Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

Wu, Chun-Mei; Yuan, Bo; Li, You–Rong

doi:10.3390/cryst9020072

Cited by 4 publications

(3 citation statements)

References 39 publications

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“…Once the rotation is taken into account, the centrifugal force is introduced and interacted with the capillary forces. For the mixture with small capillary ratio of −0.2 [41], the thermocapillary effect is dominant, and it was proved that rotation has similar a influence as that in pure fluid. However, for the mixture with minus one capillary ratio, the thermal and solutocapillary forces are counterbalanced.…”

Section: Introductionmentioning

confidence: 96%

“…These convections are coupled with a thermal effect, which directly leads to the sharp change of the crystal interface. After that, a series of experiments and simulations were conducted to qualify the coupling effect of the thermal and solutal-capillary effect in the silicon-germanium mixture [40,41]. Abbasoglu et al [42] pointed out that the concentration profiles is closely related with the temperature through the radial segregation.…”

Section: Introductionmentioning

confidence: 99%

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Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

Chen

2020

Crystals

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This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

Chen

2020

Crystals

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“…The present work is beneficial for improving crystal qualities in Cz crystal growth. Figure 1 gives the physical model, which is a classical simplified model of the Cz growth system [31][32][33]. A disc with the radius of r s = 23 mm contacts the free surface of Ge 1-x Si x melt.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration

Zhang

Shen

et al. 2019

Crystals

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A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.

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Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

Chen

Yuan

et al. 2019

Physics of Fluids

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The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.

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Flow Instabilities of Coupled Rotation and Thermal-Solutal Capillary Convection of Binary Mixture in Czochralski Configuration

Cited by 4 publications

References 39 publications

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration

Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

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