Effects of Axial and Centrifugal Forces on the Stability of Liquid Bridges

Abstract

The equilibrium and stability equations for liquid bridges are well known, but they are nonlinear and it is difficult to guess real behavior, such as the sensitivity of the shape to axial and rotational forces (measured by Bond and Weber numbers, respectively) or to the geometry of the solid supports that support the bridge. A parametric study by numerical methods of the different effects and the analytical solutions at the bifurcation points in the stability diagrams is presented. The well known shooting method to numerically compute equilibrium shapes of liquid bridges, and their stability limits, is applied to a five parameter case, when different disc sizes (measured by H), bridge lengths (Lr), liquid volumes (Vr), residual axial acceleration (Bo), and solid body centrifugation (We) are contemplated. The bundle of diagrams presented give an idea of the complexities of such a multiparametric analysis and may help in further research to delimitate other forms of instability. The numerical results were used to check the validity of several analytical asymptotic expressions, with perfect agreement over the range of interest (long liquid bridges), but these models only take into consideration the subset (Lr, Vr = 1, H = 0, Bo, We) of the five parameter family. These results will be of great help to plan future space experiments on liquid columns and floating zones in space and in particular will show a method to easily measure very weak residual forces in microgravity platforms.