Article pubs.acs.org/JPCA
Water Evaporation from Acoustically Levitated Aqueous Solution Droplets Published as part of The Journal of Physical Chemistry virtual special issue “Veronica Vaida Festschrift”. Nicole A. Combe† and D. James Donaldson*,†,‡ †
Department of Chemistry, University of Toronto, 80 St George Street, Toronto, Ontario, Canada, M5S 3H6 Department of Physical & Environmental Sciences, UTSC, Toronto, Ontario, Canada, M1C 1A1
‡
S Supporting Information *
ABSTRACT: We present a systematic study of the effect of solutes on the evaporation rate of acoustically levitated aqueous solution droplets by suspending individual droplets in a zero-relative humidity environment and measuring their size as a function of time. The ratios of the early time evaporation rates of six simple salts (NaCl, NaBr, NaNO3, KCl, MgCl2, CaCl2) and malonic acid to that of water are in excellent agreement with predictions made by modifying the Maxwell equation to include the time-dependent water activity of the evaporating aqueous salt solution droplets. However, the early time evaporation rates of three ammonium salt solutions (NH4Cl, NH4NO3, (NH4)2SO4) are not significantly different from the evaporation rate of pure water. This finding is in accord with a previous report that ammonium sulfate does not depress the evaporation rate of its solutions, despite reducing its water vapor pressure, perhaps due to specific surface effects. At longer evaporation times, as the droplets approach crystallization, all but one (MgCl2) of the solution evaporation rates are well described by the modified Maxwell equation.
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INTRODUCTION The liquid water content of atmospheric aerosol particles varies substantially as a response to changing relative humidity (RH) in the gas phase. This dynamic response to ambient RH depends on aerosols’ composition and is a major factor controlling aerosol size distribution, phase transitions, trace gas uptake, aqueous phase reactions, optical properties, and aerosols’ effect on Earth’s radiation budget.1−6 Both thermodynamic and kinetic processes of evaporation and condensation are required to understand how aerosol composition affects the partitioning of water in the atmosphere. In particular, the accommodation (evaporation) coefficient for vapor phase water incorporation into the bulk has been the subject of intense study (see, e.g., ref 3 and references therein), but still remains somewhat uncertain as different measurement techniques yield different results.7 Our interest in the present paper is to explore the influence of solutes on the evaporation of finite-sized aqueous droplets. Although these are considerably larger than typical atmospheric aerosols, surface curvature does not play a significant role in the vapor pressure for particle sizes greater than tens of nanometers; therefore, we expect our results to be fairly general. For droplets larger than 1 μm radius, the rates of evaporation and condensation in still air are usually limited by diffusion into the surrounding gas phase;8 thus, for well-mixed coarse mode aerosols, aerosol water content is primarily © XXXX American Chemical Society
governed by equilibrium hygroscopic response to changes in water activity. For such diffusion-controlled evaporation, the simplest treatment of mass flux between the particle and gas phase uses Fick’s first law and assumes the evaporation rate of water from a spherical droplet is simply a function of the difference in water concentrations between the droplet surface and the surrounding gas phase. Some manipulation yields the Maxwell equation for the change in droplet surface area (SA) with time,9,10 p ⎞ 8πDν M ⎛ pr dSA =− ⎜ − ∞⎟ dt T∞ ⎠ ρR ⎝ Tr
(1)
where Dν is the diffusion coefficient in the gas phase, M is the molar mass of the evaporating species, ρ is the density of the evaporating species, pr and p∞ are the partial pressures of the evaporating species at the surface of the droplet and in the ambient atmosphere, and Tr and T∞ are the temperatures of the gas phase at the surface of the droplet and in the ambient atmosphere, respectively. Generally pr, the gas phase concentration at the surface of the droplet, is assumed to be equivalent to the liquid’s equilibrium vapor ressure.11 For a water droplet, if the ambient atmosphere surrounding the droplet is Received: August 11, 2017 Published: August 30, 2017 A
DOI: 10.1021/acs.jpca.7b08050 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A maintained at 0% RH, then p∞ ≈ 0, and the expression reduces to a single term where pr = pW * , the equilibrium vapor pressure of water: *⎞ 8πDν M ⎛ pW dSA ⎜⎜ ⎟⎟ =− dt ρR ⎝ Tr ⎠
evaporation is introduced by evaporative cooling of the droplet, which leads to a difference between the droplet surface temperature (Tr in the equations above) and the ambient temperature. This temperature has been extracted in previous work by fitting the profile of the water Raman spectrum16 or by direct measurement using an IR thermography system.10 In the following, we present results of a systematic study of the evaporation rates from aqueous droplets of a variety of inorganic salts, measured while droplets were suspended in an acoustic levitator. We believe this is the first such systematic study, although previous work has examined crystallization in such droplets,17 and evaporation from some mixed aqueous− organic liquids (i.e., refs 13 and 18). Our aim is not to make quantitative, a priori predictions of droplet evaporation rates in an acoustic field, but rather to test whether a simple treatment, using eqs 3 and 4, can describe the effect of solutes on the evaporation of droplets containing single salt solutes. Future work will explore mixed organic−inorganic solutions, which represent much better the situation of real atmospheric particles. We show that eqs 3 and 4 can be used to describe the evaporation of several inorganic salt solutions, but they do not capture the evaporative behavior of ammonium salt solutions (an observation which has been previously reported16). Equation 5 is equally robust, suggesting that departures of observed evaporation rates from these predictions can indicate interesting impediments to achieving equilibrium between the droplet and its surroundings.
