Evaporation of Micro-Droplets: the "Radius-Square-Law" Revisited

Jakubczyk, D.; Kolwas, M.; Derkachov, G.; Kolwas, K.; Zientara, M.

doi:10.12693/aphyspola.122.709

Cited by 35 publications

(35 citation statements)

References 37 publications

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“…Therefore in order to find both T b À T liq and A reliably, a droplet, which during evaporation reached a size below B2 mm, was selected. The presence of impurities influences the results very severely 1,12,13 and therefore we used pure liquids. The ballistic mode of evaporation is utterly negligible for droplets larger than B6 mm.…”

Section: Experimental Determination Of Parameter Amentioning

confidence: 99%

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

2017

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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 10 nm down to 1 nm). We analyzed parameter A as a function of interactions between molecules and their masses. The rescaled parameter, A(kT/ε), is a linear function of the ratio of the molecular mass of the liquid molecules to the molecular mass of the gas molecules, m/m (for a series of chemically similar compounds). Here ε is the interaction parameter between molecules in the liquid (proportional to the enthalpy of evaporation) and T 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(kT/ε) 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 m/m = 1 and low temperature).

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Section: Experimental Determination Of Parameter Amentioning

confidence: 99%

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

2017

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“…39,40 and mixtures of liquids, see e.g. 41,42 Therefore, in this section we briefly summarize our earlier research and provide the necessary background related to droplet evaporation, evaporation-driven aggregation of nanoparticles as well as formation and slow drying process of highly spherical aggregates.…”

Section: Dynamic Of Droplet Evaporation and Aggregation Of Colloidal mentioning

confidence: 99%

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

et al. 2015

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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.

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“…This relationship can be theoretically explained by the “Diameter‐Square‐Law” of droplet evaporation, which indicates that the square of droplet diameter tends to evolve linearly in time, t ≈ d 2 . To induce phase separation in the agent system of PEGDA 40 % (v/v), glycerol 20 % (v/v), and ethanol 40 % (v/v), the change of volume ratio of ethanol to the whole droplet should reach a critical value, where V is the initial volume,

Δ V = \frac{1}{6} π (D^{3} - d^{3})

, D is the initial diameter of the droplet, and d is the diameter when phase separation happens.…”

Section: Resultsmentioning

confidence: 99%

“…These results suggest that there exists ap owerr elationship between phase separation time T and droplet size D: T % D 2 [Eq. (1)]: This relationship can be theoretically explained by the "Diameter-Square-Law" of droplete vaporation, [23] which indicates that the square of dropletd iameter tends to evolve linearly in time, t % d 2 .T oi nduce phase separation in the agent system of PEGDA 40 %( v/v), glycerol 20 %( v/v), and ethanol 40 %( v/v), the change of volume ratio of ethanol to the whole droplets hould reachacritical value, where V is the initial volume,DV ¼ 1 6 pðD 3 À d 3 Þ, D is the initial diametero fthe droplet, and d is the diameter when phase separation happens. For a certain concentration combination,t he change of volume ratiõ C to induce phase separation should be constant, which means d % D. According to theD iameter-Square-Law,t he relationship between phase separation time T and the initial droplet size D is then acquired, T % D 2 ,w hich copes well with the experimental results.…”

Section: Size-dependent Phase Separationmentioning

confidence: 99%

Size‐Dependent Phase Separation in Emulsion Droplets

Chien

Liang

et al. 2018

ChemPhysChem

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Phase separation occurs in emulsion droplets containing poly (ethylene glycol) diacrylate (PEGDA), glycerol, and ethanol to form a glycerol-in-PEGDA structure, and the phase separation process is found to depend on the droplet size. The mechanism of this size-dependent phase separation is dependent on the droplet sizes changing the phase separation time by changing the evaporation speed of mutual solvent ethanol, and the relationship between the separation time T and the droplet diameter D is derived as T≈D , which has been validated by experiment results. According to this finding, the structures of the droplets can be designed by applying UV curing at different stages of the phase separation, and the monodispersity of droplets is necessary to achieve polymerized particles with the same structure.

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Evaporation of Micro-Droplets: the "Radius-Square-Law" Revisited

Cited by 35 publications

References 37 publications

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

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

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

Size‐Dependent Phase Separation in Emulsion Droplets

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