Thermal-solutal capillary-buoyancy flow of a low Prandtl number binary mixture with a −1 capillary ratio in an annular pool

Abstract

A series of three-dimensional numerical simulations on thermal-solutal capillary-buoyancy flow in an annular pool were carried out. The pool was filled with silicon-germanium melt with an initial silicon mass fraction of 1.99%. The Prandtl number and the Lewis number of the working fluid are 6.37 × 10−3 and 2197.8, respectively. Both the radial temperature gradient and the solute concentration gradient were applied to the annular pool. The capillary ratio was assumed to be −1, which means that the solutal and thermal capillary effects were equal and opposite. Results show that the thermal-solutal capillary-buoyancy flow always occurs at this special case with the capillary ratio of −1, and even in a shallow annular pool with an aspect ratio of 0.05. With the increase of the thermal Marangoni number, four kinds of flow patterns appear orderly, including concentric rolls, petal-like, spoke, and rosebud-like patterns. These flow patterns are strongly influenced by the local interaction between the solutal and thermal capillary effects and the vertical solute concentration gradient near the outer cylinder. A small vortex driven by the dominant solutal capillary effect emerges near the inner cylinder, which is different from the flow pattern in a pure fluid. In addition, the critical thermal Marangoni number of the initial three-dimensional flow decreases with the increase of the aspect ratio of the annular pool.

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

“…The enhanced buoyancy-driven flow, due to the nonuniform solute concentration distribution in the axial direction, carries a lot of Ge 1-x Si x melt from the crucible bottom to the free surface, close to the sidewall at a large thermal capillary Reynolds number. Thus, the oscillatory spoke pattern swings in the azimuthal direction and merges, which is reported in Reference [24]. On the other hand, the amplitude of the surface solute concentration fluctuation decreases slightly, because of the increase of the wave number.…”

“…Figure 3 gives the variations of critical thermal capillary Reynolds numbers along the crystal or crucible rotation Reynolds number. This dichotomy is successfully applied for obtaining the critical thermal capillary Reynolds numbers [24,25], and maximum deviation is controlled below 100. The critical thermal capillary Reynolds number at a non-rotation Cz configuration is 4.1 × 10 3 , which is much larger than that of pure fluids [9,10].…”

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

“…They reported three different oscillatory modes and found that the onset of instability correlates with a supercritical Hopf bifurcation. Later, Yu et al [23] and Chen et al [24,25] have performed simulations on the flow pattern transitions of binary mixture with a -1 capillary ratio in an annular pool, which is a simplified model for Cz configuration. Various types of flow patterns were observed with the increase of the thermocapillary Reynolds number, such as concentric rolls, petal-like, spokes, rosebud-like patterns and vibrating spoke patterns.…”

A peculiar bifurcation transition route of thermocapillary convection in rectangular liquid layers

“…Transient intermittency in the supercritical branch is observed and physical instability mechanisms of the subcritical branch are identified. Yu et al [8] reported a counter-intuitive transition route from a perspective of the flow field in the capillary flow. They considered that the reverse transition from the three-dimensional unsteady flow to the steady flow is the reason that the spatial complexity of the flow increases as the thermal Marangoni number increases.…”