1
Evaporative Drying of Droplets and the Formation of Structured and Functional Microparticles
Florence Gregson
University of Bristol
Supervised by Prof. Jonathan Reid
Contents Abstract ................................................................................................................................................... 1
Introduction ............................................................................................................................................ 2
Evaporation Kinetics ............................................................................................................................... 2
Experimental Techniques ........................................................................................................................ 5
Optical Trapping .................................................................................................................................. 5
Measuring the bulk aerosol viscosity .............................................................................................. 5
Electrodynamic Balance: ..................................................................................................................... 6
Rapid Measurements of Evaporation in a Falling Droplet Instrument ............................................... 7
Aims of this project ................................................................................................................................. 7
Conclusions ............................................................................................................................................. 9
References .............................................................................................................................................. 9
Abstract Spray drying is a highly common industrial process, forming micron-sized particles by drying a stream
of aerosolised solution. The process through which a solid particle forms through evaporative drying
is incredibly complex, and many competing internal processes can lead to an array of different
structures of final product. The aim of this project is to put together a detailed kinetic model of the
effects of formulation and processing conditions on the evaporation of single aerosol droplets. Rapid
evaporation of droplets in an electrodynamic balance (EDB) can push conditions far out of
equilibrium and reflect the conditions within a spray drier. Optical traps (OT) can be used to
determine properties of droplets at discrete compositions, which an evaporating droplet will transit
through as it dries in an EDB. The combination of these techniques with detailed simulations of heat
and mass transport during droplet evaporation, could lead us to learn more about the mechanisms
that control particle formation in spray-drying. Ultimately, our goal is the capability to accurately
predict and control the formation of micro-structured particles for industrial applications.
2
Introduction The evaporation of liquid droplets is a highly complex problem and is still poorly understood. The
kinetics of the evaporation process can vary vastly depending on the drying conditions and
formulation of the feed solution. Advances in the understanding of process-structure relationships in
evaporating droplets in spray-driers would greatly improve product quality and reproducibility.
Spray drying is the industrial process of producing powders through the aerosolisation of a solution
or slurry, followed by rapid evaporation of the solvent by feeding the aerosol into a flow of hot air.
The remaining material takes the form of dehydrated particles in the micron-sized regime. It is
popular in the food and pharmaceutical industries because the short residence time enables the use
of heat-sensitive materials that would otherwise deteriorate under high temperatures or pressures.
(Fu et al. 2012) Examples of products made through spray-drying are milk or coffee powders, paints,
pigments and powdered drugs.
There are associated challenges with understanding spray-drying and predicting final particle
structure and phase. Although the technique has long been used industrially, the factors that govern
the development of droplet morphology through the evaporation process is still an area of ongoing
research. The process is highly condition-dependent; a single droplet can evolve into a wide array of
possible structures depending on process parameters such as the initial feed composition and
concentration, temperature of the drying chamber and the humidity. Mass and heat transfer are
strongly coupled, and mechanical instability of evaporating droplets can lead to wide varieties of
shapes. Droplets such as solid or hollow spheres, buckled flat particles, smooth or spiky surfaces,
doughnut shapes or porous shells have been observed. (Iskandar et al. 2003; Nandiyanto &
Okuyama 2011; Vladisavljević 2015; Lähde et al. 2006) The morphology of dried particles can be
highly critical for the application; for example, in the pharmaceutical industry the size and size
distribution is an important factor in dose delivery, and the solubility can be highly dependent on
size, shape and phase (amorphous or crystalline) (Pilcer & Amighi 2010). Compositions of different
constituents may not be radially homogeneous across the final particle due to internal diffusion
limitations during drying. In addition, stability of the dried microparticles against agglomeration and
crystallisation is essential to avoid product failure. (Amstad et al. 2016)
As the spray-drying process occurs in the aerosol phase, bulk studies of the solutions are not always
relevant or useful, as the characteristic deliquescence/efflorescence hysteresis loop of aerosol phase
behaviour leads to delays between saturation and crystallisation. Highly supersaturated liquids can
be formed in the aerosol phase which would are not accessible in bulk experiments. Studying single
droplet evaporation in a controlled environment could further our understanding of the
fundamental microphysics and could provide insight into the industrial process. (Sadek et al. 2015)
First, I will discuss what is currently known about evaporation kinetics of aerosol droplets, and what
challenges remain. Then I will discuss the experimental techniques available for studying droplet
drying at the single particle level, and the aims of how we will approach this project.
