Steady circular hydraulic jump on a rotating disk

The paper deals with the steady axially symmetric flow of a viscous liquid layer over a rotating disk. The liquid is fed near the axis of rotation and spreads due to inertia and the centrifugal force. The viscous shallow-water approach gives a system of ordinary differential equations governing the flow. We consider inertia, gravity, centrifugal and Coriolis forces and estimate the effect of surface tension. We found four qualitatively different flow regimes. Transition through these regimes shows the continuous evolution of the flow structure from a hydraulic jump on a static disk to a monotonic thickness decrease on a fast rotating one. We show that, in the absence of surface tension, the intensity of the jump gradually vanishes at a finite distance from the axis of rotation while the angular velocity increases. The surface tension decreases the jump radius and destroys the steady solution for a certain range of parameters.

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The existence of axially symmetric flow above a rotating disk

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1971.0146 ◽

1971 ◽

Vol 324 (1559) ◽

pp. 391-414 ◽

Cited By ~ 23

Keyword(s):

Fixed Point ◽

Angular Velocity ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Existence Of Solutions ◽

Rotating Disk ◽

Fixed Point Method ◽

Axially Symmetric ◽

Symmetric Flow ◽

Shooting Technique

The paper studies the boundary-value problem arising from the behaviour of a fluid occupying the half space x > 0 above a rotating disk which is coincident with the plane x = 0 and rotates about its axis which remains fixed. The equations which describe axially symmetric solutions of this problem are f ''' + ff ''+½( g 2 – f ' 2 ) = ½ Ω 2 ∞ , g "+ fg ' = f ' g , with the boundary conditions f (0) = a , f '(0) = 0, g (0) = Ω 0 ); f '(∞) = 0, g (∞) = Ω ∞ , where a is a constant measuring possible suction at the disk, Ω 0 is the angular velocity of the disk, and Ω ∞ is an angular velocity to which the fluid is subjected at infinity. When Ω ∞ = 0, existence of solutions has previously been proved by the ‘shooting technique’. This method breaks down when Ω 0 ǂ 0 because of oscillations in the functions f and g , but in the present paper existence is first proved by a fixed point method when Ω 0 is close to Ω ∞ and then extended for all Ω 0 , with the important restriction that Ω 0 and Ω ∞ be of the same sign.

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Rising bubbles

Journal of Fluid Mechanics ◽

10.1017/s0022112082002936 ◽

1982 ◽

Vol 123 ◽

pp. 31-41 ◽

Cited By ~ 25

Author(s):

Michael J. Miksis ◽

Jean-Marc Vanden-Broeck ◽

Joseph B. Keller

Keyword(s):

Surface Tension ◽

Normal Component ◽

Tangential Component ◽

Algebraic Equations ◽

Axially Symmetric ◽

Viscous Stress ◽

Rising Bubble ◽

Tangential Traction ◽

Surrounding Fluid ◽

Effect Of Surface

The shape of a rising bubble, or of a falling drop, in an incompressible viscous fluid is computed numerically, omitting the condition on the tangential traction at the bubble or drop surface. When the bubble is sufficiently distorted, its top is found to be spherical and its bottom is found to be rather flat. Then the radius of its upper surface is in fair agreement with the formula of Davis & Taylor (1950). This distortion occurs when the effect of gravity is large while that of surface tension is small. When the effect of surface tension is large, the bubble is nearly a sphere.The shape is found, together with the flow of the surrounding fluid, by assuming that both are steady and axially symmetric, with the Reynolds number being large. The flow is taken to be a potential flow. The boundary condition on the normal component of normal stress, including the viscous stress, is satisfied, but not that on the tangential component. The problem is converted into an integro-differential set of equations, reduced to a set of algebraic equations by a difference method, and solved by Newton's method together with parameter variation.

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

Atomization and Sprays ◽

10.1615/atomizspr.2019030936 ◽

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

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The effect of surface tension on melt ejection during micron-size laser spot welding

International Congress on Applications of Lasers & Electro-Optics ◽

10.2351/1.5060388 ◽

2004 ◽

Author(s):

V. V. Semak ◽

G. A. Knorovsky ◽

D. O. MacCallum

Keyword(s):

Surface Tension ◽

Spot Welding ◽

Laser Spot ◽

Micron Size ◽

Laser Spot Welding ◽

Effect Of Surface ◽

Melt Ejection

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Surfactant Impurities Can Explain the Jones-Ray Effect

10.26434/chemrxiv.5732976 ◽

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>

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