On the thinnest steady threads obtained by gravitational stretching of capillary jets

Abstract

Experiments and global linear stability analysis are used to obtain the critical flow rate below which the highly stretched capillary jet generated when a Newtonian liquid issues from a vertically oriented tube, is no longer steady. The theoretical description, based on the one-dimensional mass and momentum equations retaining the exact expression of the interfacial curvature, accurately predicts the onset of jet self-excited oscillations experimentally observed for wide ranges of liquid viscosity and nozzle diameter. Our analysis, which extends the work by Sauter & Buggisch (2005), reveals the essential stabilizing role played by the axial curvature of the jet, being the latter effect especially relevant for injectors with a large enough diameter. Our findings allow us to conclude that, surprisingly, the size of the steady threads produced at a given distance from the exit can be reduced by increasing the nozzle diameter.

arXiv comment12 pages, 5 figures

References in corpus (4)

• Drop Formation in a One-Dimensional Approximation of the Navier-Stokes Equation
• Hydro-dynamical models for the chaotic dripping faucet
• The Shape and Stability of a Viscous Thread
• The effect of viscous relaxation on the spatiotemporal stability of capillary jets

Cited by in corpus (8)

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• Global stability of stretched jets: conditions for the generation of monodisperse micro-emulsions using coflows
• Natural break-up and satellite formation regimes of surfactant-laden liquid threads
• Global stability analysis of axisymmetric liquid-liquid flow focusing
• The nonlinear states of viscous capillary jets confined in the axial direction
• Frequency selection in a gravitationally stretched capillary jet in the jetting regime
• Wavemaker and endogeneity of gravitationally stretched weakly viscoelastic jets
• PDEs on deformable domains: Boundary Arbitrary Lagrangian-Eulerian (BALE) and Deformable Boundary Perturbation (DBP) methods