Oscillations of a rotating liquid drop

1984 ◽  
Vol 142 ◽  
pp. 1-8 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Surface Tension ◽  
Circular Polarization ◽  
Coriolis Force ◽  
Liquid Drop ◽  
Centrifugal Distortion ◽  
Axis Of Rotation ◽  
First Approximation ◽  
Rotating Liquid ◽  
Surrounding Fluid

The effect of rotation on the frequencies of oscillations of a liquid drop is investigated. It is assumed that the drop is imbedded in a fluid of the same or different density and that a constant surface tension acts on the interface. Rotation influences the oscillations through the Coriolis force and through the centrifugal distortion of the drop. For non-axisymmetric oscillations only the Coriolis force is important in first approximation and causes the expected splitting of the frequency for the two modes differing in their sign of circular polarization with respect to the axis of rotation. In the case of axisymmetric oscillations the centrifugal distortion and the Coriolis force combine to increase the frequency whenever the density ρi of the drop exceeds the density of ρ° of the surrounding fluid. For ρi < ρ° a decrease of the frequency of oscillation is possible for some modes of higher degree.

The stability of a rotating liquid drop

1965 ◽  
Vol 286 (1404) ◽  
pp. 1-26 ◽  
Keyword(s):  
Surface Tension ◽  
Liquid Drop ◽  
Remarkable Similarity ◽  
Interfacial Surface ◽  
Rotating Liquid ◽  
Figures Of Equilibrium ◽  
Dissipative Mechanism ◽  
Parameter Sequence ◽  
Neutral Mode ◽  
The Stability

In this paper, the stability of a rotating drop held together by surface tension is investigated by an appropriate extension of the method of the tensor virial. Consideration is restricted to axisymmetric figures of equilibrium which enclose the origin. These figures form a one parameter sequence; and a convenient parameter for distinguishing the members of the sequence is Σ = ρΩ 2 a 3 /8 T , where Ω is the angular velocity of rotation, a is the equatorial radius of the drop, ρ is its density, and T is the interfacial surface tension. It is shown that Σ ⩽ 2.32911 ( not 1 + √2 as is sometimes supposed) if the drop is to enclose the origin. It is further shown that with respect to stability, the axisym metric sequence of rotating drops bears a remarkable similarity to the Maclaurin sequence of rotating liquid masses held together by their own gravitation. Thus, at a point along the sequence (where Σ = 0.4587) a neutral mode of oscillation occurs without in stability setting in at that point (i.e. provided no dissipative mechanism is present); and the in stability actually sets in at a subsequent point (where Σ = 0.8440) by overstable oscillations with a frequency Ω. The dependence on Σ of the six characteristic frequencies, belonging to the second harmonics, is determined (tables 3 and 4) and exhibited (figures 3 and 4).

STABLE SPHEROIDAL CAP SHAPES OF DEPOSITED ATOMIC CLUSTERS

2010 ◽  
Vol 24 (17) ◽  
pp. 3411-3423 ◽  
Author(s):  
D. N. POENARU ◽  
R. A. GHERGHESCU ◽  
W. GREINER
Keyword(s):  
Surface Tension ◽  
Interaction Energy ◽  
Liquid Drop ◽  
Atomic Clusters ◽  
Liquid Drop Model ◽  
Analytical Results ◽  
Modified Surface

Neutral short and long spheroidal cap clusters have been investigated within the liquid drop model. Analytical results have been obtained for the deformation-dependent surface and curvature energies. A large variety of experimentally determined shapes (both oblate and prolate) are explained by simulating the interaction energy with the substrate with a modified surface tension of the base, and by changing the missing or extended height of the cap, d. The results are illustrated for Na 56 and Na 148 atomic clusters.

The influence of Coriolis force on surface-tension-driven convection

1966 ◽  
Vol 26 (4) ◽  
pp. 807-818 ◽  
Author(s):  
A. Vidal ◽  
Andreas Acrivos
Keyword(s):  
Surface Tension ◽  
Flow Pattern ◽  
Coriolis Force ◽  
Fluid Layer ◽  
Functional Relation ◽  
Wave Number ◽  
Neutral Stability ◽  
Uniform Rotation ◽  
Critical Marangoni Number ◽  
Deep Layers

The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc = 4·42T½ and ac = 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number.The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T > 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis.

scholarly journals In situoptical measurement of liquid drop surface tension in gas metal arc welding

1998 ◽  
Vol 31 (16) ◽  
pp. 1963-1967 ◽  
Author(s):  
S Subramaniam ◽  
D R White ◽  
D J Scholl ◽  
W H Weber
Keyword(s):  
Surface Tension ◽  
Arc Welding ◽  
Liquid Drop ◽  
Gas Metal Arc Welding ◽  
Drop Surface ◽  
Metal Arc Welding

Deformation of a Droplet in a Channel Flow

2008 ◽  
Vol 5 (4) ◽  
Author(s):  
Ebrahim Shirani ◽  
Shila Masoomi
Keyword(s):  
Surface Tension ◽  
Channel Flow ◽  
Polymer Electrolyte Membrane ◽  
Droplet Deformation ◽  
Navier Stokes Equation ◽  
Droplet Shape ◽  
Viscous Forces ◽  
Electrolyte Membrane ◽  
Wide Range ◽  
Surrounding Fluid

Formation of droplets especially in microchannels, micro-electro-mechanical systems (MEMS) and polymer electrolyte membrane fuel cells and their effects on the performance of these devises, as well as scientific aspect of the droplet behavior in the fluid flow motion, makes the subject of the droplet deformation and motion an attractive problem. In this work, we numerically simulate the deformation of a drop of water attached to the wall of a channel flow using full two-dimensional Navier–Stokes equation and the volume-of-fluid method for capturing the interface. The effects of channel inlet velocity, the density and viscosity of the surrounding fluid, and the surface tension coefficient on the flow structures both inside and outside of the droplet as well as the deformation of the droplets are examined. Several test cases, which cover rather wide range of the Reynolds and capillary numbers, based on the surrounding fluid properties and the diameter of the droplet are performed. The Reynolds number, Re, range is from 24 to 1800 and the capillary number, Ca, is from 0.014 to 0.219. It is found that the droplet shape changes and depending on the capillary and Reynolds numbers, it eventually reaches an equilibrium state when there is balance between the surface tension, inertia, and the viscous forces. It is also found that the deformation of the droplet does not depend on the capillary numbers, when Ca is small, but it is a strong function of Ca, when it is large.

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