Evaporation of freely suspended single droplets: experimental, theoretical and computational simulations

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.

Plasma extracellular vesicle test sample to standardize flow cytometry measurements

Background

Extracellular vesicles (EVs) in body fluids are explored as disease biomarkers, but EV concentrations measured by flow cytometers (FCMs) are incomparable.

Objectives

To improve data comparability, new reference materials with physical properties resembling EVs and reference procedures are being developed. The validation of new reference materials and procedures requires biological test samples. We developed a human plasma EV test sample (PEVTES) that i) resembles subcellular particles in plasma, ii) is ready-to-use, iii) is flow cytometry-compatible, and iv) is stable.

Methods

The PEVTES was prepared from human plasma of 3 fasting donors. EVs were immunofluorescently stained with antibodies against platelet-specific (CD61) and erythrocyte-specific (CD235a) antigens or lactadherin. To reduce the concentration of soluble proteins, lipoproteins, and unbound reagents, stained EVs were isolated from plasma by size-exclusion chromatography. After isolation, the PEVTES was filtered to remove remnant platelets. PEVTESs were diluted in cryopreservation agents, dimethyl sulfoxide, glycerol, or trehalose and stored at -80 °C for 12 months. After thawing, stained EV concentrations were measured with a calibrated FCM (Apogee A60-Micro).

Results

We demonstrate that the developed PEVTES resembles subcellular particles in human plasma when measured using FCM and that the concentrations of prestained platelet-derived, erythrocyte-derived, and lactadherin+ EVs in the PEVTES are stable during storage at -80 °C for 12 months when stored in trehalose.

Conclusion

The PEVTES i) resembles subcellular particles in plasma, ii) is ready-to-use, iii) is flow cytometry-compatible, and iv) is stable. Therefore, the developed PEVTES is an ideal candidate to validate newly developed reference materials and procedures.

Deviations from classical droplet evaporation theory

In this article, we show that significant deviations from the classical quasi-steady models of droplet evaporation can arise solely due to transient effects in the gas phase. The problem of fully transient evaporation of a single droplet in an infinite atmosphere is solved in a generalized, dimensionless framework with explicitly stated assumptions. The differences between the classical quasi-steady and fully transient models are quantified for a wide range of the 10-dimensional input domain and a robust predictive tool to rapidly quantify this difference is reported. In extreme cases, the classical quasi-steady model can overpredict the droplet lifetime by 80%. This overprediction increases when the energy required to bring the droplet into equilibrium with its environment becomes small compared with the energy required to cool the space around the droplet and therefore establish the quasi-steady temperature field. In the general case, it is shown that two transient regimes emerge when a droplet is suddenly immersed into an atmosphere. Initially, the droplet vaporizes faster than classical models predict since the surrounding gas takes time to cool and to saturate with vapour. Towards the end of its life, the droplet vaporizes slower than expected since the region of cold vapour established in the early stages of evaporation remains and insulates the droplet.

Off-Lattice Monte-Carlo Approach for Studying Nucleation and Evaporation Phenomena at the Molecular Scale

Droplet nucleation and evaporation are ubiquitous in nature and many technological applications, such as phase-change cooling and boiling heat transfer. So far, the description of these phenomena at the molecular scale has posed challenges for modelling with most of the models being implemented on a lattice. Here, we propose an off-lattice Monte-Carlo approach combined with a grid that can be used for the investigation of droplet formation and evaporation. We provide the details of the model, its implementation as Python code, and results illustrating its dependence on various parameters. The method can be easily extended for any force-field (e.g., coarse-grained, all-atom models, and external fields, such as gravity and electric field). Thus, we anticipate that the proposed model will offer opportunities for a wide range of studies in various research areas involving droplet formation and evaporation and will also form the basis for further method developments for the molecular modelling of such phenomena.

A dynamical overview of droplets in the transmission of respiratory infectious diseases

The outbreak of the coronavirus disease has drawn public attention to the transmission of infectious pathogens, and as major carriers of those pathogens, respiratory droplets play an important role in the process of transmission. This Review describes respiratory droplets from a physical and mechanical perspective, especially their correlation with the transmission of infectious pathogens. It covers the important aspects of (i) the generation and expulsion of droplets during respiratory activities, (ii) the transport and evolution of respiratory droplets in the ambient environment, and (iii) the inhalation and deposition of droplets in the human respiratory tract. State-of-the-art experimental, computational, and theoretical models and results are presented, and the corresponding knowledge gaps are identified. This Review stresses the multidisciplinary nature of its subject and appeals for collaboration among different fields to fight the present pandemic.

