Capillary Jet Research Articles

Magnetohydrodynamic stability of cylindrical liquid bridges under a uniform axial magnetic field

The effect of a uniform axial magnetic field on the stability of cylindrical liquid bridges of negligible viscosity and resistivity is examined in this paper, in the limit case when magnetic forces dominate inertia forces. The analysis yields the bifurcation curve and the growth factor in the neighborhood of the stability limit points as a function of two dimensionless parameters: Λ, the slenderness of the bridge and M, a nondimensional quantity proportional to the magnetic field. It is found that bridges of any slenderness can be stabilized by magnetic fields when M≳1/√2. The results are compared to those existing for capillary liquid jets, showing that the stability curves coincide and that the stabilizing effects are greater for liquid bridges than for infinite columns.

An Upper Bound on the Growth Rate of the Linear Instability in a Capillary Jet

An Upper Bound on the Growth Rate of the Linear Instability in a Capillary Jet

Induced capillary jet breakdown

A model is proposed for the induced capillary breakdown of a liquid jet with small surface tension and viscosity, on the basis of numerical solution of the quasione-dimensional equations of jet flow. The algorithm employed permits the description of flow from the source to the point of breakdown.

Decay of electrified rotating capillary jets

A study was made of the effect of electrification and rotation of the nonmono-disperse decay of capillary jets. The study was conducted within the framework of the complete system of equations of hydrodynamics by the Bubnov-Galerkin method.

Nonmonodisperse breakup of capillary jets in a variable electric field

The electrical charging of capillary jets has a strong influence on their stability [1–10]. Well-known theoretical studies have been devoted to the linear [1–6], weakly linear [7], or finite-amplitude [10] stability of such jets in a constant electric field. In the present paper, an investigation is made in the framework of the full nonlinear equations. The main attention is devoted to effects associated with allowance for a time-variable electric field. It is shown that a sharp decrease of the surface charge may lead to an appreciable decrease in the size of the satellite droplets; allowance for the long-wavelength background also leads to a decrease in the size of the satellite droplets. In contrast, a sharp increase of the surface charge increases the relative contribution of the satellite droplets. At the same time, introduction of small-scale “background” perturbations can lead to a decrease in the contribution of the fine satellite droplets and to a weakening of their reaction to a rapidly increasing electric field. It is shown that the degree of monodisperseness can be increased by a relatively slowly varying electric field. An “averaged” effect of an electric field that varies rapidly in time is found. Appreciable increase of the initial perturbation amplitude in the case of a periodically varying electric field can lead to an appreciable increase in the degree of monodisperseness. The introduction of short-wavelength perturbations in a periodic electric field with large amplitude of the pulsations can lead to disappearance of the satellite droplets.

Control of Surface Tension Flows: Instability of a Liquid Jet

A technique of controlling surface tension flows using thermal radiation is proposed. This method takes advantage of the dependence on temperature of the surface tension forces to produce the desired controlling effects. In this research, a capillary water jet is taken as an example of a surface tension dominated flow. The ability to cancel a preexisting unstable perturbation is demonstrated. First an acoustical disturbance that dominates the naturally occurring perturbations is applied to the jet. This causes jet breakup at a shorter and constant distance from the orifice. Next, a CO2 laser beam, modulated at the same frequency as the primary disturbance, is focused on the surface of the jet. By proper adjustment of intensity and phase the two perturbations cancel each other and the natural breakup of the jet is recovered. The influences of phase and intensity mismatches were tested and are reported. In addition to its application to delaying breakup of capillary jets, this technique is a promising method of controlling both suface tension driven flows and instabilities in different industrial applications.

Satellite formation in capillary jet breakup

Computations of finite-amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh’s linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near-linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.

A nonlinear theory for describing the propagation of disturbances on a capillary jet

The problem of the growth of disturbances on a capillary jet has received much attention in the past. However, previous theories have produced only limited correlation with experimental evidence. Traditional perturbation approaches to the problem are not well suited to describing the highly nonlinear behavior of disturbances on a capillary jet, especially near the tip of the jet where it breaks up into isolated drops. On the other hand, numerical solutions necessitate the use of an extremely fine spatial resolution over a large extent to follow disturbances as they progress along the jet and grow in amplitude over several orders of magnitude. In this paper, a new approach to this well-studied problem is described. The new approach is based on a weighted residual technique and takes advantage of the particular strengths of both analytical and numerical methods. The method is shown to correctly predict many of the nonlinear phenomena observed on actual jets and offers some fresh insight into the dynamical processes taking place within the jet.

