A review on the stability of liquid bridges

Abstract

Errors in theAlthough early studies dealing with the stability of liquid bridges were published long time ago, these studies were mainly concerned with the stability of axisymmetric liquid bridges between parallel, coaxial, equal-in-diameter solid disks, with regard to axisymmetric perturbations. Results including effects such as solid rotation of the liquid column, supporting disks of different diameters and an axial acceleration acting parallel to the liquid column can be found in several works published in the early eighties, although most of these analysis were restricted to liquid bridge configurations having a volume of liquid equal or close enough to that of a cylinder of the same radius. Leaving apart some asymptotic studies, the analysis of non-axisymmetric effects on the stability of liquid bridges (lateral acceleration, eccentricity of the supporting disks) and other not so-classical effects (electric field) has been initiated much more recently, the results concerning these aspect of liquid bridge stability being yet scarce.

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

“…As previously stated, Qian et al 24 reported small drop sizes in a pressure-controlled deposition due to fast dynamics near the contact line. Here, achieving a fast-receding contact line is assisted by the withdrawal of the liquid near primary and satellite drops upon stability loss at the maximum-height stability limit 19 . Thus, the chain of drops arising upon breakup is the most stable (having the deepest potential well) state that is dynamically accessible to unstable bridges.…”

“…Quantifying liquid-bridge and jet breakup upon stability loss dates to the works of Plateau 15 and Rayleigh 16 , 17 . While early investigations of crystal growth and purification focused on determining the minimum liquid volume that can be held between circular discs 18,19 , the drop-size distribution following breakup is of prime interest in contact-drop dispensing and liquid-transfer applications [20][21][22] . Minimizing the dispensed-drop size relative to the needle diameter is central to surface patterning based on direct-write lithographic techniques 3,23 .…”

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.)…”

Oscillations of a liquid bridge resulting from the coalescence of two droplets

“…The stability of non-cynlidrical liquid bridges has been considered in several works 21,22 but the eigenmodes of oscillations have not been determined so far.…”