Evaporation Kinetics Evaporation of a droplet within a spray-drier involves the coupling of heat and mass transfer. The
driving force for drying is the difference between the solvent vapour pressure above the droplet
surface and the solvent partial pressure within the gas phase. The energy of vaporisation of the
solvent balances with the energy transfer to the droplet’s surface to determine the evaporation rate,
which is often quantified by the decrease in surface area of the droplet with time. (Miller et al. 1998)
3
The Peclet number is a dimensionless number used to describe the conditions for droplet drying
during the spray drying process. It is a dimensionless number representing the ratio between the
rate of the solvent evaporation and the rate of diffusional solute motion, thus reflecting the chance
of the composition remaining homogeneous. A Peclet number lower than 1 indicates that
homogeneous mixing of components will remain fast throughout the drying process relative to the
rate at which the surface recedes, leading to solid, dense and crystalline particles. Conversely, a
Peclet number greater than 1 leads to surface enrichment of solute, leading to dried particles that
are hollow or porous (see Fig. 1). However, it is still a simple depiction and does not fully describe
the process, especially when more than one solute is present.
Figure 1: Glycoprotein particles produced by a monodisperse droplet chain dispenser in dry air. The Peclet number for each evaporation process (from left to right) is 2.7, to 5.6, to 16.8, for the drying temperatures of 25, 50 and 125 °C respectively. (Reprinted (adapted) with permission from (Vehring 2008). Copyright 2008 Springer.)
Control over the mechanisms of crystallisation in evaporating aerosol is still poorly achieved. The
particles can enter supersaturation regimes due to delayed crystallisation. If supersaturation is
reached, the viscosity can rise leading to slow diffusion and a reduced rate of nucleation, delaying
crystallisation further (Lee et al. 2016). The precipitation window is the time window during which
crystallisation could occur: between the point of supersaturation of the solute on the surface, to the
completion of the evaporation process (see Fig. 2). The solute can begin to precipitate at any point in
the precipitation window, although this could be as an amorphous solid.
In multi-component systems, every component in the solution will have a different precipitation
window. It has been suggested that the component with the longest precipitation window
dominates the particle formation process, as it probably crystallises first, and is hence more likely to
reside in the outer shell of the dried particle. (Baldelli et al. 2016) The radial distribution of co-spray
dried components has been shown to be controllable by adjusting the precipitation windows,
through fine-tuning the formulation. (Baldelli & Vehring 2016)
4
Figure 2: Schematic to show the evolution of surface concentration with time through the drying process until the point of crystallisation.
The precipitation window (ts) for a solvent begins when the surface concentration equals its solubility, and ends at crystallisation.
The longer the precipitation window for a solution, the higher the chance of forming a shell earlier in
the drying process. Thus, long precipitation windows make the presence of an internal void more
likely, leading to a lower density. Density control is highly desired in particle engineering across
many industries; for example hollow, low density particles are often desired for their dispersibility in
lung drug delivery applications. (Edwards et al. 1997) There are examples of work on controlling
density by inducing early precipitation of one component through its weak solubility in the solvent,
leading to heterogeneous crystallisation of the other components. (Vanbever et al. 1999) Also,
particles with an incredibly low density (as low at 0.1 g cm-3) have been produced using emulsion
aerosol droplets. A dispersed solvent evaporates rapidly leaving large pores in the final particle shell.
(Dellamary et al. 2000)
The mechanical properties of the shell also can dictate the final particle morphology, leading to
collapsed particles or spherical particles that retain their shape throughout the evaporation process.
