Microdroplet Dissolution into a Second-Phase Solvent Using a Micropipet Technique:  Test of the Epstein−Plesset Model for an Aniline−Water System

Duncan, P. Brent; Needham, David

doi:10.1021/la053314e

Cited by 77 publications

(138 citation statements)

References 28 publications

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“…The micropipette technique for liquid microdroplets has been explained in a previous paper by Duncan. 7 Briefly, micropipettes are formed from glass capillary tubes, which were then microforged to provide a flat tip of about 8 -10 m internal diameter. These pipettes were then treated with hexamethyldisilazane to make them hydrophobic.…”

Section: B Methodsmentioning

confidence: 99%

“…The micropipette technique has been used in previous work by Duncan and Needham,7 which has shown that the Epstein-Plesset model accurately predicts the radius versus time behavior of various two phase microsystems both for liquid-in-liquid 7 and gas bubble-in-liquid systems 8 from which mass is transferred purely through diffusion, and where the parameters of diffusion coefficients and solubility are known.…”

Section: ͑1͒mentioning

confidence: 99%

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The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

Duncan²,

Momaya³

et al. 2010

The Journal of Chemical Physics

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114

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While the Stokes-Einstein ͑SE͒ equation predicts that the diffusion coefficient of a solute will be inversely proportional to the viscosity of the solvent, this relation is commonly known to fail for solutes, which are the same size or smaller than the solvent. Multiple researchers have reported that for small solutes, the diffusion coefficient is inversely proportional to the viscosity to a fractional power, and that solutes actually diffuse faster than SE predicts. For other solvent systems, attractive solute-solvent interactions, such as hydrogen bonding, are known to retard the diffusion of a solute. Some researchers have interpreted the slower diffusion due to hydrogen bonding as resulting from the effective diffusion of a larger complex of a solute and solvent molecules. We have developed and used a novel micropipette technique, which can form and hold a single microdroplet of water while it dissolves in a diffusion controlled environment into the solvent. This method has been used to examine the diffusion of water in both n-alkanes and n-alcohols. It was found that the polar solute water, diffusing in a solvent with which it cannot hydrogen bond, closely resembles small nonpolar solutes such as xenon and krypton diffusing in n-alkanes, with diffusion coefficients ranging from 12.5ϫ 10 −5 cm 2 / s for water in n-pentane to 1.15ϫ 10 −5 cm 2 / s for water in hexadecane. Diffusion coefficients were found to be inversely proportional to viscosity to a fractional power, and diffusion coefficients were faster than SE predicts. For water diffusing in a solvent ͑n-alcohols͒ with which it can hydrogen bond, diffusion coefficient values ranged from 1.75ϫ 10 −5 cm 2 / s in n-methanol to 0.364ϫ 10 −5 cm 2 / s in n-octanol, and diffusion was slower than an alkane of corresponding viscosity. We find no evidence for solute-solvent complex diffusion. Rather, it is possible that the small solute water may be retarded by relatively longer residence times ͑compared to non-H-bonding solvents͒ as it moves through the liquid.

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Section: B Methodsmentioning

confidence: 99%

Section: ͑1͒mentioning

confidence: 99%

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

Duncan²,

Momaya³

et al. 2010

The Journal of Chemical Physics

Self Cite

114

View full text Add to dashboard Cite

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“…More recently their approach has been extended to the dissolution or growth of single-component drops in an immiscible liquid [6,7] and to the study of nanodrops and nanobubbles [8]. As long as surface tension and dynamical effects are negligible, whatever the bubble radius, the gas pressure in the bubble balances the constant ambient pressure and the dissolved gas concentration at the bubble surface remains constant, according to Henry's law.…”

Section: Introductionmentioning

confidence: 99%

History effects on the gas exchange between a bubble and a liquid

Chu

Prosperetti

2016

Phys. Rev. Fluids

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Diffusive processes exhibit a strong dependence on history effects. For a gas bubble at rest in a liquid, such effects arise when the concentration of dissolved gas at the bubble surface, dictated by Henry's law, depends on time. In this paper we consider several such situations. An oscillating ambient pressure field causes the occurrence of rectified diffusion of gas into or out of the bubble. Unlike previous investigators, who considered the opposite limit, we study this process for conditions when the diffusion length is larger than the bubble radius. It is found that history effects are important in determining the threshold conditions. Under a static ambient pressure, the time dependence of the gas concentration can arise due to the action of surface tension, which increases the gas pressure as the bubble dissolves or, when the bubble contains a mixture of two or more gases, due to the different rates at which they dissolve. In these latter cases history effects prove mostly negligible for bubbles larger than a few hundred nanometers.

