Influence of viscosity on the capillary instability of a stretching jet (original) (raw)
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Journal of Fluid Mechanics, 1985
The stability of a capillary jet of an ideal liquid with a linear variation of axial velocity is investigated. Because of the time dependence in the basic extensional flow the evolution of surface perturbations in the jet is an initial-value problem instead of an eigenvalue one (as in the case of non-stretching jets). The amplification of any given perturbation is found to depend on the relative effects of surface tension and inertia terms associated with the extensional flow as well as on the initial wavenumber and the specific time when the perturbation is introduced in the flow field. The simulation of a shaped-charge jet by the present model is discussed. The results obtained are found to give a good description of the essential features of the breakup phenomenon of such jets.
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).
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.
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.
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.
Whipping instability characterization of an electrified visco-capillary jet
Journal of Fluid Mechanics, 2011
The charged liquid micro-jet issued from a Taylor cone may develop a special type of non-axisymmetric instability, usually referred to in the literature as a whipping mode. This instability usually manifests itself as a series of fast and violent lashes of the charged jet, which makes its characterization in the laboratory difficult. Recently, we have found that this instability may also develop when the host medium surrounding the Taylor cone and the jet is a dielectric liquid instead of air. When the oscillations of the jet occur inside a dielectric liquid, their frequency and amplitude are much lower than those of the oscillations taking place in air. Taking advantage of this fact, we have performed a detailed experimental characterization of the whipping instability of a charged micro-jet within a dielectric liquid by recording the jet motion with a high-speed camera. Appropriate image processing yields the frequency and wavelength, among the other important characteristics, of ...
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.
Instability of Elliptic Liquid Jets
Journal of Fluid Mechanics
INSTABILITY OF ELLIPTIC LIQUID JETS GHOBAD AMINI-BAZIANI The motion of liquid jets ejected from elliptical orifices is studied theoretically and experimentally. In the theoretical part of the study, the linear evolution of initially small disturbances on the inviscid jets is investigated using a three-dimensional analysis. In addition, to study the viscous free-surface flows, an approach based on the Cosserat theory (also called directed theory) is used. Temporal and spatial analyses are performed and the dispersion equations of waves on the jet column are derived to show the growth rate of disturbances for different modes under various conditions. An equation for the jet profile is suggested which describes the axis-switching phenomenon and breakup for various conditions. The equations are approximated for small and large ellipticities, and wellknown dispersion relations of circular and planar jets are retrieved. It is shown that in the xvi "The history of science teaches only too plainly the lesson that no single method is absolutely to be relied upon, that sources of error lurk where they are least expected, and that they may escape the notice of the most experienced and conscientious worker."
Study of instability of liquid jets under gravity
AIP Conference Proceedings, 2017
Breakup of water jets under gravity is a commonplace phenomenon. The role of surface tension in the instability of water jets was recognized by Rayleigh and the theory propounded goes by the name of Plateau-Rayleigh theory. The necks and bulges down along the jet-length that are created by perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the jet to breakup into drops. The effect of perturbation waves have been investigated experimentally and found to confirm the essentials of the theory. However, there is no unanimity about the origin of these perturbation waves. Recently, the idea of recoil capillary waves as an important source of the perturbation waves has been emphasized. The recoil of the end point of the remaining continuous jet at its breakup point is considered to travel upward as a recoil capillary wave which gets reflected at the mouth of the nozzle from which the jet originates. The reflected capillary wave travels along the jet downward with its Doppler shifted wavelength as a perturbation wave. We set up an experiment to directly verify the existence and effect of the recoil capillary waves and present some preliminary results of our experiment.