplet (case D). Consequently, the composite droplet must dispel water to recover the size of the initial trapped droplet, and thus the scattering intensity at t ≫ 0 s in Figure 9 returns to the level observed at t ≫ 0 s.
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SUMMARY AND CONCLUSION Dense sprays of aqueous aerosol have been generated by a medical nebulizer, and the binary coalescence of micrometersized droplets in an optical trap has been examined. The examples of coalescence events that have been illustrated include those between aqueous droplets with the same composition and an aqueous droplet containing different concentrations of dissolved salt. Conditions have also been varied by switching between a wavelength for the trapping laser near the wavelength at which the extinction coefficient of water is a minimum to avoid significant heating of droplets, and a laser wavelength with a significant extinction coefficient in water to perturb the temperature of droplets. High speed video recording illustrates the different stages involved in the coalescence of droplets in an optical trap, including the trajectory of both the incoming droplet and the newly formed composite droplet under the influence of the optical field. By measuring the time dependence of elastic-scattered light from the trapping laser, we are able to measure both the fast relaxation due to morphology changes following binary coalescence of droplets, and the times taken for equilibration of the composite droplet to the ambient relative humidity by evaporation of water. Shape fluctuations in a composite droplet are observed, at frequencies in excess of 100 kHz, immediately following the collision of droplets in an optical trap. If the temperature perturbation caused by the trapping laser is significant, then a slightly longer time is observed following the binary coalescence of droplets for the shape to relax to a spherical geometry. Examples of binary coalescence events in which there exist a difference in solute concentration between the colliding droplets results in a mismatch between the vapor pressure of the composite droplet and the surrounding partial pressure of water. A time interval of approximately 1 s is required for the equilibration of a composite droplet to the ambient conditions of relative humidity. This result is in good agreement with theoretical simulations of heat and mass transfer to the surroundings. For the studied examples of coalescence in which the trapping laser significantly perturbs the droplet temperature, the added volume to the initial trapped droplet undergoes rapid optical heating, >1 K, leading to a significant and transient elevation in vapor pressure. This is brought back into balance with the surrounding partial pressure of water by a dramatic loss of water from the composite droplet, which is on the same time scale as the equilibration of the vapor pressure due to the mixing of aqueous droplets with different concentrations of dissolved salt. Further parameters required to provide a detailed description of the binary coalescence of droplets are the accurate sizes for the initial trapped droplet and the final composite droplets, and the velocity of the incoming droplet prior to the coalescence event, in addition to the relative humidity and temperature. In the future, a systematic study of binary coalescence will be made by determining the initial droplet size, and the composite droplet size, from the frequencies of morphology-dependent resonances in cavity-enhanced Raman spectra. High speed
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS A.H., J.P.R., and R.P. acknowledge the EPSRC for financial support through an Advanced Research Fellowship, a Leadership Fellowship, and a project studentship, respectively. S.A. thanks the Schlumberger Faculty for the Future program for support. A.A. would like to thank the government of Saudi Arabia and King Abdulaziz University for the support of a Ph.D.
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