Adjusting the ionic strength and Debye length of colloids in an evaporating droplet has been shown
to drastically change the mechanical stability of the shell (see Fig. 3). (Lintingre et al. 2015) The shell
remains spherical when there is a balance between the electrostatic colloidal repulsion and the
Darcy pressure, which is the pressure induced by solvent flux to the surface during drying. (Tsapis et
al. 2005)
Figure 3. The morphology of spray-dried particles of colloidal zirconia-water suspensions, at different weight percentages of Polyacrylic Acid (PAA). Values are given in wt%/zirconia; images shown with a 1mm scale bar. The dried particles retain their spherical shape only at low absolute values of PAA (between -25 mV and 25 mV). ( Reprinted (adapted) with permission from Lintingre et al., 2015. Copyright 2015 Royal Society of Chemistry.)
5
Experimental Techniques Single particle techniques to study evaporation can be carried out with a sessile droplet, i.e. one
deposited on a surface (Larson 2014), with a free-falling chain of droplets (Baldelli & Vehring 2016),
in a suspended droplet (Renksizbulut & Yuen 1983) or by levitating it in free air. Levitation methods
could be optical, acoustic, electrodynamic, (Knezic et al. 2004; Paul 1990) or thermal i.e. using the
Leidenfrost technique. (Biance, Clanet, & Quéré, 2003)
In my project, I will be using optical trapping, the electrodynamic balance technique and the
monodisperse droplet chain technique to study evaporating aerosol droplets. Combining these
techniques with detailed simulations of heat and mass transport from collaborators, we will aim to
produce a detailed kinetic model which accurately demonstrates the transfer of mass and heat in an
evaporating droplet, progressing from simple multicomponent mixtures of soluble and miscible
components through to mixed phase systems including emulsion droplets.
Optical Trapping Optical traps (OTs) can be made by passing a laser beam through an objective of high numerical
aperture causing it to very tightly focus. Injecting a cloud of micron-sized aerosol droplets into the
trapping chamber results in a droplet becoming trapped at the focus of the laser. A trapped droplet
equilibrates at a particular relative humidity (RH), controlled by a gas-flow, and its properties can be
spectroscopically probed. The radius and refractive index can be measured with Raman
spectroscopy by detecting the inelastic scattering of the trapping laser. Total internal reflection of
the Raman light inside the droplet results from the existence of discrete Whispering Gallery Modes,
which are dependent on both the droplet size and refractive index. (Chen et al. 1991) The droplet’s
size and refractive index can be extracted in an offline computational step using Mie theory, which is
an exact solution to Maxwell’s equations describing monochromatic light passing through spherical
dielectric particles. (Carruthers et al. 2010) Please refer to a previous publication for a more detailed
description of the set-up. (Song et al. 2016)
Measuring the bulk aerosol viscosity The viscosity of an aerosol particle can be measured in droplet coalescence experiments using the
OTs. If two droplets are held in separate traps and brought together in space, the time constant for
the relaxation in shape following coalescence can give the solution viscosity at the water activity
dictated by the RH. (Bzdek et al. 2016) Assuming the two droplets have homogeneous compositions,
when the two droplets coalesce the resulting particle will oscillate in shape. The particle shape
initially is far from spherical, and capillary forces induce its relaxation back to a sphere to minimise
the surface energy. (Song et al. 2016) These oscillations are under-damped for very low-viscosity
solutions (on the order of 10-3 Pa s) and can be observed through the elastic back-scattering of the
trapping laser to retrieve the time constant τ (see Fig. 4). The viscosity can then be retrieved using
equation 1. (Power & Reid 2014)
𝜏1 =𝑎2𝜌
(𝑙 − 1)(2𝑙 + 1)𝜂
where a is the final (relaxed) droplet radius and ρ and η are the droplet’s density and
viscosity, respectively. l is the deformation mode for the relaxing sphere, with the l=2 mode can be
assumed to be the most dominant.
