COMPOSITIONALLY CONVECTIVE AND MORPHOLOGICAL INSTABILITIES OF A FLUID LAYER OF BINARY ALLOY WITH FREEZING AT THE LOWER BOUNDARY

• Other Authors: JOU, JONG-JHY.
• Format: Others
• Subjects: Applied Mechanics
• Online Access: http://purl.flvc.org/fsu/lib/digcoll/etd/3085324

A fluid layer of binary alloy is cooled from above with solidification occurring at the lower boundary. Some latent heat and light material is released at the freezing boundary. We assume, due to a small cooling rate and a large thermal diffusivity, that the net effect of thermal buoyancy is insignificant and convection is mainly driven by compositional buoyancy associated with the release of light material. The freezing interface advances upward at a slow speed as a result of solidified binary alloy. A stability problem is formulated for the eigenvalue R as a function of Q and S, where R is a ratio of the release rate of light material at the lower boundary to that diffused by pressure gradient, Q is associated with light material diffused by pressure gradient and S is a ratio of the specific volume change upon solidification to that due to compositional change. Before the onset of convective instability, material is diffused by the pressure and compositional gradients. Convective instability is possible provided R > 1. For infinite Schmidt number P(,L), instability sets in stationarily at the marginal state and the mode having the smallest minimum eigenvalue becomes dominant. Three different modes of instabilities, depending on Q and S, are shown: cellular convective modes of both long and short wavelength and morphological mode of short wavelength. Morphological instabilities, associated with the unstable growth of the freezing interface, occur when the conducting layer near the freezing interface is constitutionally supercooled. The results indicate that cellular convective modes require R 1 + S. Nonlinear analysis shows that disturbances just past the marginal state behave like (R-R(,c))(' 1/2), where R(,c) is the critical eigenvalue. Subcritical instabilities are possible for cellular convective modes of long wavelength other than rolls. Taking into === account the effect of the curved interface, the surface tension tends to suppress the unstable growth of the freezing interface. For fixed values of Q and S, morphological modes with surface tension have larger minimum eigenvalues than those without surface tension. === Source: Dissertation Abstracts International, Volume: 43-04, Section: B, page: 1170. === Thesis (Ph.D.)--The Florida State University, 1982.