Revisiting the constant growth angle: Estimation and verification via rigorous thermal modeling

Methods for estimating growth angle (θgrθgr) values, based on the a posteriori   analysis of directionally solidified material (e.g. drops) often involve assumptions of negligible gravitational effects as well as a planar solid/liquid interface during solidification. We relax both of these assumptions when using experimental drop shapes from the literature to estimate the relevant growth angles at the initial stages of solidification. Assumed to be constant, we use these values as input into a rigorous heat transfer and solidification model of the growth process. This model, which is shown to reproduce the experimental shape of a solidified sessile water drop using the literature value of θgr=0∘θgr=0∘, yields excellent agreement with experimental profiles using our estimated values for silicon (θgr=10∘θgr=10∘) and germanium (θgr=14.3∘θgr=14.3∘) solidifying on an isotropic crystalline surface. The effect of gravity on the solidified drop shape is found to be significant in the case of germanium, suggesting that gravity should either be included in the analysis or that care should be taken that the relevant Bond number is truly small enough in each measurement. The planar solidification interface assumption is found to be unjustified. Although this issue is important when simulating the inflection point in the profile of the solidified water drop, there are indications that solidified drop shapes (at least in the case of silicon) may be fairly insensitive to the shape of this interface.