Seminar: Paul Griffiths, Reader at Aston University

Molten aluminium alloys, widely used for the casting of lightweight parts, tend to oxidise very quickly when first exposed to external ambient conditions. Thin oxide films, usually less than one micrometer thick, develop at the liquid metal-air interface which, in turn, affects casting processes. The oxide film can be encapsulated and further dragged away into the bulk under the effect of surface agitation. The encapsulation process necessarily leads to embedded oxide films (bi-films) between which air can be trapped. As a result, micro-porosities are formed after the solidification process, which can have major consequences on the quality and fatigue life of the cast parts. The selection of the right boundary condition to be applied along the surface of the liquid metal flow is not straightforward because of the complexity of the stress balance between the molten metal and the ambient surroundings (air). Irrespective of the mechanical behaviour of the oxide layer that covers the surface, one of two boundary conditions are considered by default: either a slip condition as usual for water-based flows, or a no-slip condition when the oxide film is considered to behave as a deformable wall. In fact, the reality is somewhat in between these two conditions: the continuous formation of an oxide film at the metal-air interface leads to a local and evolutive change in the boundary condition that can strongly affect the surface flow by increasing viscous dissipation. Recent experimental investigations have shed new light on the complex dynamics associated with these liquid-metal-type flow problems. Both the non-Newtonian behaviour of the oxide layer over the melted metal surface and the curvature of the interface due to wetting effects were observed via scanning electron microscopy techniques. In this talk we develop a mathematical model to describe flows of this nature. Working in the low Reynolds number regime, we make use of the Bingham fluid model in order to capture viscoplastic surface effects. We develop both asymptotic and numerical analyses and report on the surface characteristics (velocity and shear profiles) as well as the important effects of surface curvature.