Numerical Study of the Nonlinear Instability of a Compound Capillary Jet Including the Effect of the Discontinuity of the Undisturbed Axial Velocity (original) (raw)

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).

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.

The study of the behaviour of a disturbed semi-infinite liquid jet using a spatial instability method

Fluid Dynamics Research, 2001

A study has been made of the behaviour of a disturbed semi-inÿnite liquid jet using a spatial instability method. A sinusoidal disturbance in the axial component of jet velocity at the nozzle is considered which resulted in an elliptic free surface boundary value problem with two non-linear boundary conditions. The system is linearised using perturbation techniques and the ÿrst order solution resulted in the dispersion relation. The jet stability is found to depend explicitly on the frequency of the disturbance and the Weber number. The second and third order solutions have been derived analytically which are used to predict on jet break-up and satellite formation.

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.

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.

Unforced Rayleigh instability of an immersed liquid jet

E3S Web of Conferences

Motivated by the occurrence of the injection of liquids in various technical processes, we study the capillary instability of a liquid jet surrounded by another liquid. The study focuses on the natural developing Rayleigh instability, hence without an imposed perturbation. We also point out the influence of viscosity on the main drop diameter, resulted after jet breakup, and on the breakup length itself. Modifications brought by a decrease of the capillary nozzle are also emphasized for a particular case.

Weakly nonlinear instability of a Newtonian liquid jet

Journal of Fluid Mechanics, 2018

A weakly nonlinear stability analysis of an axisymmetric Newtonian liquid jet is presented. The calculation is based on a small-amplitude perturbation method and performed to second order in the perturbation parameter. The obtained solution includes terms derived from a polynomial approximation of a viscous contribution containing products of Bessel functions with different arguments. The use of such an approximation is not needed in the inviscid case and the planar case, since the equations of those problems can be solved in an exact form. The developed model depends on three dimensionless parameters: the initial perturbation amplitude, the perturbation wavenumber and the liquid Ohnesorge number, the latter being the dimensionless liquid viscosity. The influence of the approximate terms was shown to be relatively small for a large range of Ohnesorge numbers so that they can be ignored. This simplification provides a jet model as simple to use as the previous ones, but taking into a...

Analytical description of the breakup of liquid jets

Journal of Fluid Mechanics, 1995

A viscous or inviscid cylindrical jet with surface tension in a surrounding medium of negligible density tends to pinch owing to the mechanism of capillary instability. We construct similarity solutions which describe this phenomenon as a critical time is encountered, for three distinct cases: (i) inviscid jets governed by the Euler equations, (ii) highly viscous jets governed by the Stokes equations, and (iii) viscous jets governed by the Navier-Stokes equations. We look for singular solutions of the governing equations directly rather than by analysis of simplified models arising from slender-jet theories. For Stokes jets implicitly defined closed-form solutions are constructed which allow the scaling exponents to be fixed. Navier-Stokes pinching solutions follow rationally from the Stokes ones by bringing unsteady and nonlinear terms into the momentum equations to leading order. This balance fixes a set of universal scaling functions for the phenomenon. Finally we show how the pi...