Stability of an isorotating liquid bridge between equal disks under zero-gravity conditions

Abstract

The stability of the relative equilibrium of an isorotating axisymmetric liquid bridge between two equal-radius coaxial disks under zero-gravity conditions has been investigated in detail. The free surface is assumed to be pinned to the edges of the disks and in equilibrium and only perturbations compatible with this pinning are considered. In the plane of the dimensionless variables characterizing the liquid bridge length and the liquid bridge volume, the stability regions for a set of values of the Weber number have been calculated. The stability region structure and the nature of critical perturbations change when the Weber number, W, passes through the values W0 (2.05<W0<2.06) and W1 (2.44<W1<2.45). It has been found that, for W<W0, the stability region is connected, and the neutral stability may take place with respect to nonaxisymmetric perturbations as well as to axisymmetric ones. In the latter case, it has been established whether the critical axisymmetric perturbations are reflectively symmetric or reflectively antisymmetric about the equatorial plane. When the increasing Weber number passes through the value W0, the stability region breaks into two disconnected parts. The first exists for all Weber numbers larger than W0. For the states belonging to the boundary of this part, only nonaxisymmetric perturbations are critical. The second part exists only for Weber numbers between W0 and W1. Its boundary is determined by the states that may be neutrally stable to nonaxisymmetric perturbations or to axisymmetric ones. The characteristics of the shape of the neutrally stable surfaces have been calculated for a wide range of the Weber number.