Existence and shapes of menisci in detached Bridgman growth

In detached Bridgman growth, the crystal radius is less than the crucible radius and a meniscus bridges the gap between the crystal and crucible wall. Existence of detached growth depends upon the contact angle of the melt with the crucible wall, the growth angle of the solidifying crystal, the pressure differential across the meniscus, and the Bond number. The Young-Laplace capillary equation is used to calculate the crystal radii of detached states as a function of the pressure differential across the meniscus. Both terrestrial and microgravity conditions are considered. A variety of solution states is found, and multiple solutions with different crystal radii can exist for a given value of the pressure differential. The meniscus shapes for the detached states vary from simply convex or concave to shapes with numerous inflections. An approximate solution to the Young-Laplace equation for small Bond numbers is derived.