(1)
6
Figure 4: An example of the decay in elastic light scattering for two aerosol droplets during coalescence and relaxation to a single spherical particle. The peaks can be fitted to a first order exponential decay to extract the time constant, τ, for the coalescence, which can be used to determine the viscosity of the solution at that particular RH. Shown here, sodium nitrate aerosol droplets at a RH of 83.40%.
If the viscosity is higher than a critical value (depending on the size of the particle, but ~20 mPa s for
the droplet sizes appropriate for our work), the particle relaxes in a slowly creeping viscous mode
rather than an oscillation. This leads to an overdamped decay of reducing aspect ratio of the shape
with time, which can be detected using Bright-field imaging (see Fig. 5). This techniques offers the
capability to thus measure the viscosity of aerosol particles over a range from 10-3 to 1010 Pa s.
Figure 5: An example of analysis of the Bright-field images of a coalescence between two droplets to determine the time constant, τ. The reducing aspect ratio with time can be fitted to an exponential decay. The aspect ratio cannot be measured when the particles re-orient inside the trap during relaxation. This example shows sucrose droplets at a RH of 41%. From Y. C. Song 2016.
Electrodynamic balance: The electrodynamic balance (EDB) can probe rapid, dynamic out-of-equilibrium evaporation kinetics,
with conditions that closely replicate those within an industrial spray-drier. It can produce a curve of
decreasing radius with time, (Rovelli et al. 2016) of a droplet drying over the course of a few seconds
0.00000 0.00002 0.00004 0.00006 0.00008 0.00010
0.001
0.002
0.003
0.004
0.005
0.006
Am
plit
ude
Time / s
7
or as long as a few hours. During evaporation, the droplet transitions through compositions that can
be characterised using the steady conditions accessed in OT measurements. For example, the time-
dependent composition can be related to a time-dependent composition that can be presented as a
time-dependent viscosity based on the OT studies.
A droplet-on-demand generator produces individual droplets and injects them through an induction
electrode to become charged. They pass into the EDB cell which has a set of concentric cylindrical
electrodes above and below the droplet path, and when a AC/DC field is applied, the droplet
becomes trapped in the chamber as a result of the balance between the electric field, gravity and
Stokes drag force from a gas flow. This enables studies of rapid evaporation in an environment of
tuneable RH and temperature, with high reproducibility (see Fig. 6). (Miles et al. 2016)
Figure 6: (NH4)2SO4 solution droplets evaporating into different RHs in an EDB. (Reprinted (adapted) with permission from Rovelli et al., 2016. Copyright 2016 American Chemical Society)
Rapid Measurements of Evaporation in a Falling Droplet Instrument Another tool used in this project will be a new piece of equipment for measuring droplet
evaporation dynamics on timescales shorter (<10 ms) than the EDB (seconds). It will be similar in set-
up to the droplet chain producer used by Vehring et al. (Baldelli et al. 2015) Droplets will be
generated in a monodisperse chain, with a known generation frequency, produced as a result of an
electric pulse at a piezoceramic dispenser. The droplets then fall in a controlled path onto a
collection filter, and the path is illuminated by a diode laser which is pulsed in order to match the
droplet dispenser for stroboscopic image collection by a digital camera. The spacing between the
droplets in the images can be used to calculate the droplet velocity. There is a known gas-flow
velocity, so from the droplets’ terminal velocity the aerodynamic diameter of the falling droplets
with time can be determined. This can lead to information about the particle density with time
through the droplet evaporation process. Although these calculations only hold for spherical
particles prior to shell formation, this method has been demonstrated to be useful in measuring
saturation times, and precipitation windows. (Hoe et al. 2014) An additional benefit of this
technique is the ease of collection of the dried product, which can then be analysed with scanning
electron microscopy imaging to see the final morphology, or X-Ray diffraction for crystallinity data.
Aims of this project From the combination of these techniques as well as modelling support from collaborators, we will
aim to produce a detailed kinetic model which accurately demonstrates the transfer of mass and
heat in an evaporating droplet.
