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Liquid bridge stabilization: Theory guides a codimension-two experiment. (English) Zbl 0947.76025

Summary: Subject only to surface tension, a cylindrical liquid bridge is unstable at lengths longer than its circumference, the Plateau-Rayleigh limit. Perturbed by gravity and an axial flow, the liquid bridge becomes near-cylindrical with a modified stability. An unfolding captures the interactions between gravity and flow-induced pressure near the Plateau-Rayleigh limit. The stress balance of the free interface is determined using a lubrication-flow approximation and Lyapunov-Schmidt method. Stabilization is predicted when the two perturbations counter-balance one another. Where accurate measurements are possible, experiment gives good comparison with predictions. The attempt to use theory to guide experiment to the most delicate predictions is only partially successful, however. ‘Why?’ is addressed.

MSC:

76E17 Interfacial stability and instability in hydrodynamic stability
76D45 Capillarity (surface tension) for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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