The interface shape function for the pure material directional solidification system with temperature disturbances on the heater and cooler is derived. It is approximately a fraction function including cosine terms in the denominator and the numerator. Calculation of the function shows the interface shape can respond to the temperature disturbance. When both the solidification rate V and the interface cooler distance α determined by the boundary temperatures are lower than critical value deteimined by a formula, the interface shape changes from sinusoidal wave to figures pattern with the increase of the rate or the distance. Once the rate or the distance reaches the critical value, the interface branches at the bottom of the grooves between figures and then the branches expand along the sidewall of the figures with further increase of the rate or the distance. According to that, we conclude that the sinusoidal interface shape assumption always used by the interface instability analyses is not always valid and the interface shape in Hele-Shaw solidification experiments in fact maybe is not planar but a cellular interface with quite small amplitude, and the role of temperature disturbance should be considered in experiments studying solidification interface stability.
Comments: 17 pages
[v1] 22 Oct 2010
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