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We use molecular dynamics (MD) simulations of a two-component Lennard-Jones (LJ) fluid to analyze the energy flux from an inert gas to the interface of an evaporating liquid droplet. Using this analysis we derive an analytical equation for the radius of the droplet, R(t), as a function of time, t. The formula is valid for evaporation of droplets of any material or size into the gas characterized by the mean free path, l, much larger than the molecular diameter, s. We find linear dependence R(t) $ t, for high l/R(t) ratios and standard law R 2 (t) $ t for small l/R(t) ratios. We apply equation for R(t) to experimental results of evaporation of water micro-droplets into air and glycerol, diethylene glycol and triethylene glycol microdroplets into the nitrogen gas evaporating in time from seconds to tens of minutes. The experimental results together with computer simulations span 12 orders of magnitude of evaporation times and more than 3 orders of magnitude of droplets' radii. In the experiments the evaporation rate is governed by a very small difference in temperatures (from one tenth of mK to a few K) between the gas far from the droplet and evaporating liquid. From MD simulations we also obtain suitable boundary conditions for the energy flux at the interface, used in irreversible thermodynamics, and the accommodation coefficients used in kinetic models of evaporation.

International audienceThis paper outline and discuss basic considerations for the optical characterization of nanoparticles and their aggregates: particle models, light scattering theories and main experimental setups, regarding their interest for the study of plasma flows. It emphasizes that there are now powerful alternatives to the Lorenz-Mie theory and its simple homogeneous sphere model, which allow accurate calculations of the optical properties of particles with complex sub-structures and shapes. (c) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinhei

In this article, a detailed introduction of the light extinction spectrometry (LES) diagnostics is given. LES allows the direct in situ measurement of the particle size distribution and absolute concentration of dust clouds levitating in plasmas. Using a relatively simple and compact experimental set-up, the dust cloud parameters can be recovered with a good accuracy making minimum assumptions on their physical properties. Special emphases are given to the inversion procedure of light extinction spectra and all the required particle shape, refractive index and light extinction models. The parameter range and the limitations of LES are discussed. Two measurements in low-pressure gas discharges are presented: (i) in a direct-current (DC) glow discharge in which nanoparticles are growing from the sputtering of a tungsten cathode and (ii) in an argon–silane radio-frequency discharge. They demonstrate the capabilities of the LES technique to characterise, in situ and in real-time, the growth dynamics of nanoparticles in the size range 5–100 nm and volume concentrations in the range from a few ppb to a few ppm.

The formation of highly ordered spherical aggregates of silica nanoparticles by the evaporation of single droplets of an aqueous colloidal suspension levitated (confined) in the electrodynamic quadrupole trap is reported. The transient and final structures formed during droplet evaporation have been deposited on a silicon substrate and then studied with SEM. Various successive stages of the evaporation-driven aggregation of nanoparticles have been identified: formation of the surface layer of nanoparticles, formation of the highly ordered spherical structure, collapse of the spherical surface layer leading to the formation of densely packed spherical aggregates, and rearrangement of the aggregate into the final structure of a stable 3D quasi-crystal. The evaporation-driven aggregation of submicrometer particles in spherical symmetry leads to sizes and morphologies of the transient and final structures significantly different than in the case of aggregation on a substrate. The numerical model presented in the article allows us to predict and visualize the observed aggregation stages and their dynamics and the final aggregates observed with SEM.

We introduce numerical methods and algorithms to estimate the main parameters of fractal-like particle aggregates from their optical structure factor (i.e. light scattering diagrams). The first algorithm is based on a direct and simple method, but its applicability is limited to aggregates with large size parameter and intermediate fractal dimension. The second algorithm requires to build calibration curves based on accurate particle agglomeration and particle light scattering models. It allows analyzing the optical structure factor of much smaller aggregates, regardless of their fractal dimension and the size of the single particles. Therefore, this algorithm as well as the introduction of a criterial curve to detect the different scattering regimes, are thought to be powerful tools to perform reliable and reproducible analysis.

Models describing evaporation or condensation of a droplet have existed for over a century, and the temporal evolutions of droplet radius and temperature could be predicted. However, the accuracy of results was questionable, since the models contain free parameters and the means of accurate calibration were not available. In previous work (Hołyst et al. Soft Matter 2013, 9, 7766), a model with an efficacious parametrization in terms of the mean free path was proposed and calibrated with molecular dynamics numerical experiment. It was shown that it is essentially possible to determine reliably the temperature of a steadily evaporating/condensing homogeneous droplet relative to ambient temperature when the evolution of the droplet radius is known. The accuracy of such measurement can reach fractions of mK. In the case of an evaporating droplet of pure liquid, the (droplet) temperature is constant during the stationary stage of evaporation. In this paper, we show that, in many cases, it is also possible to determine the temporal evolution of droplet temperature from the evolution of the droplet radius if the droplet (initial) composition is known. We found the droplet radius evolution with high accuracy and obtained the evolution of droplet temperature (and composition) for droplets of (i) a two-component mixture of pure liquids; (ii) solutions of solid in liquid, one that is non-surface-active and another that is; and (iii) suspensions of non-light-absorbing and light-absorbing particles.