Existence of a Surface Tension Discontinuity at a Liquid Free Surface

Nature ◽  
1968 ◽  
Vol 217 (5128) ◽  
pp. 536-538 ◽  
Author(s):  
R. H. J. SELLIN
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Free Surface

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.

A Thermocapillary Convection Experiment in Microgravity

1995 ◽  
Vol 117 (3) ◽  
pp. 611-618 ◽  
Author(s):  
Y. Kamotani ◽  
S. Ostrach ◽  
A. Pline
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Temperature Distribution ◽  
Laser Beam ◽  
Thermocapillary Convection ◽  
Silicone Oil ◽  
Free Surfaces ◽  
Numerical Predictions ◽  
Liquid Free Surface ◽  
Infrared Imager

Results are reported of the Surface Tension Driven Convection Experiment (STDCE) aboard the USML-1 Spacelab, which was launched on June 25, 1992. In the experiment, 10 cSt silicone oil was placed in an open 10-cm-dia circular container, which was 5 cm deep. The fluid was heated either by a cylinderical heater (1.11 cm diameter) located along the container centerline or by a CO2 laser beam to induce thermocapillary flow. Several thermistor probes were placed in the fluid to measure the temperature distribution. The temperature distribution along the liquid-free surface was measured by an infrared imager. Tests were conducted over a range of heating powers, laser-beam diameters, and free surface shapes. An extensive numerical modeling of the flow was conducted in conjunction with the experiments. Some results of the temperature measurements with flat free surfaces are presented in this paper and they are shown to agree well with the numerical predictions.

Numerical Simulation of Cone Formation in Electrospraying Process

2010 ◽  
Author(s):  
Mohammad Passandideh-Fard ◽  
Mortaza Rahimzadeh ◽  
Sajad Pooyan
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Electric Field ◽  
Capillary Tube ◽  
Surface Profile ◽  
Surface Tension Force ◽  
Transient Behavior ◽  
Perfect Conductor ◽  
Electric Force ◽  
Liquid Free Surface

A numerical model is developed to study the transient behavior of a liquid jet leaving a capillary tube under an electrostatic field. The surface profile of the deforming jet is defined using the Volume-of-Fluid (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 that of surface tension using the CSF method. The developed model is validated by a comparison between the calculated results and measurements for an electrowetting scenario for which experimental results are available in the literature.

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.

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