scholarly journals The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170050 ◽  
Author(s):  
Christopher C. Green ◽  
Christopher J. Lustri ◽  
Scott W. McCue
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Bubble Velocity ◽  
Number Of Solutions ◽  
Branch Number ◽  
Single Solution ◽  
Countably Infinite ◽  
Prime Function ◽  
Hele Shaw Cell ◽  
Effect Of Surface

New numerical solutions to the so-called selection problem for one and two steadily translating bubbles in an unbounded Hele-Shaw cell are presented. Our approach relies on conformal mapping which, for the two-bubble problem, involves the Schottky-Klein prime function associated with an annulus. We show that a countably infinite number of solutions exist for each fixed value of dimensionless surface tension, with the bubble shapes becoming more exotic as the solution branch number increases. Our numerical results suggest that a single solution is selected in the limit that surface tension vanishes, with the scaling between the bubble velocity and surface tension being different to the well-studied problems for a bubble or a finger propagating in a channel geometry.

The motion of a viscous drop sliding down a Hele-Shaw cell

1986 ◽  
Vol 163 ◽  
pp. 59-67 ◽  
Author(s):  
Kalvis M. Jansons
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Contact Angle Hysteresis ◽  
Leading Edge ◽  
Governing Equations ◽  
Drop Shape ◽  
Viscous Drop ◽  
Special Case ◽  
Hele Shaw Cell ◽  
Effect Of Surface

The motion of a viscous drop in a vertical Hele-Shaw cell is studied in a limit where the effect of surface tension through contact-angle hysteresis is significant. It is found that a rectangular drop shape is a possible steady solution of the governing equations, although this solution is unstable to perturbations on the leading edge. Even though the unstable edge is one where a viscous fluid is moving into a less viscous fluid, in this case air, this is shown to be a special case of the well-known Saffman—Taylor instability. An experiment is performed with an initially circular drop in which it is observed that the drop shape becomes approximately rectangular except at the leading edge, where it becomes rounded and sometimes has a ragged appearance.A drop sliding down a vertical Hele-Shaw cell is an example of a system where the action of surface tension is not always one of smoothing, since in this case it leads to the formation of right-angle corners at the back of the drop (rounded only slightly on the lengthscale of the gap thickness of the cell).

scholarly journals The effect of surface tension on the shape of fingers in a Hele Shaw cell

1981 ◽  
Vol 102 ◽  
pp. 455-469 ◽  
Author(s):  
J. W. McLean ◽  
P. G. Saffman
Keyword(s):  
Surface Tension ◽  
Experimental Results ◽  
Two Dimensional ◽  
Singular Perturbation Analysis ◽  
Linearized Stability ◽  
Finger Width ◽  
The Stability ◽  
Hele Shaw Cell ◽  
Effect Of Surface ◽  
Small Disturbances

The experimental results of Saffman & Taylor (1958) and Pitts (1980) on fingering in a Hele Shaw cell are modelled by two-dimensional potential flow with surface-tension effects included at the interface. Using free streamline techniques, the shape of the free surface is expressed as the solution of a nonlinear integro-differential equation. The equation is solved numerically and the solutions are compared with experimental results. The shapes of the profiles are very well predicted, but the dependence of finger width on surface tension is not quantitatively accurate, although the qualitative behaviour is correct. A conflict between the numerics and a formal singular perturbation analysis is noted but not resolved. The stability of the steady finger to small disturbances is also examined. Linearized stability analysis indicates that the two-dimensional fingers are not stabilized by the surface-tension effect, which disagrees with the experimental observations. A possible reason for the discrepancy between theory and experiment is suggested.

DECOUPLING THE EFFECT OF SURFACE TENSION AND VISCOSITY ON SPRAY CHARACTERISTICS UNDER DIFFERENT AMBIENT PRESSURES: NEAR-NOZZLE BEHAVIOR AND MACROSCOPIC CHARACTERISTICS

2019 ◽  
Vol 29 (7) ◽  
pp. 629-654
Author(s):  
Zehao Feng ◽  
Shangqing Tong ◽  
Chenglong Tang ◽  
Cheng Zhan ◽  
Keiya Nishida ◽  
...  
Keyword(s):  
Surface Tension ◽  
Spray Characteristics ◽  
Effect Of Surface

Surfactant Impurities Can Explain the Jones-Ray Effect

2018 ◽  
Author(s):  
Timothy Duignan ◽  
Marcel Baer ◽  
Christopher Mundy
Keyword(s):  
Surface Tension ◽  
Electrostatic Potential ◽  
Driving Forces ◽  
Salt Water ◽  
Fundamental Property ◽  
Apparent Contradiction ◽  
Low Salt ◽  
Air Water Interface ◽  
Added Salt ◽  
Effect Of Surface

<div> <p> </p><div> <div> <div> <p>The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration the surface tension decreases in apparent contradiction with thermodynamics. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we show that this surface tension decrease can be explained by surfactant impurities in water that create a substantial negative electrostatic potential at the air-water interface. This potential strongly attracts positive cations in water to the interface lowering the surface tension and thus explaining the signature of the Jones-Ray effect. At higher salt concentrations, this electrostatic potential is screened by the added salt reducing the magnitude of this effect. The effect of surface curvature on this behavior is also examined and the implications for unexplained bubble phenomena is discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces. </p> </div> </div> </div> </div>

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

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