Bifurcation of the equilibrium states of a weightless liquid bridge

Abstract

Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh limit under microgravityThe bifurcation of the solutions of the nonlinear equilibrium problem of a weightless liquid bridge with a free surface pinned to the edges of two coaxial equidimensional circular disks is examined. The bifurcation is studied in the neighborhood of the stability boundary for axisymmetric equilibrium states with emphasis on the boundary segment corresponding to nonaxisymmetric critical perturbations. The first approximations for the shapes of the bifurcated equilibrium surfaces are obtained. The stability of the bifurcated states is then determined from the bifurcation structure. Along the maximum volume stability limit, depending on values of the system parameters, loss of stability with respect to nonaxisymmetric perturbations results in either a jump or a continuous transition to stable nonaxisymmetric shapes. The value of the slenderness at which a change in the type of transition occurs is found to be ⌳ s ϭ0.4946. Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for ⌳Ͻ⌳ s , the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state.

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

“…Russo and Steen 27 determined the maximum-volume stability limit in a similar set-up, showing that axisymmetric liquid bridges nonaxisymmetrically bulge when their interface is tangent to the discs. The experiments of Slobozhanin et al 28 provided further insights on this stability limit. They showed that above (below) the slenderness Λ ≃ 0.4946, liquid bridges continuously (abruptly) bulge into a non-axisymmetric shape.…”

The motion, stability and breakup of a stretching liquid bridge with a receding contact line

“…For low syringe retraction speeds, U , the contact line radius slowly expands, and arbitrarily large drops can be generated. In these regions, the drop sizes, r d , were shown to vary as U −1/2 , and due to the low syringe speed and the slow contact line motion, the bridge evolution and breakup was well-predicted by quasi-static theory using RayleighPlateau instability theory, and its extensions for non-cylindrical bridges (Meseguer 1984;Slobozhanin et al 1997;Slobozhanin & Alexander 1998). However, for higher values of U , the contact line recedes, and the process is more complex, and was observed to be comprised of two phases (Qian et al 2009): an initial phase characterized by a slow (quasi-static) contact line retraction, followed by a very rapid phase in which the contact line speed is comparable to the capillary wave speed, and during which the contact angle is seen to depend on the speed, and to be significantly lower than its quasi-static receding value.…”

On the breaking of long, axisymmetric liquid bridges between unequal supporting disks at minimum volume stability limit

“…3. Five curves are represented in this plot: the straight (dashed) lines correspond to the results provided by expression (11) whereas solid lines represent results obtained by using expression (9). Dot-dashed line corresponds to exact theoretical results already published [21,22].…”

“…In this case, the calculation of the roots of the equation dk/ds = 0 requires a much more involved algebra. The dependence of the parameter s on the reduced slenderness k, as resulting from expression (9), is shown in Fig. 2.…”

“…The simplest non-trivial (non-cylindrical) liquid bridge configuration consists of an axisymmetric drop of liquid spanning between two parallel, coaxial, equal in diameter solid disks, in absence of body forces. Early stability studies concerning basic configurations were published three decades ago (Haynes [1], Erie, Gillette and Dyson [2], Gillette and Dyson [3]), although the most relevant result concerning the stability of such configuration were published at the end of the decade of the seventies (Martinez [4]), and in the last two decades (Sanz and Martinez [5], Russo and Steen [6], Boucher and Jones [7], Lowry and Steen [8], Slobozhanin, Alexander and Resnick [9], amongst other). Concerning the influence of axial gravity, different attempts have been made to calculate the minimum volume stability limits as well as the maximum volume stability limits both from a theoretical and an experimental point of view [10][11][12], being this problem extensively analyzed in the nineties by Slobozhanin and Perales [13].…”