Vibration of a liquid with a free surface in a spinning spherical tank

1981 ◽  
Vol 76 (1) ◽  
pp. 83-93 ◽  
Author(s):  
M. El-Raheb ◽  
P. Wagner
Keyword(s):  
Free Surface ◽  
Spherical Tank

Analytically approximate natural sloshing modes for a spherical tank shape

2012 ◽  
Vol 703 ◽  
pp. 391-401 ◽  
Author(s):  
Odd M. Faltinsen ◽  
Alexander N. Timokha
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Laplace Equation ◽  
Three Dimensional ◽  
Analytical Continuation ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Spherical Tank ◽  
The Mean ◽  
Multimodal Method

AbstractThe multimodal method requires analytical (exact or approximate) natural sloshing modes that exactly satisfy the Laplace equation and boundary condition on the wetted tank surface. When dealing with the nonlinear sloshing problem, the modes should also allow for an analytical continuation throughout the mean free surface. Appropriate analytically approximate modes were constructed by Faltinsen & Timokha (J. Fluid Mech., vol. 695, 2012, pp. 467–477) for the two-dimensional circular tank. The present paper extends this result to the three-dimensional, spherical tank shape and, based on that, establishes specific properties of the linear liquid sloshing.

On the role of tin underlays for the prevention of thermal grooving in thin gold films

1986 ◽  
Vol 44 ◽  
pp. 732-733
Author(s):  
Jin Young Kim ◽  
R. E. Hummel ◽  
R. T. DeHoff
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Grain Boundary ◽  
Beneficial Effect ◽  
Failure Mechanism ◽  
Failure Mechanisms ◽  
Distinct Advantage ◽  
Gold Films ◽  
Gold Thin Film

Gold thin film metallizations in microelectronic circuits have a distinct advantage over those consisting of aluminum because they are less susceptible to electromigration. When electromigration is no longer the principal failure mechanism, other failure mechanisms caused by d.c. stressing might become important. In gold thin-film metallizations, grain boundary grooving is the principal failure mechanism.Previous studies have shown that grain boundary grooving in gold films can be prevented by an indium underlay between the substrate and gold. The beneficial effect of the In/Au composite film is mainly due to roughening of the surface of the gold films, redistribution of indium on the gold films and formation of In2O3 on the free surface and along the grain boundaries of the gold films during air annealing.

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