Testing a Paul trap through determining the evaporation rate of levitated single semi-volatile organic droplets

Rigorous knowledge of the optical fingerprint of droplets is imperative for the understanding of complex aerosol processes. Here, a Paul trap is operated to store single semi-volatile organic droplets in air. The droplets are illuminated with a green laser and the elastic scattering is collected on a CMOS camera. The setup provides excellent performance in terms of confinement and stability, allowing us to detect size changes of the order of few nanometres. The stability also allows us to measure vapour pressures with remarkable reproducibility. This approach supplies a robust method for the optical interrogation in the sub-micron range.

Initiation of condensation of toluene and octane vapours on a Si surface

The adsorption of toluene and octane vapours on a homogenous silicon surface was measured under steady, thermal disequilibrium conditions where a vapour at a temperature T ^V is exposed to a solid surface at a lower temperature, T ^S. Zeta adsorption isotherm theory was used along with Gibbsian thermodynamics to examine the adsorption results analytically and to investigate the wetting conditions for these vapours. Further, from the prediction of the cluster distribution in the adsorbate, the conditions for the initiation of a liquid phase are predicted. Finally, the mechanism that determines the condensation mode of hydrocarbons on a silicon surface is investigated.

Lifetime of a Nanodroplet: Kinetic Effects and Regime Transitions

A transition from a d^{2} to a d law is observed in molecular dynamics (MD) simulations when the diameter (d) of an evaporating droplet reduces to the order of the vapor's mean free path; this cannot be explained by classical theory. This Letter shows that the d law can be predicted within the Navier-Stokes-Fourier (NSF) paradigm if a temperature-jump boundary condition derived from kinetic theory is utilized. The results from this model agree with those from MD in terms of the total lifetime, droplet radius, and temperature, while the classical d^{2} law underpredicts the lifetime of the droplet by a factor of 2. Theories beyond NSF are also employed in order to investigate vapor rarefaction effects within the Knudsen layer adjacent to the interface.

Nanometre-sized droplets from a gas dynamic virtual nozzle

This paper reports on improved techniques to create and characterize nanometre-sized droplets from dilute aqueous solutions by using a gas dynamic virtual nozzle (GDVN). It describes a method to measure the size distribution of uncharged droplets, using an environmental scanning electron microscope, and provides theoretical models for the droplet sizes created. The results show that droplet sizes can be tuned by adjusting the gas and liquid flow rates in the GDVN, and at the lowest liquid flow rates, the size of the water droplets peaks at about 120 nm. This droplet size is similar to droplet sizes produced by electrospray ionization but requires neither electrolytes nor charging of the solution. The results presented here identify a new operational regime for GDVNs and show that predictable droplet sizes, comparable to those obtained by electrospray ionization, can be produced by purely mechanical means in GDVNs.

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.

Evaporative characteristics of sessile nanofluid droplet on micro-structured heated surface

Micro-structure patterned substrates attract our attention due to the special and programmable wettabilities. The interaction between the liquid and micro/nano structures gives rise to controllable spreading and thus evaporation. For exploration of the application versatility, the introduction of nanoparticles in liquid droplet results in interaction among particles, liquid and microstructures. In addition, temperature of the substrates strongly affects the spreading of the contact line and the evaporative property. The evaporation of sessile droplets of nanofluids on a micro-grooved solid surface is investigated in terms of liquid and surface properties. The patterned nickel surface used in the experiments is designed and fabricated with circular and rectangular shaped pillars whose size ratios between interval and pillars is fixed at 5. The behavior is firstly compared between nanofluid and pure liquid on substrates at room temperature. For pure water droplet, the drying time is relatively longer due to the receding of contact line which slows down the liquid evaporation. Higher concentrations of nanoparticles tend to increase the total evaporation time. With varying concentrations of graphite at nano scale from 0.02% to 0.18% with an interval at 0.04% in water droplets and the heating temperature from 22 to 85°C, the wetting and evaporation of the sessile droplets are systematically studied with discussion on the impact parameters and the resulted liquid dynamics as well as the stain. The interaction among the phases together with the heating strongly affects the internal circulation inside the droplet, the evaporative rate and the pattern of particles deposition.

Dynamic sessile micro-droplet evaporation monitored by electric impedance sensing

Studies of liquid evaporation on a solid surface are useful for wettability phenomena-related research, and can be applied in a series of scientific and industrial areas. However, traditional methods are not easy to be intergrated into small size to monitor evaporation process of a micro-droplet. In this paper, a micro-electrode array was used to measure the impedance of an electrolyte droplet, indicating the dynamic process of evaporation. This method uses the relationship between concentration and conductivity of the water solution to dynamically monitor the evaporation process. The dynamic impedance results were compared to weight and imaging data of droplet evaporation and demonstrate high correlation coefficient of the earlier 90% part of the sodium chloride droplet evaporation process (R ² = 0.99). Our study proved that the height of the droplet will affect the impedance sensing result, and the solution used for droplet evaporation can be expanded to mixture of strong electrolyte solution such as phosphate buffered solution. Then the "impedance imaging" of the array monitored the evaporating speed differences of different sites of a sessile droplet. As the electrode array can be integrated into small size, this method is compatible for many other experimental systems and can be further used for evaporation studies and corresponding application areas.