8
In this project I will combine the techniques of OTs, the EDB and the falling droplet instrument to
assess the radial composition of a droplet throughout the evaporation process, across a broad range
of different formulations and processing conditions. I will try to produce a kinetic model that
accurately demonstrates the transfer of mass and heat in an evaporating droplet. The EDB and the
falling droplet instrument both replicate the rapid out-of-equilibrium evaporation occurring in a
spray drier, and can produce accurate measurements of changing radius and density with time. On
the other hand, optical tweezers can be used to equilibrate droplets for longer periods of time to a
specific RH, enabling us to probe the viscosity of droplets at different levels of supersaturation.
Many different levels of supersaturation may be present in a rapidly evaporating droplet. In high
Peclet number conditions, droplet evaporation occurs rapidly and the diffusional solute motion is
not fast enough to redistribute components within the droplet, leading to inhomogeneous particles.
The rate of diffusion at the surface of a droplet is much lower than at the core of the particle.
Modelling radial responses to step changes in RH allows us to determine the compositional
dependence of diffusion constants, so can lead to knowledge about the water activity at different
radial slices within a droplet. (O’Meara et al. 2016) We can use the tweezer measurements, and
assumptions about the Stokes Einstein relationship, (Chenyakin et al. 2016) to predict the diffusion
of components at each radial slice in a droplet for an accurate picture of how rapidly evaporating
droplets evolve in microstructure throughout the spray-drying process.
An example of a model performed by Andrew Bayly et al., collaborators on this project, is shown in
Figure 7. (Handscomb et al. 2009) The goal of this work will be to build on these principles and
experimentally replicate this study with a range of different formulations and processing conditions.
A commonly used model to observe evaporation or hygroscopic growth relies on assumptions such
as homogeneous composition, uncoupled heat and mass transfer, and mass accommodation
coefficients being equal to 1. (Kulmala et al. 1992) As previously discussed, these assumptions do not
hold in the context of spray-drying, due to the surface enrichment of solutes occurring during fast
out-of-equilibrium evaporation.
Figure 7: A simulation of the mass fraction at 5 s intervals of different radial positions within an aerosol droplet of aqueous sodium sulphate, as it evaporates. The dashed line at t=78 s is the point of shell formation, and the bold line at t=45 s indicates the point of surface saturation i.e. when the concentration of solute at the surface is equal to the solubility at that temperature. From Handscomb et al. (Reprinted (adapted) with permission from Handscomb et al. 2009. Copyright 2009 American Chemical Society)
In this project I will be pushing the conditions of an evaporating droplet far out of equilibrium, to
replicate the spray-drying conditions. The assumptions held for current evaporation models can be
deliberately broken, to see how well the model would describe the kinetics. For example, the mass
accommodation coefficient can be reduced down from a value of 1 using sequential addition of
9
surfactants.(Karapetsas et al. 2016; Truskett & Stebe 2003) The diffusion within a particle could be
modified using additional bulky polymer components. In addition, it is possible that the extent of
coupling between heat and mass transport in an evaporating droplet could possibly be adjusted by
modifying the thermal diffusivity in the gas flow of the EDB. For example, a neon gas flow instead of
nitrogen would be much more thermally conducting, and thus heat flux between the droplet and the
surrounding air would be larger, enabling a greater mass flux in the presence of neon gas than
nitrogen. The effects of these changes in conditions can be addressed in simple solutions, such as
aqueous inorganic salts, followed by mixtures of solutes and co-solvents, and we could investigate
more complex formulations such as emulsions or solutions containing nanoparticles.
Conclusions In summary, the process of spray-drying aerosol droplets to produce powders is a widely used
commercial technique, however there are still many aspects of the kinetics of droplet evaporation
that are poorly understood. The current literature presents a vast array of studies on products
formed under different conditions, however in many cases it could be considered an art rather than
science. Rather than a bottom-up approach of predicting how a particle may form and using it to
engineer products, most research characterises why certain morphologies were produced under
different conditions. If the particle drying process can be predicted and controlled, a huge area of
particle engineering applications could be opened up across the food, pharmaceutical and cosmetic
industries.
References Amstad, E., Spaepen, F. & Weitz, D.A., 2016. Stabilization of the Amorphous Structure of Spray-Dried Drug Nanoparticles.
