Three-dimensional linear flow instabilities and initial formation of chimneys in a mushy region during solidification of a binary alloy are investigated. Chimneys are vertical channels that can lead to freckles in the solidified material. Freckles are imperfections that interrupt the uniformity of the solidified material and cause areas of mechanical weakness. A stability analysis and numerical computations for deformed liquid-mush and mush-solid interfaces provide information on the neutral stability curve, velocity data and density data for the solid fraction perturbation in the mushy layer that leads to local regions of chimney formation. The results for the flow pattern in the form of hexagons indicate two distinct hexagonal modes of convection. The importance and roles of these two modes are discussed in relation to chimney formation in the mushy layer, as well as to future nonlinear instability and high gravity research with application to freckles elimination.
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