Mold surface wavelength effect on gap nucleation in solidification

A theoretical model that predicts the time and position of gap nucleation a long the metal-shell interface during solidification of a pure metal on a s inusoidal mold surface is presented. The ratio of the mold surface amplitud e to its wavelength is assumed to be much less than one and hence it is use d as a perturbation parameter in the analysis. The molten metal perfectly w ets the mold surface prior to the beginning of solidification, and this lea ds to a corresponding undulation of the metal shell thickness. A nonuniform distortion develops in the shell due to the lateral temperature gradient i nduced by the modest spatial variation of the mold surface. This causes a v ariation in the contact pressure so that the growing shell pushes harder on the mold in some places, but in other places it starts to pull away from t he mold. Gap nucleation is assumed to occur when the contact pressure falls to zero. The conditions for gap nucleation in the surface troughs are exam ined since a corresponding increase in pressure at the crests signals the p ossibility of a growth instability in the shell at later stages of the proc ess. A series expansion for the contact pressure is presented which is appr opriate for early solidification times. This reveals how the contact pressu re varies with the mold surface wavelength. This solution is compared with a numerical solution for the contact pressure that is not limited to early solidification times. Gap nucleation times are calculated for pure aluminum and iron shells for selected mold surface wavelengths. The associated mean shell thicknesses are calculated as a function of wavelength at selected m ean molten metal pressures. [S0021-8936(00)02901-9].