A perturbation analysis of the stability of long liquid bridges between almost circular supporting disks

Abstract

The stability of an isothermal liquid mass of constant properties (density and surface tension) held by capillary forces between two solid disks placed a distance L apart (the so-called liquid bridge model) is considered. For a weightless liquid bridge that is a right circular cylinder, the well-known Rayleigh stability limit holds, and the liquid column becomes unstable when its length is larger than its circumference. Many perturbations from this ideal configuration have been studied in the past, but the supporting disk shape has always been assumed circular. In this Brief Communication the influence of noncircular supports on stability limits of almost cylindrical liquid bridges is analyzed through an asymptotic analysis. Closed form expressions for the stability limits are presented.