Stability of liquid bridges between equal disks in an axial gravity field

Abstract

The stability of axisymmetric liquid bridges spanning two equal-diameter solid disks subjected to an axial gravity field of arbitrary intensity is analyzed for all possible Uquid volumes. The boundary of the stability region for axisymmetric shapes (considering both axisymmetric and nonaxisymmetric perturbations) have been calculated. It is found that, for sufficiently small Bond numbers, three different unstable modes can appear. If the volume of liquid is decreased from that of an initially stable axisymmetric configuration the bridge either develops an axisymmetric instability (breaking in two drops as already known) or detaches its interface from the disk edges (if the length is smaller than a critical value depending on contact angle), whereas if the volume is increased the unstable mode consists of a nonaxisymmetric deformation. This kind of nonaxisymmetric deformation can also appear by decreasing the volume if the Bond number is large enough. A comparison with other previous partial theoretical analyses is presented, as well as with available experimental results.

Remnants from fast liquid withdrawal

“…11 The impact of axial stretching on the stability of a liquid ligament has also a long history, 12,13 the lesson being that instability is suppressed as soon as the stretching rate overcomes the capillary instability rate based on the current ligament radius. 7,9,14,15 When formed by the rapid extension of a liquid bridge (a volume of liquid held by surface tension on supporting solid rods [16][17][18][19] ), the ligament linking the distant pulling supports thus breaks up at its extremities, 20 and does so first in the region close to the solid where stretching vanishes. 8,9,21 (This is almost always true: the breakup can occur in other places for low stretching speeds.)…”

Forced dynamics of a short viscous liquid bridge

“…For each set of parameters, it has a constant curvature K D . Figure 2(a) shows how the curvature K D ( 0 , S) varies as a function of 0 and S. The limits of the domain correspond to stability boundaries (see for instance Gillette & Dyson 1970;Slobozhanin & Perales 1993). The equilibrium states are symmetric with respect to the median plane z = /2.…”

Stability of liquid bridges between twisted elliptical disks

“…The first configuration studied in literature was a cylindrical shape held between two parallel, coaxial circular disks of the same diameter. The response of the mentioned configuration subjected to various disturbances has been studied, including the calculation of the equilibrium shapes and their stability limits (Slobozhanin and Perales, 1993;Slobozhanin and Alexander, 1998;Lowry and Steen, 1997;Marr-Lyon et al, 1997;Gonzalez and Castellanos, 1993;Mahajan et al, 1999;Parra et al, 2002;Luengo et al, 2003). The influence of different perturbations on the stability of liquid bridges has been extensively analyzed from both the theoretical and the experimental point of view.…”