Thermocapillary suppression of the PlateauRayleigh instability: a model for long encapsulated liquid zones

Abstract

A cylindrical liquid bridge is unstable when its length is longer than its circumference, the Plateau–Rayleigh limit. This capillary instability is modified by fluid motions adjacent to the interface, which can be induced by thermocapillary stress, among other means. A simple flow model with symmetry that mimics the situation in encapsulated floating zones is analysed. The interfacial balance equation is formulated as a bifurcation problem, appropriate when the flows are nearly rectilinear. This balance captures the competition between capillary stress and the flow-induced pressure. The fluid motions are shown to have a stabilizing effect; bridges much longer than the classical limit are stabilized. Numerical branch-tracing and the Lyapunov–Schmidt reduction methods provide the bifurcation structures of branching solutions. A normal-form analysis predicts standing-wave patterns due to mode–mode interaction. The model is proposed as an explanation for the extra long float zones observed in various spacelab experiments.

Thermocapillary effect on the dynamics of viscous beads on vertical fiber

“…Xu and Davis [21] have studied the stability of long axisymmetric liquid zones subjected to axial temperature gradients which induce steady flows driven by thermocapillarity. Chen et al [22] have studied the effect of thermocapillarity on the Plateau-Rayleigh instability of a cylindrical liquid bridge. It has been shown that the thermocapillarity induced by axial temperature gradients has a stabilizing effect [21,22].…”

“…Chen et al [22] have studied the effect of thermocapillarity on the Plateau-Rayleigh instability of a cylindrical liquid bridge. It has been shown that the thermocapillarity induced by axial temperature gradients has a stabilizing effect [21,22].…”

“…[21] and [22] where the temperature gradients are parallel to the axial direction. In our problem, most of the physical parameters are the same with those of experiments by Kliakhandler et al [8].…”

Scalable attoliter monodisperse droplet formation using multiphase nano-microfluidics

“…The formation of a liquid filament is then a mandatory preliminary step for producing a droplet (Chen et al 2003). This procedure is widely applied in flow-focusing devices.…”

Three-dimensional oscillatory thermocapillary flow in encapsulated liquid bridge

“…Then many researchers obtained some asymptotic solutions of thermocapillary convection in encapsulated liquid bridge at low Ma number. [13][14][15][16] The influence of various factors on thermocapillary convection is also analyzed. Meanwhile, Li et al 17 and Prakash et al 18 analyzed the stability of thermocapillary convection in encapsulated liquid bridge using the analysis method of the linear stability and got the critical Ma numbers under various conditions.…”