Stability of plane-front and dendritic solidification of binary liquids: The effects of rotation
Oztekin, Alparslan
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https://hdl.handle.net/2142/23082
Description
Title
Stability of plane-front and dendritic solidification of binary liquids: The effects of rotation
Author(s)
Oztekin, Alparslan
Issue Date
1992
Doctoral Committee Chair(s)
Pearlstein, Arne J.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Science and Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
Convective and morphological instabilities in horizontally unbounded binary liquids solidified by cooling from below are studied by linear stability analysis. Use of uniform rotation about the vertical to suppress onset of buoyancy-driven convection is considered for plane-front solidification (PFS) and dendritic solidification (DeS).
For dilute Pb-Sn alloys, onset is suppressed significantly at modest rotation rates. PFS is stable at higher Sn concentrations in a rotating configuration than in a nonrotating one. Predicted inhibitory effects of rotation are discussed relative to previous studies of rotating single-component fluids heated from below and thermally and solutally stratified binary fluids.
For Hg$\sb{\rm 1-x}$Cd$\sb{\rm x}$Te, the liquid density depends nonmonotonically on temperature for small CdTe bulk mole fractions (x$\sb\infty).$ For certain operating parameters (solidification rate, liquid-side temperature gradient, x$\sb\infty)$ there exists a critical x$\sb\infty$ below which PFS is unstable at all dimensionless solidification rates $\gamma$, whereas in the normal case in which density depends monotonically on temperature (e.g., Pb-Sn) PFS is stable at any x$\sb\infty$ for sufficiently small $\gamma$. When density varies nonmonotonically with temperature, there exists a critical $\gamma\sb{\rm c}$ such that for $\gamma > \gamma\sb{\rm c}$ PFS is unstable for all x$\sb\infty$ and for $\gamma < \gamma\sb{\rm c}$ PFS is stable for a finite range of x$\sb\infty$. This differs from the normal case, for which at all $\gamma$, PFS is stable for x$\sb\infty$ sufficiently small. These results are discussed in terms of a thermally destabilizing sublayer adjacent to the interface. For Hg$\sb{\rm 1-x}$Cd$\sb{\rm x}$Te, modest rotation rates significantly suppress onset of convection.
For DeS, the mushy zone, consisting of liquid and solid phases, is modeled as a porous medium with anisotropic permeability. Local porosity and locations of boundaries separating solid, mushy zone, and liquid are treated as dynamical variables. The basic state, computed using a thermodynamically self-consistent nonlinear solidification model, exists for only some operating parameters. The dendritic solution also exists when PFS is linearly stable. This is discussed in light of previous nonlinear morphological stability analyses. Division of the parameter space according to existence and stability of PFS and DeS is discussed for Pb-Sn. Uniform rotation is shown to be less stabilizing for DeS than for PFS.
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