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(k_BT_b/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 T_b 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(k_BT_b/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).

From adsorption to condensation: the role of adsorbed molecular clusters

Phase transition from an adsorbed vapour to an adsorbed liquid at a subcooling temperature of 2.7 ± 0.4 K.

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.

Formation of Highly Ordered Spherical Aggregates from Drying Microdroplets of Colloidal Suspension

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.

Multirelaxation-time lattice Boltzmann model for droplet heating and evaporation under forced convection

We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D(2) law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail.

Bubble evolution and properties in homogeneous nucleation simulations

We analyze the properties of naturally formed nanobubbles in Lennard-Jones molecular dynamics simulations of liquid-to-vapor nucleation in the boiling and the cavitation regimes. The large computational volumes provide a realistic environment at unchanging average temperature and liquid pressure, which allows us to accurately measure properties of bubbles from their inception as stable, critically sized bubbles, to their continued growth into the constant speed regime. Bubble gas densities are up to 50% lower than the equilibrium vapor densities at the liquid temperature, yet quite close to the gas equilibrium density at the lower gas temperatures measured in the simulations: The latent heat of transformation results in bubble gas temperatures up to 25% below those of the surrounding bulk liquid. In the case of rapid bubble growth-typical for the cavitation regime-compression of the liquid outside the bubble leads to local temperature increases of up to 5%, likely significant enough to alter the surface tension as well as the local viscosity. The liquid-vapor bubble interface is thinner than expected from planar coexistence simulations by up to 50%. Bubbles near the critical size are extremely nonspherical, yet they quickly become spherical as they grow. The Rayleigh-Plesset description of bubble-growth gives good agreement in the cavitation regime.

Lattice-Boltzmann simulations of droplet evaporation

We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes.

Patterned deposition at moving contact lines

When a simple or complex liquid recedes from a smooth solid substrate it often leaves a homogeneous or structured deposit behind. In the case of a receding non-volatile pure liquid the deposit might be a liquid film or an arrangement of droplets depending on the receding speed of the meniscus and the wetting properties of the system. For complex liquids with volatile components as, e.g., polymer solutions and particle or surfactant suspensions, the deposit might be a homogeneous or structured layer of solute--with structures ranging from line patterns that can be orthogonal or parallel to the receding contact line via hexagonal or square arrangements of drops to complicated hierarchical structures. We review a number of recent experiments and modelling approaches with a particular focus on mesoscopic hydrodynamic long-wave models. The conclusion highlights open question and speculates about future developments.

Metastability Limit for the Nucleation of NaCl Crystals in Confinement

We study the spontaneous nucleation and growth of sodium chloride crystals induced by controlled evaporation in confined geometries (microcapillaries) spanning several orders of magnitude in volume. In all experiments, the nucleation happens reproducibly at a very high supersaturation S ∼ 1.6 and is independent of the size, shape, and surface properties of the microcapillary. We show from classical nucleation theory that this is expected: S ∼ 1.6 corresponds to the point where nucleation first becomes observable on experimental time scales. A consequence of the high supersaturations reached at the onset of nucleation is the very rapid growth of a single skeletal (Hopper) crystal. Experiments on porous media also reveal the formation of Hopper crystals in the entrapped liquid pockets in the porous network and consequently underline the fact that sodium chloride can easily reach high supersaturations, in spite of what is commonly assumed for this salt.

Nonequilibrium kinetic boundary condition at the vapor-liquid interface of argon

A boundary condition for the Boltzmann equation (kinetic boundary condition, KBC) at the vapor-liquid interface of argon is constructed with the help of molecular dynamics (MD) simulations. The KBC is examined at a constant liquid temperature of 85 K in a wide range of nonequilibrium states of vapor. The present investigation is an extension of a previous one by Ishiyama, Yano, and Fujikawa [Phys. Rev. Lett. 95, 084504 (2005)] and provides a more complete form of the KBC. The present KBC includes a thermal accommodation coefficient in addition to evaporation and condensation coefficients, and these coefficients are determined in MD simulations uniquely. The thermal accommodation coefficient shows an anisotropic behavior at the interface for molecular velocities normal versus tangential to the interface. It is also found that the evaporation and condensation coefficients are almost constant in a fairly wide range of nonequilibrium states. The thermal accommodation coefficient of the normal velocity component is almost unity, while that of the tangential component shows a decreasing function of the density of vapor incident on the interface, indicating that the tangential velocity distribution of molecules leaving the interface into the vapor phase may deviate from the tangential parts of the Maxwell velocity distribution at the liquid temperature. A mechanism for the deviation of the KBC from the isotropic Maxwell KBC at the liquid temperature is discussed in terms of anisotropic energy relaxation at the interface. The liquid-temperature dependence of the present KBC is also discussed.