The Journal of Physical Chemistry B, p.acs.jpcb.6b05417. Available at: http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.6b05417.
Baldelli, A. et al., 2015. Analysis of the Particle Formation Process of Structured Microparticles. Molecular Pharmaceutics, 12(8), pp.2562–2573.
Baldelli, A. et al., 2016. Effect of crystallization kinetics on the properties of spray dried microparticles. Aerosol Science and Technology, 50(7), pp.693–704. Available at: http://www.tandfonline.com/doi/abs/10.1080/02786826.2016.1177163.
Baldelli, A. & Vehring, R., 2016. Control of the Radial Distribution of Chemical Components in Spray Dried Crystalline Microparticles. Aerosol Science and Technology, 6826(August).
Biance, A.L., Clanet, C. & Quéré, D., 2003. Leidenfrost drops. Physics of Fluids, 15(6), pp.1632–1637.
Bzdek, B.R. et al., 2016. Dynamic measurements and simulations of airborne picolitre-droplet coalescence in holographic optical tweezers. Journal of Chemical Physics, 145(5).
Carruthers, a E., Reid, J.P. & Orr-Ewing, a J., 2010. Longitudinal optical trapping and sizing of aerosol droplets. Optics express, 18(13), pp.14238–14244.
Chen, G. et al., 1991. Frequency splitting of degenerate spherical cavity modes: stimulated Raman scattering spectrum of deformed droplets. Optics letters, 16(16), pp.1269–71. Available at: http://www.ncbi.nlm.nih.gov/pubmed/19776941.
Chenyakin, Y. et al., 2016. Diffusion coefficients of organic molecules in sucrose-water solutions and comparison with Stokes-Einstein predictions. Atmospheric Chemistry and Physics Discussions, 38(August), pp.1–29. Available at: http://www.atmos-chem-phys-discuss.net/acp-2016-740/.
Dellamary, L.A. et al., 2000. Hollow porous particles in metered dose inhalers. Pharmaceutical Research, 17(2), pp.168–174.
Edwards, D.A. et al., 1997. Large Porous Particles for Pulmonary Drug Delivery. Science, 276(5320), pp.1868–1871. Available at: http://www.sciencemag.org/cgi/doi/10.1126/science.276.5320.1868\n<Go to ISI>://A1997XF10300051.
10
Fu, N., Woo, M.W. & Chen, X.D., 2012. Single Droplet Drying Technique to Study Drying Kinetics Measurement and Particle Functionality: A Review. Drying Technology, 30(15), pp.1771–1785. Available at: http://www.tandfonline.com/doi/abs/10.1080/07373937.2012.708002.
Handscomb, C.S., Kraft, M. & Bayly, A.E., 2009. A new model for the drying of droplets containing suspended solids. Chemical Engineering Science, 64(4), pp.628–637.
Hoe, S. et al., 2014. Use of a fundamental approach to spray-drying formulation design to facilitate the development of multi-component dry powder aerosols for respiratory drug delivery. Pharmaceutical research, 31(2), pp.449–465.
Iskandar, F., Gradon, L. & Okuyama, K., 2003. Control of the morphology of nanostructured particles prepared by the spray drying of a nanoparticle sol. Journal of Colloid and Interface Science, 265(2), pp.296–303.
Karapetsas, G., Chandra Sahu, K. & Matar, O.K., 2016. Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants. Langmuir, 32(27), pp.6871–6881.
Knezic, D., Zaccaro, J. & Myerson, A.S., 2004. Nucleation induction time in levitated droplets. Journal of Physical Chemistry B, 108(30), pp.10672–10677.
Kulmala, M., Vesala, T. & Wagner, P.E., 1992. An analytical expression for the rate of binary condensational particle growth: Comparison with numerical results. Journal of Aerosol Science, 23(SUPPL. 1), pp.133–136.
