The diffusion-controlled dissolution of spheres

Cable, M.; Frade, J.R.

doi:10.1007/bf01132424

Cited by 20 publications

(16 citation statements)

References 10 publications

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“…The radius-time relation is rather complex for a droplet of this kind when the moving nature of the droplet is fully taken into account. [35][36][37] Further, an encapsulating polymer-rich barrier is expected to develop at the droplet interface during solvent extraction, thereby inhibiting interfacial transport. We are therefore dealing with a highly complex transport problem.…”

Section: Resultsmentioning

confidence: 99%

Microfluidic Approach to the Formation of Internally Porous Polymer Particles by Solvent Extraction

et al. 2014

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We report the controlled formation of internally porous polyelectrolyte particles with diameters ranging from tens to hundreds of micrometers through selective solvent extraction using microfluidics. Solvent-resistant microdevices, fabricated by frontal photopolymerization, encapsulate binary polymer (P)/solvent (S1) mixtures by a carrier solvent phase (C) to form plugs with well-defined radii and low polydispersity; the suspension is then brought into contact with a selective extraction solvent (S2) that is miscible with C and S1 but not P, leading to the extraction of S1 from the droplets. The ensuing phase inversion yields polymer capsules with a smooth surface but highly porous internal structure. Depending on the liquid extraction time scale, this stage can be carried out in situ, within the chip, or ex situ, in an external S2 bath. Bimodal polymer plugs are achieved using asymmetrically inverted T junctions. For this demonstration, we form sodium poly(styrenesulfonate) (P) particles using water (S1), hexadecane (C), and methyl ethyl ketone (S2). We measure droplet extraction rates as a function of drop size and polymer concentration and propose a simple scaling model to guide particle formation. We find that the extraction time required to form particles from liquid droplets does not depend on the initial polymer concentration but is rather proportional to the initial droplet size. The resulting particle size follows a linear relationship with the initial droplet size for all polymer concentrations, allowing for the precise control of particle size. The internal particle porous structure exhibits a polymer density gradient ranging from a dense surface skin toward an essentially hollow core. Average particle porosities between 10 and 50% are achieved by varying the initial droplet compositions up to 15 wt % polymer. Such particles have potential applications in functional, optical, and coating materials.

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Section: Resultsmentioning

confidence: 99%

Microfluidic Approach to the Formation of Internally Porous Polymer Particles by Solvent Extraction

et al. 2014

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“…In contrast, for gas bubbles the liquid and gas phases are of two different chemical natures; the driving physical mechanisms are the dissolution of the gas into the liquid to maintain equilibrium at its surface as quantified by Henry's law [8], and the slow diffusion of the dissolved gas into the liquid phase. Note that this second case presents many formal similarities with the dissolution process of droplets [22], their evaporation [23] or even dissolving solids [24].…”

Section: Introductionmentioning

confidence: 87%

Collective dissolution of microbubbles

2018

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A microscopic bubble of soluble gas always dissolves in finite time in an under-saturated fluid. This diffusive process is driven by the difference between the gas concentration near the bubble, whose value is governed by the internal pressure through Henry's law, and the concentration in the far field. The presence of neighbouring bubbles can significantly slow down this process by increasing the effective background concentration and reducing the diffusing flux of dissolved gas experienced by each bubble. We develop theoretical modelling of such diffusive shielding process in the case of small microbubbles whose internal pressure is dominated by Laplace pressure. We first use an exact semi-analytical solution to capture the case of two bubbles and analyse in detail the shielding effect as a function of the distance between the bubbles and their size ratio. While we also solve exactly for the Stokes flow around the bubble, we show that hydrodynamic effects are mostly negligible except in the case of almost-touching bubbles. In order to tackle the case of multiple bubbles, we then derive and validate two analytical approximate yet generic frameworks, first using the method of reflections and then by proposing a self-consistent continuum description. Using both modelling frameworks, we examine the dissolution of regular one-, two-and three-dimensional bubble lattices. Bubbles located at the edge of the lattices dissolve first, while innermost bubbles benefit from the diffusive shielding effect, leading to the inward propagation of a dissolution front within the lattice. We show that diffusive shielding leads to severalfold increases in the dissolution time which grows logarithmically with the number of bubbles in one dimensional lattices and algebraically in two and three dimensions, scaling respectively as its square root and 2/3-power. We further illustrate the sensitivity of the dissolution patterns to initial fluctuations in bubble size or arrangement in the case of large and dense lattices, as well as non-intuitive oscillatory effects.

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“…Dissolution is of course an important process for a variety of other systems such as solid granules and polymeric particles, especially in the context of drug delivery [28][29][30][31] and even gas bubbles [32][33][34] . As such, a plethora of experimental methods and theoretical approaches have been used to understand and describe the process.…”

Section: Introductionmentioning

confidence: 99%

Dissolution of anionic surfactant mesophases

2017

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Linear and circular solvent penetration experiments are used to study the dissolution of anionic SLES surfactant mesophases in water. We show that a lamellar (L) phase in contact with water will transit through a series of cubic, hexagonal, and micellar phase bands with sharp interfaces identified from their optical textures. In both linear and circular geometries, the kinetics of front propagation and eventual dissolution are well described by diffusive penetration of water, and a simple model applies to both geometries, with a different effective diffusion coefficient for water D as the only fitting parameter. Finally, we show a surprising variation of dissolution rates with initial surfactant concentration that can be well explained by assuming that the driving force for solvent penetration is the osmotic pressure difference between neat water and the aqueous fraction of the mesophase that is highly concentrated in surfactant counterions.

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The diffusion-controlled dissolution of spheres

Cited by 20 publications

References 10 publications

Microfluidic Approach to the Formation of Internally Porous Polymer Particles by Solvent Extraction

Microfluidic Approach to the Formation of Internally Porous Polymer Particles by Solvent Extraction

Collective dissolution of microbubbles

Dissolution of anionic surfactant mesophases

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