Unforced Rayleigh instability of an immersed liquid jet (original) (raw)
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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).
Chemical Engineering Science, 2015
This work investigates the effects of multiple jet interactions and single jet instability on jet breakup and droplet size using experimental and computational techniques. In particular, the jet separation distance, jet breakup length and droplet diameter were measured as a function of initial nozzle separation distance and jet volumetric flow rate. It was found that the two jets moved closer to each other to reach an equilibrium separation distance that was approximately 70% of the spacing between the two nozzles. The distance at which the instabilities were first observed on the surface of the jet was also a function of the initial separation distance. However, it was weakly dependent on the jet velocity. The jet breakup length and resultant droplet diameter were both influenced by flow rate and nozzle separation distance. The jet breakup length was found to decrease with reduction in nozzle spacing at the high flow rates. Interestingly, a linear relationship between droplet diameter and breakup length was found that was largely independent of nozzle spacing and consist with conventional Rayleigh jet breakup theory. The implications of the experimental observations on the design of multi-jet systems are discussed. Furthermore, computational fluid dynamics simulations were also used to identify the mechanism and dynamics of jet instability in the single jet systems. The simulation results were analysed to study the effect of instability on various parameters such as jet breakup, droplet formation and size of emulsion droplets. It was found that at higher volumetric flow rates, the droplets size increased during the jet breakup due to an asymmetric instability. The asymmetric instability was caused by the pressure gradient in the continuous phase and was prevented in double jet systems.
Liquid Jet Stability in a Laminar Flow Field
Chemical Engineering & Technology, 2002
The breakup of a Newtonian liquid jet into droplets injected horizontally into another flowing immiscible Newtonian fluid was studied experimentally under creeping flow conditions. Different breakup mechanisms take place in different flow regions. No filament is generated at very low velocities of the continuous phase when the droplets peel off directly at the nozzle tip. As soon as the flow rate of the continuous phase exceeds a critical value, a filament of a characteristic length begins to grow. The filament breaks up due to instabilities in terms of developing interfacial waves. The laminar breakup length of the filament is found to correlate with the flow rates of both phases and their viscosity ratio. The impact of the capillary diameter, through which the disperse phase is injected, on the filament length was investigated and the maximum droplet size was estimated.
Influence of viscosity on the capillary instability of a stretching jet
Journal of Fluid Mechanics, 1987
The hydrodynamic stability of a rapidly elongating, viscous liquid jet such as obtained in shaped charges is presented. The flow field depends on three characteristic timescales associated with the growth of perturbations (due esaentially to the effect of the surface tension), the elongation of the jet, and the inward diffusion of vorticity from the free surface, respectively. The latter process introduces a time lag resulting in the current values of the free-surface perturbation and its time derivative being a function of their past history. Solutions of the integro-differential equation for the evolution of disturbances exhibit a novel dual role played by the viscosity : besides the traditional damping effect it is associated with a destabilizing mechanism in the elongating jet. The wavelength of maximum instability is also a function of time elapsed since the jet formation, longer wavelengths becoming dominant at later stages. Understanding of these instability processes can help in both promoting and delaying instability as required by specific applications.
Instability of a liquid jet emerging from a droplet upon collision with a solid surface
Physics of Fluids, 2000
A linear perturbation theory is developed to investigate the interface instabilities of a radially-expanding, liquid jet in cylindrical geometries. The theory is applied to rapidly spreading droplets upon collision with solid surfaces as the fundamental mechanism behind splashing. The analysis is based on the observation that the instability of the liquid sheet, i.e., the formation of the fingers at the spreading front, develops in the extremely early stages of droplet impact. The shape evolution of the interface in the very early stages of spreading is numerically simulated based on the axisymmetric solutions obtained by a theoretical model. The effects that factors such as the transient profile of an interface radius, the perturbation onset time, and the Weber number have on the analysis results are examined. This study shows that a large impact inertia, associated with a high Weber number, promotes interface instability, and prefers high wave number for maximum instability. The numbers of fingers at the spreading front of droplets predicted by the model agree well with those experimentally observed.
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.
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.