Exact solution of the problem of gas segregation in the process of crystallization

Fedorchenko, Alexander I.; Chernov, A. A.

doi:10.1016/s0017-9310(02)00349-6

Cited by 32 publications

(39 citation statements)

References 5 publications

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“…δ Pe with our dimensionless variables, Eqs. (17). We therefore assume quasi-parallel flows and we use the standard lubrication approximation [27] to derive a 1D solute conservation equation from the above model.…”

Section: Advection-dispersion Equation In the Framework Of The Lubmentioning

confidence: 99%

“…along with a solute no-flux boundary condition at X = 0 as we consider non-volatile solutes. Fedorchenko and Chernov investigated theoretically this equation in the context of gas segregation induced by a moving solidification front [17] (see also Ref. [18] who used the same equation to describe stratification in drying films of colloidal dispersions).…”

Section: Introductionmentioning

confidence: 99%

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Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Salmon

Doumenc

2020

Phys. Rev. Fluids

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We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (nonvolatile solute + solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one dimensional non-linear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long time scales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

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Section: Advection-dispersion Equation In the Framework Of The Lubmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Salmon

Doumenc

2020

Phys. Rev. Fluids

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“…To circumvent these difficulties, the results given in [8,9] can be used. They show that solutions of the problems involving nucleation, diffusion and convection contain the complementary error function erfc(t).…”

Section: Theorymentioning

confidence: 99%

Visualization of the hot chocolate sound effect by spectrograms

Trávníček

Fedorchenko

Pavelka

et al. 2012

Journal of Sound and Vibration

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“…Understanding and controlling pore formation are important (Tane and Nakajima, 2006;Cox et al 2009). Since gas solubility in solid is usually much less than that in liquid, gas is accumulated ahead of the solidification front (Fedorchenko and Chernov, 2003). Super-saturation thus induces nucleation of bubbles on the solidification front (Wei et al 2003).…”

Section: Introductionmentioning

confidence: 99%

Pore Formation from Bubble Entrapment by a Solidification Front

Wei¹,

Hsiao²

2015

AJHMT

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Mechanism of the pore shape in solid resulted from a tiny bubble captured by a solidification front is theoretically and generally investigated. Pore formation and its shape in solid are one of the most critical factors affecting properties, microstructure, and stresses in materials, and biosciences, global warming, etc. This work is an extension of the previous original work (Wei and Hsiao, 2012) to reveal additional mechanisms. For simplicity without loss of generality, the tiny bubble beyond the solidification front is considered to have a spherical cap, whose contact angle is identical to inclination angle of the pore at the solidification front. The contact angle of the bubble cap is thus governed by the Abel's equation of the first kind in terms of displacement of the solidification front. The controlling parameter is the bubble growth ratesolidification rate ratio. It is found that inclination angle of the pore in the upper region depends on the bubble growth rate-to-solidification rate ratio. Isolated pore cannot occur, provided that contact angle of the bubble cap cannot reach 90 0 . The predicted pore shape and contact angle agree with predictions and observations. Manipulating either bubble growth rate or solidification rate can control pore formation in solid.

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Exact solution of the problem of gas segregation in the process of crystallization

Cited by 32 publications

References 5 publications

Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Visualization of the hot chocolate sound effect by spectrograms

Pore Formation from Bubble Entrapment by a Solidification Front

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