Instability Of Capillary Jets Research Articles

A nonlinear analysis of the effect of heat transfer on capillary jet instability

Breakup of slender liquid jets under isothermal conditions has been studied extensively. In this work, we investigate the breakup of a viscous jet emanating from an orifice in the presence of convective heat transfer. We study the case where heat is transferred from the jet to the ambient fluid. The temperature varies axially and both viscosity and surface tension are taken to be temperature dependent. Marangoni stresses caused by a thermally induced surface tension gradient are included here. A numerical model based on a one-dimensional slender jet approximation of the equations of motion and heat transfer is used. This results in three coupled nonlinear partial differential equations, which are solved using the method of lines. The advantages of using this approximation lie in (i) its computational elegance and (ii) the physical insight that it provides. We compare the model predictions of both spatial and temporal stability analysis with experiments of a jet of molten Woods metal in water. Molten Woods metal emanating from various orifice diameters (1-10 mm) into water under the action of gravity is analysed for drop sizes and these are compared with the numerical predictions. The presence of heat transfer is found to shorten the breakup length of the jet. This is attributed to the increase in surface tension induced by the heat loss from jet to the ambient. It is found that including the effect of temperature dependence of viscosity and surface tension, however, does not affect the drop size. A critical dimensionless number (Π1 ∼ 10) is found to exist beyond which the breakup is dominated by Marangoni stresses. Below this critical number, the jet breaks up due to the combined effects of the capillary force and the Marangoni stresses. It is shown that including the effect of gravity is necessary to predict the drop size accurately. The results of this work have implications in evaluating safety strategies in the event of a core disruptive accident in a nuclear reactor. A wider application of this analysis is in improving the efficiency of thermally modulated inkjet printing.

Spatiotemporal instability of a confined capillary jet

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.

Effect of initial disturbance amplitude in gravity affected jet break-up

The initial disturbance amplitude has an effect on stretching jets that is not observed for capillary jet instability where gravitational acceleration is not significant. For inviscid and viscous fluids, gravity diminishes the effect that the initial amplitude has on jet length and its ability to prevent satellite formation. In stretching jets, not only the dimensionless frequency of the disturbance but also its initial amplitude must be known to properly study their satellite forming nature. Indirect methods of relating the applied disturbance energy to an initial velocity perturbation are not simple when the gravity parameter G is changing. When G ≠ 0 , the optimum disturbance frequency Ω opt and the initial disturbance amplitude are related, with Ω opt ∝ f ( G ) × ln ( 1 / ε v ) . Results from numerical simulations and experiments are presented here.

Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Froude number. The optimum disturbance frequency Ωopt was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between Ωopt and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability.

Dynamic surface tension measurements with submillisecond resolution using a capillary-jet instability technique.

An oscillating capillary jet method is implemented to measure surface tension of aqueous nonionic surfactant solutions as a function of surface age from the jet orifice. The experimental technique captures the evolution of jet swells and necks continuously along the jet propagation axis and is used in conjunction with an existing linear, axisymmetric, constant-property model to determine surface tension of liquids. The method is first validated using deionized water and isopropyl alcohol (constant surface tension test fluids) and a procedure is described to identify the optimum wavelength from the breakup point, which produces the smallest error in surface tension measurements. Dynamic surface tension data of concentrated aqueous Tergitol NP-8 surfactant solutions is then presented. The measurements are performed over a spatial length of approximately 1.5 wavelengths, a span corresponding to 0.6-4.2 ms time window from the jet orifice. Submillisecond surface age measurements are made possible by decreasing the jet diameter. Increased surfactant concentrations make the liquid jet more stable and allow measurements at higher surface ages. The correlation of Hua and Rosen fits well the dynamic surface tension data, which includes submillisecond surface ages. Finally, the time required for surface tension to reach equilibrium levels is estimated using a simple adsorption kinetics theory of surfactant molecules on the liquid/air interface.

Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Froude number. The optimum disturbance frequency Ω opt was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between Ω opt and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability.

Quantitative liquid jet instability measurement system using asymmetric magnification and digital image processing

A new technique for measuring the growth of instabilities on the surface of liquid jets flowing into gas is demonstrated. A collimated beam of white light illuminates the jet from behind, forming a shadow image. A pair of cylindrical lenses are arranged to provide different magnifications in the streamwise and cross-stream directions. A number of streamwise diameters and one cross-stream diameter are thus captured with maximum resolution in a single image on a charge-coupled device (CCD) electronic camera. A short-duration spark is used to freeze the jet motion. A mask representing the theoretical edge-response of the imaging system is digitally convolved with the cross-stream gray scale data to obtain sub-pixel resolution of the jet edge profile. The method is demonstrated using the well-known capillary jet instability and a ratio of streamwise to cross-stream magnifications of 40. Well-resolved single images show the development of the instability from small perturbations through the formation of the first drop. The system forms an accurate automated method of measuring the development of liquid jet instabilities. It can readily be applied to practical problems including liquid jet atomization.

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.

Flow and instability of capillary jets interacting with the surrounding medium

The flow of an axially symmetric capillary jet of a viscous incompressible liquid in the space occupied by another liquid is investigated. The problem of stationary flow in the jet and in the surrounding medium under the action of viscosity, capillary forces, and gravity was obtained numerically. The instability problem of this flow to small perturbations in the form of running waves is stated and solved numerically. The values of the dimensionless Reynolds, Weber, and Froude numbers are explained, as well as the effect of the initial velocity profile in the jet, its instability, and subsequent jet decay into drops.

The instability of capillary jets

At high jet velocity the aerodynamic interaction between a capillary jet and the surrounding medium leads to an enhanced growth rate of axisymmetric disturbances. The available theories which account for this effect fail to agree with experimental observations. The difference is attributed, in part, to the relaxation of the velocity profile in jets formed by fully developed laminar pipe flow. The profile relaxation has a destabilizing effect just as does the aerodynamic interaction. In the absence of velocity-profile relaxation it is shown that the available theories overestimate the aerodynamic effect. A consideration of the viscosity of the ambient fluid yields a semi-empirical modification to the theory which shows good agreement with experimental values.

XL.Instability of liquid jets

Summary The degree of instability of capillary jets is examined experimentally. Spark photographs produced under varying conditions are included, from which measurement of the size and spacing of the drops formed at the end of the jet enables a comparison with theory to be made.