Influence of viscosity on the capillary instability of a stretching jet

1987 ◽  
Vol 185 ◽  
pp. 361-383 ◽  
Author(s):  
I. Frankel ◽  
D. Weihs
Keyword(s):  
Differential Equation ◽  
Surface Tension ◽  
Free Surface ◽  
Flow Field ◽  
Past History ◽  
Time Lag ◽  
Time Derivative ◽  
Liquid Jet ◽  
Jet Formation ◽  
Damping Effect

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 essentially 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 and breakup of charged liquid jets

1971 ◽  
Vol 49 (2) ◽  
pp. 361-372 ◽  
Author(s):  
A. L. Huebner ◽  
H. N. Chu
Keyword(s):  
Differential Equation ◽  
Surface Tension ◽  
Physical Properties ◽  
Small Perturbation ◽  
Perturbation Analysis ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Drop Diameter ◽  
Breakup Process ◽  
Electric Effects

Drops formed from the breakup of charged cylindrical liquid jets have been shown to be smaller than those formed in the unelectrified case. This change has been related to electrically induced instabilities on the jet. Small-perturbation analysis was used to formulate the Lagrangian and write the differential equation for the jet. Non-dimensionalized plots of the solutions exhibit the stabilizing or destabilizing influences of surface tension and electric effects, and allow these influences to be related back to liquid physical properties. Drop diameter to be expected from breakup of the electrified jet was calculated as a function of jet diameter, physical properties of the liquid, jet electrification, and the mode of instability dominating the breakup process.

Numerical Simulation of Electrostatic Atomization in Spindle Mode

2010 ◽  
Author(s):  
Mohammad Passandideh Fard ◽  
Mohammad Reza Mahpeykar ◽  
Sajad Pooyan ◽  
Mortaza Rahimzadeh
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Stable State ◽  
Surface Shape ◽  
Liquid Jet ◽  
Perfect Conductor ◽  
Electric Force ◽  
Electrostatic Atomization ◽  
Liquid Free Surface

The behavior of a liquid jet in an electrostatic field is numerically simulated. The simulations performed correspond to a transient liquid jet leaving a capillary tube maintained at a high electric potential. The surface profile of the deforming jet is defined using the VOF scheme and the advection of the liquid free surface is performed using Youngs’ algorithm. Surface tension force is treated as a body force acting on the free surface using continuum surface force (CSF) method. To calculate the effect of the electric field on the shape of the free surface, the electrostatic potential is solved first. Next, the surface density of the electric charge and the electric field intensity are computed, and then the electric force is calculated. Liquid is assumed to be a perfect conductor, thus the electric force only acts on the liquid free surface and is treated similar to surface tension using the CSF method. To verify the simulation results, a simplified case of electrowetting phenomenon is simulated and free surface shape in stable state is compared with experimental results. Then the electrostatic atomization in spindle mode is simulated and the ability of the developed code to simulate this process is demonstrated.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

scholarly journals Unsteady flow induced by a withdrawal point beneath a free surface

2005 ◽  
Vol 47 (2) ◽  
pp. 185-202 ◽  
Author(s):  
T. E. Stokes ◽  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Unsteady Flow ◽  
Critical Values ◽  
The Other ◽  
Withdrawal Rate ◽  
Steady Solutions

AbstractThe unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

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