Source: Dissertation Abstracts International, Volume: 69-06, Section: B, page: 3474.

Adviser: John S. Wettlaufer.

The following work marries theoretical and experimental approaches to study the interaction of an external shear flow with a solidifying porous medium. The porous medium, a dendritic 'mushy layer', is created when a super-eutectic binary alloy is cooled leading to solid crystals bathed in an interstitial fluid which is compositionally enriched. This compositional enrichment leads to natural buoyant instabilities in the solidifying porous medium coupled with instabilities in the adjoining liquid layer.

Theoretically, the effect of an external shear flow on the convective instabilities inherent to this mushy layer is investigated using a linear stability analysis. The external flow is coupled to advective perturbations in the liquid and to flow in the mush through a perturbed mush-liquid interface. A complete numerical solution of the stability of the system is performed and a critical porous medium Rayleigh number is found which is a function of both the external flow speed and the wavenumber of the interfacial perturbations. By neglecting the effects of buoyancy in the liquid and solving only for the pressure perturbations on the corrugated mush-liquid interface induced by the external flow, a reduced model is constructed and solved analytically.

These theoretical results are compared with experimental observations obtained in a laboratory flume in which an ammonium-chloride solution is solidified from below at a constant rate. The experimental results reveal that at flow speeds above critical, convection is forced within the mush leading to a series of zero solid fraction tesselations aligned perpendicular to the applied shear flow. The results of the experiments compare favorably to the linear stability analysis.