Stationary flow of composite capillary jets

Stationary flow of composite capillary jets

The effect of a vertical magnetic field on the capillary instability of a liquid—liquid jet

The effect of a vertical magnetic field on the capillary instability of a liquid jet in axial motion and its break-up in another liquid medium is investigated, and two cases are considered. The first one when the fluids inside and outside the cylinder jet are moving at equal axial velocities, and the second when there is a small gradient present between the axial velocities of the inner and outer fluid. In the first case it is found that the vertical magnetic field has a stabilizing effect on the capillary jet flow, while the second one shows a destabilizing role for the axial velocities gradient, which leads to a decrease in the jet length and diminished droplets produced by the jet disintegration process.

Instability and fractionation of two-layer capillary jets

Instability and fractionation of two-layer capillary jets

A numerical comparison of one-dimensional fluid jet models applied to drop-on-demand printing

This paper presents a numerical simulation of capillary jets motivated by the study of dropon-demand ink-jet printing. Two sets of 1-dimensional equations for an inviscid axisymmetric fluid jet are integrated using a numerical scheme suggested by MacCormack's predictor-corrector algorithm. The difference between the two sets of equations is the inclusion or exclusion of the terms that account for radial inertia. When these terms are included the numerical scheme necessary to solve the equations is more complicated. The results from both schemes are, presented for three Weber numbers with a simplified nozzle entry pressure history that has been converted to a velocity history at the nozzle exit by a momentum integral applied to the nozzle region. The results indicate that at higher Weber numbers the omission of radial inertia has a greater effect on the drop profiles than at lower Weber numbers. The conditions under which each numerical scheme might be a useful simulation are also discussed.

Instability of capillary jets with thermocapillarity

Long axisymmetric liquid zones are subject to axial temperature gradients which induce steady viscous flows driven by thermocapillarity. The approximately parallel flow in a cylindrical zone is examined for linearized instabilities. Capillary, surfacewave and thermal modes are found. Capillary breakup can be retarded or even suppressed for small Prandtl number and large Biot number B, which measures heat transfer from the liquid to the surrounding atmosphere. In the limiting case B → ∞ the zone becomes an isothermal jet subject to axial ‘wind stress’ on its interface. It is then possible to suppress capillary breakup entirely so that one can maintain long coherent jets.

One-dimensional linear analysis of the compound jet

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges)

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 peturbation is found to depend on the elative effects of surface tension and intertia 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 esults obtained are found to give a good description of the essential features of the breakup phenomenon of such jets.

Elastic stresses in capillary jets of dilute polymer solutions

The elastic longitudinal stresses associated with the flow of jets of dilute polymer solutions from a short nozzle and their effect on the stability of the free jet are investigated theoretically and experimentally. The results obtained make it possible to take a fresh look at the ways in which a polymer additive affects the stability of high-velocity capillary jets.

Flow of a free jet of rheologically complex fluid from a vibrating capillary

The propagation of finite-amplitude waves along a vibrating capillary jet is studied. The standing wave equation is derived.

Effect of deformation conditions of fibre-formation in spinning from heterogeneous mixtures of polymers

Capillary diameter, shear stress, and jet stretch all affect the phenomenon of specific fibre formation in extrudates of the mixtures POM-copolyamide 548, POM-polystyrene, POM-ethylene-vinyl acetate copolymer, POM-polyvinyl alcohol, and low-pressure polyethylene-copolyamide 548.

Stability of capillary cylindrical jets in external flow

The stability of cylindrical capillary jets is studied, when the surrounding medium has both axial and tangential velocity components in the undisturbed state; viscosity is neglected in both fluids. It is shown that non axisymmetric disturbances can be unstable. When the external flow is purely axial, the highest growth rate is obtained for axisymmetric disturbances, but for large enough tangential velocities of the surrounding medium the dominant disturbances are proportional to exp(inθ) withn>0.

Hydrodynamic instability of the axisymmetric flow of an ideal fluid with an interphase

We study the instability under simultaneous rotational and translational flow of a fluid and ambient medium in the cases of a cylindrical annular jet, capillary jet, and cylindrical fluid layers on the inner and outer surfaces of a cylinder.