(2)
In ideal solutions of nonvolatile solutes, the equilibrium vapor pressure of water depends on its mole fraction in solution, which will change with time due to evaporation. With respect to the solute mole fraction (xu) and degree of dissociation, given by the van’t Hoff factor (i), eq 2 may be written: * (1 − i·x u) ⎞ 8πDν M ⎛ pW dSA ⎜⎜ ⎟⎟ =− dt Tr ρR ⎝ ⎠
(3)
If known, the water activity coefficient (γW) can be used to account for deviations from ideality and improve the calculation of water vapor pressure above a solution droplet: * (1 − i·x u) ·γ ⎞ 8πDν M ⎛ pW dSA W⎟ ⎜⎜ =− ⎟ dt Tr ρR ⎝ ⎠
(4)
Once an evaporating aqueous salt solution reaches saturation, the equilibrium vapour pressure of water is fixed by the salt’s deliquescence relative humidity (DRH). We may thus describe the instantaneous evaporation rate above a saturated solution by * ·DRH ⎞ 8πDν M ⎛ pW dSA ⎜⎜ ⎟⎟ =− dt Tr ρR ⎝ ⎠
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EXPERIMENTAL SECTION Ten binary aqueous solutions were investigated, as well as protonated and deuterated water: NaCl, NaNO3, NaBr, KCl, MgCl2, CaCl2, NH4Cl, NH4NO3, (NH4)2SO4, and malonic acid. The chemicals all had stated purity ≥99%, except for magnesium chloride, which is reported to contain 12 h. Single droplets, 1.0−1.4 μL initial volume, were suspended in the acoustic field of a 100 kHz ultrasonic levitator contained within a 70 mm inner diameter cylindrical chamber of volume ∼250 cm3, purchased from tec5.19 Images of the levitated droplets were collected using a charge-coupled device (CCD) camera with a 1/3″ CCD sensor. To remove the dependence of image magnification on object distance, an object-space telecentric lens (2X, 110 mm WD) was used; thus, the field of view was 2.4 mm. Droplets were suspended directly in a 500 sccm stream of dry nitrogen in order to remove water vapor from the droplet surface and maintain the relative humidity in the chamber near 0%. Reference 12 shows that, for air flows up to this value around similar-sized droplets, the evaporation rate is not strongly affected. The relative humidity within the chamber was measured using a thermohygrometer before and after each test and was always below 8%; temporal variations in the apparatus, including chamber relative humidity, were accounted for by analyzing a water droplet before and after each salt droplet. Images of the levitated droplets were collected at regular time intervals until crystallization was visible. The horizontal and vertical diameters of the droplet were measured from the collected images using ImageJ, a public-domain image processing software package. The systematic uncertainty in the diameter measurements was determined by imaging
(5)
This paper describes our first studies of aqueous solution droplet evaporation rates as a function of solute species. The experiments were performed on single droplets suspended in a 100 kHz ultrasonic levitator coupled to a CCD camera. In this apparatus, particles are suspended in a standing longitudinal wave that is generated underneath the particle by a piezoelectric transducer and reflected back along the vertical axis by a concave reflector. This allows for contactless observation of particles with diameters on the order of 100−1000 μm. Acoustic levitation has not been widely used for studies of atmospheric processes, although several evaporation studies have been reported.11−14 The treatment described above assumes that evaporation reflects the approach to equilibrium of an unperturbed droplet, with no other forces acting upon it. In a laboratory setting, most work to date in the area of single-particle evaporation and chemistry of atmospherically important particles has been carried out on much smaller (sub 10 μm) particles using electrodynamic or optical traps, or by studying particles that are deposited onto an inert substrate.15 The present study uses an acoustic field to hold a single droplet in position for interrogation. Such acoustic traps have been used for some time, and it is known that acoustic streaming and convection within and at the surface of the drop play a role in it evaporation rate.12−14 In our work, we introduce a further complexity by flowing dry air past the droplet in order to maintain a near-zero relative humidity environment near the droplet. These effects have been corrected for in earlier evaporation studies by the use of the Sherwood number10 or more complex terms (i.e., refs 11−13) as correction factors in eq 1 or 2. A further complication in laboratory studies of B
DOI: 10.1021/acs.jpca.7b08050 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
on the moles of salt present. A detailed procedure for generating model predictions using eqs 3 and 4 is described in the Supporting Information.
levitated nylon balls with 1.6 mm diameter, purchased from Polysciences, Inc. The experimentally measured diameter of the nylon balls was
