The Stability of Two Connected Pendant Drops

The stability of an equilibrium system of two drops suspended from circular holes is examined. The drop surfaces are disconnected surfaces of a connected liquid body. For holes of equal radii and identical pendant drops axisymmetric perturbations are always the most dangerous. The stability region for two identical drops differs considerably from that for a single drop. Loss of stability leads to a transition from a critical system of identical drops to a stable system of axisymmetric non-identical. This system of non-identical drops reaches its own stability limit (to isochoric or non-isochoric paturbations). For non-identical drops, loss of stability results in dripping or streaming from the holes. Critical volumes for non-identical drops have been calculated as functions of the Bond number, B. For unequal hole radii, stability regions have been constructed for a set of hole radius, K. The dependence of critical volumes on K and B is analyzed

Bifurcation of The Equilibrium States of A Weightless Liquid Bridge

The 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 Λs=0.4946. Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for Λ\u3cΛs, the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state

Bifurcation of The Equilibrium States of A Weightless Liquid Bridge

The 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 Λs=0.4946. Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for Λ\u3cΛs, the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state

Stability of Liquid Bridges between Equal Disks in an Axial Gravity Field

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 liquid 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

Capillary Pressure of a Liquid Between Uniform Spheres Arranged in a Square-Packed Layer

The capillary pressure in the pores defined by equidimensional close-packed spheres is analyzed numerically. In the absence of gravity the menisci shapes are constructed using Surface Evolver code. This permits calculation the free surface mean curvature and hence the capillary pressure. The dependences of capillary pressure on the liquid volume constructed here for a set of contact angles allow one to determine the evolution of basic capillary characteristics under quasi-static infiltration and drainage. The maximum pressure difference between liquid and gas required for a meniscus passing through a pore is calculated and compared with that for hexagonal packing and with approximate solution given by Mason and Morrow [l]. The lower and upper critical liquid volumes that determine the stability limits for the equilibrium capillary liquid in contact with square packed array of spheres are tabulated for a set of contact angles

Stability Limits and Dynamics of Nonaxisymmetric Liquid Bridges

Liquid bridges have been the focus of numerous theoretical and experimental investigations since the early work by Plateau more than a century ago. More recently, motivated by interest in their physical behavior and their occurrence in a variety of technological situations, there has been a resurgence of interest in the static and dynamic behavior of liquid bridges. Furthermore, opportunities to carry out experiments in the near weightless environment of a low-Earth-orbit spacecraft have also led to a number of low-gravity experiments involving large liquid bridges. In this paper, we present selected results from our work concerning the stability of nonaxisymmetric liquid bridges, the bifurcation of weightless bridges in the neighborhood of the maximum volume stability limit, isorotating axisymmetric bridges contained between equidimensional disks, and bridges contained between unequal disks. For the latter, we discuss both theoretical and experimental results. Finally, we present results concerning the stability of axisymmetric equilibrium configurations for a capillary liquid partly contained in a closed circular cylinder

Stability of liquid bridges between coaxial equidimensional disks to axisymmetric finite perturbations: A review

This paper reviews the dynamics of breaking or oscillating axisymmetric liquid bridges, and estimates of the energy which is needed to break a liquid bridge. We consider a liquid bridge spanning two coaxial equal disks with sharp edges and held by surfacetension forces. The liquid volume is assumed to be conserved under perturbations, and the contact lines are pinned to the disk edges. The perturbations are finite and axisymmetric. An analysis is based on the one-dimensional models previously used in capillary jet theory and last several decades for study a liquid bridge dynamics. According to the scientific project JEREMI (Japanese and European Research Experiment on Marangoni Instabilities), the first stage of the space experiment on ISS will involve an isothermal liquid bridge with a gas blowing parallel to the axial direction of the bridge. The geometry corresponds to a cylindrical volume liquid bridge coaxially placed into an outer cylinder with solid walls. The gas enters the annular duct bounded by the outer cylinder and the internal system consisting of supporting vertical rods and the liquid bridge. Considering that the bridge is small (the rod's radii are 3 mm) and the gas velocity is typically (0.25 / 0.37) m/s, the perturbations cannot be considered small. Thus, one may assume that the amplitude of the liquid bridge perturbations is sufficiently large that departures from linearity must be considered. © Springer Science+Business Media B.V. 2012.SCOPUS: re.jinfo:eu-repo/semantics/publishe