Combined effect of disk inequality and axial gravity on axisymmetric liquid bridge stability

The stability of an axisymmetric liquid bridge between unequal circular disks in an axial gravity field is examined for all possible values of the liquid volume and disk separation. The parameter defining the disk inequality is K, the ratio between the radii of the smaller and larger disks. Both axisymmetric and nonaxisymmetric perturbations are considered. The parameter space chosen to delimit the stability regions is the Λ-V plane. Here, Λ is the slenderness (ratio of the disk separation to the mean diameter, 2r 0 , of the two support disks), and V is the relative volume (ratio of the actual liquid volume to the volume of a cylinder with a radius equal to r 0 ). Wide ranges of the Bond number and the ratio K are considered. Emphasis is given to previously unexplored parts of the stability boundaries. In particular, we examine the maximum volume stability limit for bridges of arbitrary Λ and the minimum volume stability limit for small Λ bridges. The maximum volume stability limit was found to have two distinct properties: large values of the critical relative volume at small Λ, and the possibility that stability is lost to axisymmetric perturbations at small values of K. For a set of K, the maximum Bond number beyond which stability of the bridge is no longer possible for any combination of V and Λ is determined. In addition, the maximum value of the actual liquid volume of a stable bridge that can be held between given disks for all possible disk separations was examined for fixed Bond number. It is found that this volume decreases as K decreases and (depending on the sign of the Bond number) tends to the critical volume of a sessile or pendant drop attached to the larger disk.