Evaporation of a free microdroplet of a binary mixture of liquids with different volatilities.

We have investigated fine details of evaporation of free microdroplets of liquid binary mixtures comprising ethylene glycol (EG), diethylene glycol (DEG), triethylene glycol (TEG), glycerol and water. The microdroplets were kept and studied in an electrodynamic trap. Several phenomena associated with their evaporation are identified, discussed and modelled analytically. In particular, we've observed distillation at the microscale manifesting as a sigmoid transition of the evaporation rate (surface change rate). Sigmoid transition is known to be a characteristic feature for the evolution of the population (amount) with limited resources. We have shown that the transition itself can be comprehended using a stationary evaporation model under instantaneous mixing conditions. The condition is discussed and justified. The more general findings are primarily exemplified by a practical case of DEG contaminated with water by considering a humid and a dry ambient atmosphere. The influence of the composition of the droplet and the ambient atmosphere on the initial (pre-transition) stage of evaporation is considered in a general manner. Three types of conditions are discussed concerning the presence of an admixture in liquid and vapour phases (exemplified by the DEG/water system): (i) "dry" liquid - dry atmosphere, (ii) "wet" liquid - dry atmosphere, and (iii) "wet" liquid - wet atmosphere. Case (i) has been successfully verified against the theoretical prediction. Case (ii) has the requirement of considering non-stationary liquid-in-liquid diffusion. Case (iii) has led to a study of evaporation of a liquid mixture microdroplet with the more volatile component in equilibrium with its vapour.

Evaporation of liquid droplets of nano- and micro-meter size as a function of molecular mass and intermolecular interactions: experiments and molecular dynamics simulations.

Transport of heat to the surface of a liquid is a limiting step in the evaporation of liquids into an inert gas. Molecular dynamics (MD) simulations of a two component Lennard-Jones (LJ) fluid revealed two modes of energy transport from a vapour to an interface of an evaporating droplet of liquid. Heat is transported according to the equation of temperature diffusion, far from the droplet of radius R. The heat flux, in this region, is proportional to temperature gradient and heat conductivity in the vapour. However at some distance from the interface, Aλ, (where λ is the mean free path in the gas), the temperature has a discontinuity and heat is transported ballistically i.e. by direct individual collisions of gas molecules with the interface. This ballistic transport reduces the heat flux (and consequently the mass flux) by the factor R/(R + Aλ) in comparison to the flux obtained from temperature diffusion. Thus it slows down the evaporation of droplets of sizes R ∼ Aλ and smaller (practically for sizes from 103 nm down to 1 nm). We analyzed parameter A as a function of interactions between molecules and their masses. The rescaled parameter, A(kBTb/ε11)1/2, is a linear function of the ratio of the molecular mass of the liquid molecules to the molecular mass of the gas molecules, m1/m2 (for a series of chemically similar compounds). Here ε11 is the interaction parameter between molecules in the liquid (proportional to the enthalpy of evaporation) and Tb is the temperature of the gas in the bulk. We tested the predictions of MD simulations in experiments performed on droplets of ethylene glycol, diethylene glycol, triethylene glycol and tetraethylene glycol. They were suspended in an electrodynamic trap and evaporated into dry nitrogen gas. A changes from ∼1 (for ethylene glycol) to approximately 10 (for tetraethylene glycol) and has the same dependence on molecular parameters as obtained for the LJ fluid in MD simulations. The value of x = A(kBTb/ε11)1/2 is of the order of 1 (for water x = 1.8, glycerol x = 1, ethylene glycol x = 0.4, tetraethylene glycol x = 2.1 evaporating into dry nitrogen at room temperature and for Lennard-Jones fluids x = 2 for m1/m2 = 1 and low temperature).

A molecular dynamics test of the Hertz-Knudsen equation for evaporating liquids.

The precise determination of evaporation flux from liquid surfaces gives control over evaporation-driven self-assembly in soft matter systems. The Hertz-Knudsen (HK) equation is commonly used to predict evaporation flux. This equation states that the flux is proportional to the difference between the pressure in the system and the equilibrium pressure for liquid/vapor coexistence. We applied molecular dynamics (MD) simulations of one component Lennard-Jones (LJ) fluid to test the HK equation for a wide range of thermodynamic parameters covering more than one order of magnitude in the values of flux. The flux determined in the simulations was 3.6 times larger than that computed from the HK equation. However, the flux was constant over time while the pressures in the HK equation exhibited strong fluctuations during simulations. This observation suggests that the HK equation may not appropriately grasp the physical mechanism of evaporation. We discuss this issue in the context of momentum flux during evaporation and mechanical equilibrium in this process. Most probably the process of evaporation is driven by a tiny difference between the liquid pressure and the gas pressure. This difference is equal to the momentum flux i.e. momentum carried by the molecules leaving the surface of the liquid during evaporation. The average velocity in the evaporation flux is very small (two to three orders of magnitude smaller than the typical velocity of LJ atoms). Therefore the distribution of velocities of LJ atoms does not deviate from the Maxwell-Boltzmann distribution, even in the interfacial region.

Surface diagnostics of evaporating droplets of nanosphere suspension: Fano interference and surface pressure.

The evaporation of a single, levitating microdroplet of glycols containing SiO2 nanospheres, both of similar refraction indices, was studied by observing changes in the interference pattern and intensities of polarized and depolarized scattered laser light. The evolution of the effective radius of the droplet has been found on the basis of Mie scattering theory supplemented by the "electrical weighting" measurement of droplet mass evolution. During formation of a layer of nanospheres on the droplet surface, the asymmetric Fano profile was observed which was found to be due to the destructive and constructive interference of overlapping processes: (i) the scattering on single nanospheres emerging on the droplet surface and (ii) the scattering on ensembles of closely spaced (comparing to the light wavelength) nanospheres of an evolving surface film. Therefore we report the first observation of the Fano interference in the time domain rather than in the spectral domain. The optical surface diagnostics was complemented with the thermodynamics-like analysis in terms of the effective droplet surface pressure isotherm and with numerical simulations illustrating evaporation driven changes in the distribution of nanospheres. The reported study can serve as the basis for a wide range of novel diagnostic methods for studying configuration changes in complex systems of nano- and microparticles evolving at the sub-wavelength scale.

Chromatic dispersion and thermal coefficients of hygroscopic liquids: 5 glycols and glycerol.

Chromatic dispersion and thermal coefficients of 6 hygroscopic liquids: ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, propylene glycol (propane-1, 2-diol), and glycerol were measured in the range from 390 to 1070 nm for temperatures from 1 to 45 °C. A modified Abbe refractometer was utilised. Special care was taken to avoid contaminating the liquids under the test with water and solid particles. The measurement uncertainties were analysed. It was noticed that (in the given range and within the available measurement accuracy) the dependence of the refractive indices on the wavelength and temperature could be considered independently. Thus, thermal coefficients were found for each wavelength used, and their weak dependence on the wavelength was recognised. Then the Sellmeier equation was fitted to the experimental results for each temperature.

Local-field resonance in light scattering by a single water droplet with spherical dielectric inclusions.

Light scattering by an evaporating water droplet several micrometers in size with spherical dielectric inclusions was investigated. The evolution of the droplet radius and the effective refractive index was determined. A deviation from predictions by standard effective-medium theories in the form of a resonance was encountered. Simple analysis of the phenomenon was conducted, and a qualitative explanation was proposed.