Lähde, A. et al., 2006. Aerosol Synthesis of Inhalation Particles via a Droplet-to-Particle Method. Particulate Science and Technology, 24(1), pp.71–84. Available at: http://www.tandfonline.com/doi/abs/10.1080/02726350500403199#.VMu9KmiHhUs.
Larson, R.G., 2014. Transport and deposition patterns in drying sessile droplets. AIChE Journal, 60(5), pp.1538–1571.
Lee, S. et al., 2016. Multiple pathways of crystal nucleation in an extremely supersaturated aqueous potassium dihydrogen phosphate (KDP) solution droplet. Proceedings of the National Academy of Sciences, 113(48), p.201604938.
Lintingre, É. et al., 2015. Controlling the buckling instability of drying droplets of suspensions through colloidal interactions. Soft Matter, 11(18), pp.3660–3665. Available at: http://xlink.rsc.org/?DOI=C5SM00283D.
Miles, R.E.H., Davies, J.F. & Reid, J.P., 2016. The influence of the surface composition of mixed monolayer films on the evaporation coefficient of water. Physical Chemistry Chemical Physics, 18(29), pp.19847–19858. Available at: http://dx.doi.org/10.1039/C6CP03826C.
Miller, R.S., Harstad, K. & Bellan, J., 1998. Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations. International Journal of Multiphase Flow, 24(6), pp.1025–1055.
Nandiyanto, A.B.D. & Okuyama, K., 2011. Progress in developing spray-drying methods for the production of controlled morphology particles: From the nanometer to submicrometer size ranges. Advanced Powder Technology, 22(1), pp.1–19. Available at: http://dx.doi.org/10.1016/j.apt.2010.09.011.
O’Meara, S., Topping, D.O. & McFiggans, G., 2016. The rate of equilibration of viscous aerosol particles. Atmospheric Chemistry and Physics, 16(8), pp.5299–5313.
Paul, W., 1990. Electromagnetic Traps for Charged and Neutral Particles (Nobel Lecture). Angewandte Chemie International Edition in English, 29(7), pp.739–748.
Pilcer, G. & Amighi, K., 2010. Formulation strategy and use of excipients in pulmonary drug delivery. International Journal of Pharmaceutics, 392(1–2), pp.1–19.
Power, R.M. & Reid, J.P., 2014. Probing the micro-rheological properties of aerosol particles using optical tweezers. Reports on progress in physics. Physical Society (Great Britain), 77(7), p.74601. Available at: http://www.ncbi.nlm.nih.gov/pubmed/24994710.
Renksizbulut, M. & Yuen, M.C., 1983. Experimental Study of Droplet Evaporation in a High-Temperature Air Stream. Journal of Heat Transfer, 105(2), pp.384–388. Available at: http://dx.doi.org/10.1115/1.3245590.
Rovelli, G. et al., 2016. Accurate Measurements of Aerosol Hygroscopic Growth over a Wide Range in Relative Humidity. Journal of Physical Chemistry A, 120(25), pp.4376–4388.
Sadek, C. et al., 2015. Drying of a single droplet to investigate process–structure–function relationships: a review. Dairy Science and Technology, 95(6), pp.771–794.
Song, Y.C. et al., 2016. Measurements and Predictions of Binary Component Aerosol Particle Viscosity. Journal of Physical Chemistry A, 120(41), pp.8123–8137.
11
Truskett, V.N. & Stebe, K.J., 2003. Influence of surfactants on an evaporating drop: Fluorescence images and particle deposition patterns. Langmuir, 19(20), pp.8271–8279.
Tsapis, N. et al., 2005. Onset of buckling in drying droplets of colloidal suspensions. Physical Review Letters, 94(1), pp.1–4.
Vanbever, R. et al., 1999. Formulation and physical characterization of large porous particles for inhalation. Pharmaceutical Research, 16(11), pp.1735–1742.
Vehring, R., 2008. Pharmaceutical particle engineering via spray drying. Pharmaceutical Research, 25(5), pp.999–1022.
Vladisavljević, G.T., 2015. Structured microparticles with tailored properties produced by membrane emulsification. Advances in Colloid and Interface Science, 225, pp.53–87.