Measurement of the dispersion relation of a convectively unstable capillary jet under confinement (original) (raw)

Spatiotemporal instability of a confined capillary jet

Physical Review E, 2008

Recent experimental studies on the instability of capillary jets have revealed the suitability of a linear spatiotemporal instability analysis to ascertain the parametrical conditions for specific flow regimes such as steady jetting or dripping. In this work, an extensive analytical, numerical, and experimental description of confined capillary jets is provided, leading to an integrated picture both in terms of data and interpretation. We propose an extended, accurate analytic model in the low Reynolds number limit, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show remarkable accuracy when compared with the extensive experimental mapping.

Dispersion relations, capillary waves, and the Rayleigh-Plateau instability

INCAS BULLETIN

The paper shows the importance of the dispersion relation in characterizing the capillary waves seen on liquid jets. Several theoretical models are given to better understand the stability of cylindrical interfaces when various parameters are considered, such as confinement, bulk elasticity, or the viscosity ratio between the two liquid phases. Theoretical predictions are compared with experimental data in terms of the fastest-growing mode for several liquid-in-air systems. Capillary-wave decay factors are also investigated, for stationary wave trains created at the impact of a liquid jet on a horizontal liquid bath, via the dispersion relation.

Experimental investigation of capillary instability: results on jet stimulated by pressure modulations

Experiments in Fluids, 1996

We investigate the behaviour of a liquid jet stimulated by pressure disturbances using a photometric measurement of the jet shadow width. Two apparatuses involving lights of different nature are utilized and measurements are taken from the exit of the nozzle to drop breakoff for different operating conditions. Fourier analysis is applied to characterize the spatial evolution of the jet shape.

Capillary instability of an annular liquid jet

Journal of Fluid Mechanics, 1987

An analytical investigation of the stability of a viscous, annular liquid jet moving in an inviscid medium is presented. This problem is a generalization of the well-known cases of a round cylindrical jet (obtained here when the ratio of internal to external radii tends to zero) and the flat thin liquid sheet (when the ratio above tends to unity).

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

Physics of Fluids, 2014

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Effect of gravity on capillary instability of liquid jets

Physical Review E, 2013

The effect of gravity on the onset and growth rate of capillary instabilities in viscous liquid jets is studied. To this end, a spatial linear stability analysis of Cosserat's equations is performed using a multiscale expansion technique. A dispersion relation and expressions for the perturbation amplitude are derived to evaluate the growth rate of the most unstable axisymmetric disturbance mode. Modeling results are compared with classical results in the limit of zero Bond number, confirming the validity of this approach. Expressions for the critical Weber number, demarcating the transition between convective and absolute instability are derived as functions of capillary and Bond numbers. Parametric investigations for a range of relevant operating conditions (characterized by capillary, Weber, and Bond numbers) are performed to examine the jet breakup and the perturbation growth rate. In addition to the physical insight that is obtained from this investigation, the results that are presented in this work could also be of relevance as test cases for the algorithmic development and the verification of high-fidelity multiphase simulation codes.