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“…If one assumes a binary, ideal mixture, the net mass flux can be calculated by Fick's law, j 1 ¼ ÀD 0 r 1 , where D 0 is the experimentally determined diffusion coefficient. Based on this model, the seminal work by Epstein and Plesset [1], which describes successfully the t 1=2 shrinkage dynamics of a spherical air bubble in an air-water solution, has been recently extended and the t 1=2 scaling experimentally validated also for a liquid droplet (aniline or water) dissolving in a liquidliquid (water-aniline or aniline-water) solution [2].Fickian diffusion, however, is strictly limited to ideal mixtures and cannot hold for multiphase systems, even at thermodynamic equilibrium. A more general formulation for the mass flux can be found by means of nonequilibrium…”

mentioning

confidence: 99%

Dissolution of a Liquid Microdroplet in a Nonideal Liquid-Liquid Mixture Far from Thermodynamic Equilibrium

2009

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A droplet placed in a liquid-liquid solution is expected to grow, or shrink, in time as $t 1=2 . In this Letter, we report experimental evidence that when the composition in the interface is far from thermodynamic equilibrium due to the nonideality of the mixture, a droplet shrinks as $t. This scaling is due to the coupling between mass and momentum transfer known as Korteweg forces as a result of which the droplet self-propels around. The consequent hydrodynamic convection greatly enhances the mass transfer between the droplet and the bulk phase. Thus, the combined effect of nonideality and nonequilibrium modifies the dynamical behavior of the dissolving droplet. DOI: 10.1103/PhysRevLett.103.064501 PACS numbers: 47.51.+a, 64.75.Bc, 68.05.Àn The formation and dissolution of gas bubbles and liquid droplets in liquid-gas and liquid-liquid systems are major concerns in many industrial processes as they occur in mixing and separation, in dispersion of food products, and in pharmaceutically controlled drug delivery, for instance. When a gas bubble or a liquid droplet is placed in a gas-liquid or liquid-liquid mixture, it is expected to grow (or to shrink) by diffusion; this process is described by the well-known diffusion equation, as @ 1 =@t ¼ Àr Á j 1 in terms of the local concentration 1 ðr; tÞ and mass flux j 1 of component A in the mixture. If one assumes a binary, ideal mixture, the net mass flux can be calculated by Fick's law, j 1 ¼ ÀD 0 r 1 , where D 0 is the experimentally determined diffusion coefficient. Based on this model, the seminal work by Epstein and Plesset [1], which describes successfully the t 1=2 shrinkage dynamics of a spherical air bubble in an air-water solution, has been recently extended and the t 1=2 scaling experimentally validated also for a liquid droplet (aniline or water) dissolving in a liquidliquid (water-aniline or aniline-water) solution [2].Fickian diffusion, however, is strictly limited to ideal mixtures and cannot hold for multiphase systems, even at thermodynamic equilibrium. A more general formulation for the mass flux can be found by means of nonequilibrium2 are the chemical potentials of the two components, and 1 , 2 , are the mobility (or Onsager) coefficients. While the diffusivity D 0 can be a constant for a binary system, the mobility coefficients are composition dependent [4]. For an ideal mixture or in the dilute limit, this formulation reduces to Fick's law. Following Cahn and Hillard [5], for a heterogeneous system, the local molar Gibbs free-energy g can be written as the sum of a local and a nonlocal contribution: g ¼ g loc þ 1 2 a 2 RTðr Þ 2 , where a is the characteristic length scale of inhomogeneity [6] (different formulations for the free energy have also been developed [9]). Using a mobility coefficient of the form ¼ ð1 À ÞD 0 and assuming the Flory-Huggins local free energy, Mauri et al. [7] proposed the net mass flux j ¼ À ð1 À ÞD 0 r~, with~¼ 0 þ log 1À þ Éð1 À 2 Þ À a 2 r 2 where É is the Margules parameter. As a result, we can write j ¼ ÀD 0 r þ ð1...

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Microdroplet Dissolution into a Second-Phase Solvent Using a Micropipet Technique: Test of the Epstein−Plesset Model for an Aniline−Water System

Cited by 77 publications

References 28 publications

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

The effect of hydrogen bonding on the diffusion of water in n-alkanes and n-alcohols measured with a novel single microdroplet method

History effects on the gas exchange between a bubble and a liquid

Dissolution of a Liquid Microdroplet in a Nonideal Liquid-Liquid Mixture Far from Thermodynamic Equilibrium

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