Stability of an isorotating liquid bridge in an axial gravity field

Abstract

The stability problem for the axisymmetric equilibrium states of an isorotating liquid bridge between equidimensional circular disks in a constant axial gravity field is considered. In particular, we examine the stability of bridges satisfying two constraints that are typical for the floating zone method used for materials purification and single crystal growth. First we consider the constraint that the relative volume of the bridge, V, is equal to 1. Here, V is the ratio of the actual bridge volume to that of a cylinder pinned to the edges of disks. For this case, the critical values of the slenderness (Λ) (ratio of the disk separation to the diameter) and of the free surface slopes (β1,β2) at both disks have been determined for a wide range of the Bond (B) and Weber (W) numbers. The second constraint is that the surface slope β1 at one of the disks is prescribed. The chosen values are 90° and 75° and correspond to extremes in growth angle values encountered in floating zone crystal growth. For this case, the dependencies of critical Λ and V values B and W have been calculated. In addition, both axial gravity directions are considered separately and the values of the slope angle, β2, at the other disk are also analyzed for critical states. The solution of the stability problem for any liquid bridge is discussed in detail using the case for B=W=0.1 as an example. In particular, the relationship between the general boundary of the stability region and the stability of bridges subject to the constraints outlined above is examined.