Gregson, F. K. A., Robinson, J. F., Miles, R. E. H., Royall, C. P., &
Reid, J. P. (2019). Drying Kinetics of Salt Solution Droplets: Water
Evaporation Rates and Crystallization.
Journal of Physical Chemistry
B
,
123
(1), 266-276. https://doi.org/10.1021/acs.jpcb.8b09584
Peer reviewed version
Link to published version (if available):
10.1021/acs.jpcb.8b09584
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1
The Drying Kinetics of Salt Solution Droplets: Water
Evaporation Rates and Crystallisation
F. K. A. Gregson
1
, J. F. Robinson
2
, R. E. H. Miles
1
, C. P. Royall
1,2
and J. P. Reid
1,*
1 School of Chemistry, University of Bristol, Bristol, BS8 1TS
2 School of Physics, University of Bristol, Bristol, BS8 1TS
* j.p.reid@bristol.ac.uk
Abstract
The drying and crystallisation of solution droplets is a problem of broad relevance, determining the
micro-structures of particles formed in spray drying, the phase of particles delivered by, for example,
aerosol formulations for inhalation therapies, and the impact of aerosols on radiative forcing and
climate. The ephemeral nature of free-droplets, particularly when considering the drying kinetics of
droplets with highly volatile constituents, has often precluded the accurate measurement of transient
properties such as droplet size and composition, preventing the robust assessment of predictive models
of droplet drying rates, nucleation and crystallisation. Here, we report novel measurements of the drying
kinetics of individual aqueous sodium chloride solution droplets using an electrodynamic balance to
isolate and trap single aerosol droplets (radius ~ 25 µm). The initial solution droplet size and
composition is shown to be highly reproducible in terms of of drying rate and crystallisation time when
examined over hundreds of identical evaporating droplets. We introduce a numerical model that
determines the concentration gradient across the radial profile of the droplet as it dries, considering both
the surface recession due to evaporation and the diffusion of components within the droplet. Drying
induced crystallisation is shown to be fully determined for this system, with nucleation and
instantaneous crystallisation occurring once a critical supersaturation level of 2.04 ± 0.02 is achieved
at the surface of the evaporating droplet surface. This phenomenological model provides a consistent
account of the timescale and surface concentration of free-droplet crystallisation on drying for the
different drying conditions studied, a necessary step in progress towards achieving control over rates of
crystallisation and the competitive formation of amorphous particles.
Introduction
The drying of liquid droplets to form particles is an important process for a range of industries, from
agriculture and inkjet printing to the production of pharmaceutics, cosmetics and food.
1–4
In addition
the propensity of an aerosol droplet to crystallise into solid particles has been shown to dramatically
2
influence the optical properties of atmospheric aerosols and, thus, their radiative forcing.
5,6
The evolving
heterogeneities in particle microstructure as a droplet evaporates can be a highly complex process. Heat
and mass transfer can be strongly coupled.
7
The competition between surface recession and internal
flows such as convection, diffusion and Marangoni flows can result in an array of product morphologies,
size and properties.
8–10
For some solutes, nucleation and crystallisation is sufficiently rapid that dry
crystalline particles result, dependent on drying rate; for other systems, drying may lead to amorphous
glassy particles.
11,12
The crystallisation of solutes present in a droplet is often the ultimate outcome of a
droplet-drying processes. The time at which nucleation occurs within an evaporating droplet can be
directly linked to the initial droplet size and solute concentration, allowing some control over the final
crystalline particle size and morphology. Our objective here is to examine the drying kinetics and
crystallisation of inorganic solution droplets. Through refined measurements of the drying rates of
individual droplets, we will show that the crystallisation time and surface composition at crystallisation
are highly reproducible over ranges of starting droplet composition and temperature, providing a
phenomenological model for predicting the formation of crystalline particles.
Although there has been considerable work on the study of droplets drying on surfaces, i.e. sessile
droplets,
13–15
far fewer studies have examined the drying kinetics and crystallisation of free droplets or
aerosols. There are numerous unique experimental challenges associated with studying the drying
dynamics of free droplets that are easily overcome when examining sessile droplets. Free droplets are
ephemeral and difficult to follow in position unless a single particle is isolated and captured, such as
with an optical trap,
16
electrodynamic balance
17
or acoustic trap.
18
Even then, the timescales of
evaporation processes can be <1 s, presenting a significant challenge to infer characteristic properties
(e.g. size, composition at point of crystallisation) on such short timescales. Ensuring reproducibility in
droplet generation and drying events is also crucial if sufficient statistics are to be achieved to infer the
key microphysical details of the drying process. Finally, sampling the particles for off-line structural
analysis requires deposition, which may also lead to a phase change or change in particle composition.
19
However, studying free droplet evaporation remove the complexities of the substrate-droplet
interactions and Marangoni flows that occur for sessile droplets. In addition, the absence of a surface
simplifies the symmetry for modelling, reduces the possibility of heterogeneous nucleation and limits
the treatment of heat-transfer to conduction into the vapour phase. Free droplets drying in air is also
more representative of industrial processes such as crop-spraying and spray-drying. Thus, a greater
understanding of how the particle-formation process can be predicted and controlled would be integral
to improving the efficacy of many industrial drying processes.
Spray-drying is the process of rapidly drying a stream of aerosolised-solution droplets in a hot air flow,
such that micron-sized particles are formed. Its application in many industries can be attributed to the
speed and efficiency of the one-step process, and the short residence time of the droplets enables the
use of heat-sensitive precursor compounds.
20
Although widely used, the process of particle formation
3
from aerosol droplets is an active area of research as it is highly condition-dependent.
