Parametric study for dewetted Bridgman method: crystal–crucible gap dependence on the Bond and Laplace numbers and on contact angle

In order to analyze the dependence of the crystal-crucible gap on the Bo and La numbers, a parametric study has been performed for two different cases: the sum of the contact angle (θ _c) and the growth angle (α _e) is smaller or larger then 180°. The limit regimes of the main parameters \( \left( {La \to - \infty ,\;La \to + \infty ,\;Bo \to + \infty ,\;Bo \to 0} \right) \) of the problem were first studied. Then the non-dimensional Laplace equation has been solved numerically in the axi-symmetric case for various values of the parameters and the results are presented as graphical plots. It is shown that the main variations of the gap thickness are localized in the intermediary regimes. Another interesting point is that the gap thickness \( (\tilde{e} ) \) shows a maximum when the Bo and La numbers are varied. For growing crystals with a uniform radius, since, by definition, the sensitivity to small variations in the relevant parameter is minimal at the maximum, it is advisable to work at the parameter values which yield a maximum gap size.