Onset of solutal convection in liquid phase epitaxy system

Kim, Min Chan; Lee, Sang Goo

doi:10.1007/s11814-009-0004-2

Cited by 4 publications

(6 citation statements)

References 13 publications

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“…Some theoretical works addressed the question of the prefactors. For example, a semi analytical work based on the propagation theory [36,37,46], where a part of the dynamic of the base state is taken into account predicts…”

Section: Onset Of the Convection Instabilitymentioning

confidence: 99%

Solutal convection induced by dissolution

et al. 2019

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The dissolution of minerals into water becomes significant in geomorphology, when the erosion rate is controlled by the hydrodynamics transport of the solute. Even in absence of an external flow, dissolution itself can induce a convection flow due to the action of gravity. Here we perform a study of the physics of solutal convection induced by dissolution. We simulate numerically the hydrodynamics and the solute transport, in a 2D geometry, corresponding to the case, where a soluble body is suddenly immersed in a quiescent solvent. We identify three regimes. At short timescale, a concentrated boundary layer grows by diffusion at the interface. After a finite onset time, the thickness and the density reach critical values which starts the destabilization of the boundary layer. Finally, the destabilization is such as we observe the emission of intermittent plumes. This last regime is quasi-stationnary: the structure of the boundary layer as well as the erosion rate fluctuate around constant values. Assuming that the destabilization of the boundary layer occurs at a specific value of the solutal Rayleigh number, we derive scaling laws both for fast and slow dissolution kinetics. Our simulations confirm this scenario by validating the scaling laws both for onset, and the quasi-stationary regime. We find a constant value of the Rayleigh number during the quasi-stationary regime showing that the structure of the boundary layer is well controlled by the solutal convection. Finally, we apply the scaling laws previously established to the case of real dissolving minerals. We predicts the typical dissolution rate in presence of solutal convection. Our results suggest that solutal convection could occur in more natural situations than expected. Even for minerals with a quite low saturation concentration, the erosion rate would increase as the dissolution would be controlled by the hydrodynamics.

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Section: Onset Of the Convection Instabilitymentioning

confidence: 99%

Solutal convection induced by dissolution

et al. 2019

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“…The phase change rate λ can be determined by using Eqs. (11.c) (13) and (14) as: (15) and summarized as a function of St for some specific case in Fig. 3.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Note that θ 1 has the scale of α L ν/(gβd 3 ) and w 1 has the scale of α L / d. In the solid layer the dimensionless disturbance equations are obtained as (15) The boundary conditions for these disturbances equations are given by at z=0.…”

Section: Governing Equationsmentioning

confidence: 99%

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Onset of buoyancy-driven instability in a pure melt solidified from above

Hwang

Kim

2011

Korean J. Chem. Eng.

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When a pure liquid is solidified from above, convection may be induced in a thermally-unstable layer. The onset of buoyancy-driven convection during time-dependent solidification is investigated by using similarly transformed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by WKB method, and the effects of various parameters on the stability condition of melt phase are analyzed theoretically. The present constant temperature cooling model gives more unstable results than the constant solidification velocity model of Smith [1].

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“…Several approaches have been proposed for time dependent convection in various configurations (thermal or solutal convection, Navier-Stokes equations, or Darcy flow): the frozen base state assumption, [21][22][23][24] the amplification theory, [25][26][27] the propagation theory, [28][29][30] the energy stability analysis, 31 and the non-normal linear stability analysis. [32][33][34] Whereas these methods provide some insights on the physical mechanisms, they rely on strong hypotheses and on arbitrary criteria defining the onset.…”

Section: Introductionmentioning

confidence: 99%

Solutal convection instability caused by dissolution

et al. 2021

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When a soluble solid body is suddenly put in contact with water, a convection flow can be generated. Once the fluid layer charged into solute is sufficiently dense, this layer becomes unstable under the action of the buoyancy forces. We perform here a linear stability analysis in order to predict the time of appearance of the convection flow, the onset time, and the associated wavelength. As the base state evolves with time due to the solute diffusion, the usual theoretical methods cannot be used. We show that the criterion of marginal instability with a "frozen base state" used for convection in porous media fails for providing the onset parameters in fluid convection. Here, using a modified criterion, i.e., the instability growth rate must be larger than the time evolution of the base state, we find the onset parameters in satisfying agreement with the previous experimental and numerical works. Our results complete our previous numerical work [J. Philippi et al., "Solutal convection induced by dissolution," Phys. Rev. Fluids 4, 103801 (2019)] in order to determine the conditions for generating a convective flow under the action of dissolution.

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Onset of solutal convection in liquid phase epitaxy system

Cited by 4 publications

References 13 publications

Solutal convection induced by dissolution

Solutal convection induced by dissolution

Onset of buoyancy-driven instability in a pure melt solidified from above

Solutal convection instability caused by dissolution

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