21
A better
understanding of the factors governing the evaporation kinetics and how compositional heterogeneity
develops within an evaporating droplet is critical to allow ultimate fine-tuning of drying conditions and
precursor components, and to deliver tailored final dry particles with desired characteristics.
22
Within a
spray-drier, droplet evaporation is typically rapid, i.e. on timescales on the order of milliseconds to
seconds. The rate of evaporation can outcompete the rate of diffusional solute mixing leading to the
enrichment of solutes at the droplet surface; the rate at which solvent is replenished at the surface is
much slower than the rate of surface recession. The Peclet number (P
e
) is used to provide a measure of
the ratio between the diffusion rate within a particle and the evaporation rate:
(1)
where κ is the evaporation rate and D
i
is the molecular diffusion coefficient of species i within a
particle.
23
A Peclet number lower than 1 indicates that an homogeneous composition is maintained
throughout the drying process; the diffusional mixing is fast enough to replenish the surface with solvent
from the droplet bulk. However, a P
e
greater than 1 indicates that the surface is likely to become
enriched as the droplet dries, with the surface receding at a greater rate than the time scale for diffusional
mixing.
24–26
In the bulk phase, crystallisation of solutes typically occurs upon reaching saturation. However,
metastable supersaturated solute states are prevalent in the aerosol-phase, with crystallisation only
occurring at high solute concentration and a water activity much lower than the solubility limit, often
referred to as the efflorescence point. Classical nucleation theory (CNT) is built on an interplay between
the interfacial free energy of the crystal-liquid phase boundary and the chemical potential difference
between the liquid and crystalline phases.
27
The chemical potential difference rises with increasing level
of saturation within the droplet, and the interfacial free energy acts as a barrier to formation of a crystal
nucleus. Although surfaces and impurities, such as dust, can act as heterogeneous nucleation sites and
reduce the free energy barrier to nucleation, the absence of a solid surface enables an aerosol droplet to
reach very high levels of supersaturation before efflorescence occurs. Typically, inorganic solutions
effloresce at a water activity reported in terms of the gas phase moisture content, or the efflorescence
relative humidity (ERH). At atmospheric temperature and pressure, the aerosol is only able to hold the
salt in aqueous-solution form under conditions of higher moisture-content than the ERH. Homogeneous
nucleation is a rare event, and the stochastic nature means that efflorescence is typically reported over
an RH range as there is inherent randomness in the occurrence of nucleation.
28
For sodium chloride,
this range is narrow and whilst a size dependence of the droplet on the ERH has been reported
29
the
ERH for droplets of the size range in this work is reported at 44-45% RH.
30
A water activity of 0.45
corresponds to a molality of 12.68 mol kg
-1
, a concentration of 648 g L
-1
and a supersaturation level of
2.04.
31
4
A series of studies have investigated the drying of inorganic solution droplets evaporating both on
surfaces and during levitation, inferring the nucleation rate as a function of supersaturation level
reached.
32,33
We focus here on the crystallisation of evaporating sodium chloride droplets. Aqueous
sodium chloride was chosen as the system for study as the thermodynamic equilibrium behaviour of
aqueous sodium chloride aerosol is well characterised,
31
and the evaporation of water from aqueous
NaCl sessile-droplets has been studied in detail.
13,34
Sodium chloride is also a common precursor
compound used industrially. It is particularly prevalent in the preparation of food, and its particle
formation process is relevant because of a drive to reduce salt intake in populations.
35
There have been
reports stating that one can increase the intensity of salt flavour by adjusting particle size and
morphology, allowing an overall lower mass of NaCl to be used.
36,37
In addition, NaCl is a large
component of sea-spray, and thus it is important to understand its crystallisation and phase behaviour
for climate models.
38
In this work, we report measurements of the time-dependent radius of a rapidly evaporating sodium
chloride droplet throughout the drying process, and the time of crystallisation. Trapping the droplet in
free air whilst it dries eliminates any heterogeneous nucleation site such as a container wall, and only
the homogeneous nucleation of NaCl crystals is probed. These measurements are performed on a large
population of droplets, providing a comprehensive statistical analysis on the propensity to crystallise.
Homogeneous nucleation of NaCl occurs above a certain critical supersaturation, S
c
. The evaporation
kinetics results are compared with simulations of the evolving internal concentration gradients within
the evaporating droplets
Experimental Method and Assessment of the Particle Phase State
The evaporation of water from sodium chloride solution droplets was studied using the electrodynamic
balance (EDB) (see Fig.1a). In all experiments, HPLC-grade water and BioXtra ≥ 99.5% NaCl (Sigma
Aldrich) was used. The EDB instrument has been described in detail in previous work
39
and will only
be briefly reviewed here. A droplet-on-demand generator is used to produce a single droplet of known
composition which is charged (< 10 fC, for example, from an imbalance in Na
+
and Cl
-
) and injected in
to the EDB trapping chamber. An AC voltage is applied to a pair of upper and lower concentric
cylindrical electrodes, generating an electric field in which the droplet is trapped. The gravitational and
drag forces acting on the droplet are offset by a DC voltage applied to the bottom electrode. A flow of
dry nitrogen passes over the trapped particle at a rate of 0.03 m/s and the trap temperature (273 K to
323 K) is controlled by circulating ethylene glycol coolant through the electrodes.
The droplet is illuminated with a 532 nm CW laser and the resulting elastically scattered light pattern
(phase function) is collected over an ~ 24° angular range centred at 45° to the forward direction of the
laser (see Fig. 1b). During the time-period that the trapped droplet is homogeneous and spherical, it
produces regularly spaced interference fringes in the phase function which allow the size of the droplet
