Capillary instability and shear stabilization of liquid columns and bridges

Many industrial processes rely on surface tension to contain liquids during processing. However, surface tension always acts to minimize surface area and may destabilize the desired interface shape; the capillary breakup of a quiescent liquid cylinder is an example. A better understanding of interface stability is necessary to eliminate processing restrictions imposed by capillary instability. We investigate the stability of axisymmetric fluid/liquid interfaces to small, three-dimensional disturbances, and consider both static and dynamic basic states.; We begin by examining the stability of a static liquid captured between two equal-diameter end plates. As the separation distance between the two end plates is slowly decreased, the liquid bridge fattens and eventually changes shape. We find that the rotund axisymmetric bridge is first unstable to nonaxisymmetric disturbances. Using an energy stability method, we obtain the marginal stability boundary as it depends on bridge volume and aspect ratio. We map out the stability boundary experimentally using two neutrally buoyant, immiscible liquids to simulate a low gravity environment. Theory and experiment are in quantitative agreement, and predict instability when the free interface meets each end plate tangent to its flat surface.; We next examine the stability of a cylindrical interface containing a liquid in motion. We investigate the stability of an axial flow within a liquid film which coats either a rod or the inner wall of a tube. We use a continuation method to trace out stability boundaries in terms of the basic-state velocity parametrization and geometry. A long-wavelength analysis complements the numerical computations. We find that, for both rod and tube flows, shear flow can suppress capillary instability.; We complete our analysis by exploring the stabilization mechanism. We start with an analysis of the mechanical energy balance for disturbances; this allows us to identify the processes which either sustain or dissipate disturbance energy. This discussion leads to a description of the mechanism in terms of the long-wave analysis. We show that the curvature of the basic-state velocity profile results in a perturbation shear stress that drives a disturbance axial shear flow; the interaction of the basic-state and disturbance flow fields stabilizes long-wavelength disturbances.