The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. I
22 Mar 1950-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 201, Iss: 1065, pp 192-196
TL;DR: In this article, it was shown that when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa.
Abstract: It is shown that, when two superposed fluids of different densities are accelerated in a direction perpendicular to their interface, this surface is stable or unstable according to whether the acceleration is directed from the heavier to the lighter fluid or vice versa. The relationship between the rate of development of the instability and the length of wave-like disturbances, the acceleration and the densities is found, and similar calculations are made for the case when a sheet of liquid of uniform depth is accelerated.
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TL;DR: In this paper, it was shown that a flow is possible in which equally spaced fingers advance steadily at very slow speeds, such that behind the tips of the advancing fingers the widths of the two columns of fluid are equal.
Abstract: When a viscous fluid filling the voids in a porous medium is driven forwards by the pressure of another driving fluid, the interface between them is liable to be unstable if the driving fluid is the less viscous of the two. This condition occurs in oil fields. To describe the normal modes of small disturbances from a plane interface and their rate of growth, it is necessary to know, or to assume one knows, the conditions which must be satisfied at the interface. The simplest assumption, that the fluids remain completely separated along a definite interface, leads to formulae which are analogous to known expressions developed by scientists working in the oil industry, and also analogous to expressions representing the instability of accelerated interfaces between fluids of different densities. In the latter case the instability develops into round-ended fingers of less dense fluid penetrating into the more dense one. Experiments in which a viscous fluid confined between closely spaced parallel sheets of glass, a Hele-Shaw cell, is driven out by a less viscous one reveal a similar state. The motion in a Hele-Shaw cell is mathematically analogous to two-dimensional flow in a porous medium.
Analysis which assumes continuity of pressure through the interface shows that a flow is possible in which equally spaced fingers advance steadily. The ratio λ = (width of finger)/(spacing of fingers) appears as the parameter in a singly infinite set of such motions, all of which appear equally possible. Experiments in which various fluids were forced into a narrow Hele-Shaw cell showed that single fingers can be produced, and that unless the flow is very slow λ = (width of finger)/(width of channel) is close to , so that behind the tips of the advancing fingers the widths of the two columns of fluid are equal. When λ = 1/2 the calculated form of the fingers is very close to that which is registered photographically in the Hele-Shaw cell, but at very slow speeds where the measured value of λ increased from 1/2 to the limit 1.0 as the speed decreased to zero, there were considerable differences. Assuming that these might be due to surface tension, experiments were made in which a fluid of small viscosity, air or water, displaced a much more viscous oil. It is to be expected in that case that λ would be a function of μU/T only, where μ is the viscosity, U the speed of advance and T the interfacial tension. This was verified using air as the less viscous fluid penetrating two oils of viscosities 0.30 and 4.5 poises.
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TL;DR: The 1990 National Academy of Science final report of its review of the Inertial Confinement Fusion Program recommended completion of a series of target physics objectives on the 10-beam Nova laser at the Lawrence Livermore National Laboratory as the highest priority prerequisite for proceeding with construction of an ignition-scale laser facility as mentioned in this paper.
Abstract: The 1990 National Academy of Science final report of its review of the Inertial Confinement Fusion Program recommended completion of a series of target physics objectives on the 10-beam Nova laser at the Lawrence Livermore National Laboratory as the highest-priority prerequisite for proceeding with construction of an ignition-scale laser facility, now called the National Ignition Facility (NIF). These objectives were chosen to demonstrate that there was sufficient understanding of the physics of ignition targets that the laser requirements for laboratory ignition could be accurately specified. This research on Nova, as well as additional research on the Omega laser at the University of Rochester, is the subject of this review. The objectives of the U.S. indirect-drive target physics program have been to experimentally demonstrate and predictively model hohlraum characteristics, as well as capsule performance in targets that have been scaled in key physics variables from NIF targets. To address the hohlrau...
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TL;DR: A review of the fundamental and technological aspects of these subjects can be found in this article, where the focus is mainly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science.
Abstract: Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects
1,583 citations
Cites background from "The Instability of Liquid Surfaces ..."
...Taylor (1950) [416] subsequently studied the stability of a layer sandwiched between two phases of a different density....
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TL;DR: In this article, an implosion system energized by a high energy laser was proposed to compress hydrogen to more than 10,000 times liquid density by an imploding system, which makes possible efficient thermonuclear burn of small pellets of heavy hydrogen isotopes, and makes feasible fusion power reactors using practical lasers.
Abstract: Hydrogen may be compressed to more than 10,000 times liquid density by an implosion system energized by a high energy laser. This scheme makes possible efficient thermonuclear burn of small pellets of heavy hydrogen isotopes, and makes feasible fusion power reactors using practical lasers.
1,550 citations
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TL;DR: In this article, it was shown that the sign of the mutual polarizability of two bonds in a chain depends upon whether there is an even or odd number of other bonds between them.
Abstract: This part is concerned with the changes in bond order that take place in a conjugated system when the resonance integral of a bond, or the coulomb term of an atom is altered. It is shown that the sign of the mutual polarizability of two bonds in a chain depends upon whether there is an even or odd number of other bonds between them. Numerical values are given for mutual bond polarizabilities in some important hydrocarbons, and it is found that in the polyenes the effect of a perturbation decreases rapidly with distance along the chain. The effect of hetero-substitution on bond orders is considered, and the results compared with the predictions of the qualitative resonance theory.
201 citations
TL;DR: In this article, it was shown that the two-dimensional system developed by O. G. Sutton, K. Calder and E. L. Deacon for flow over aerodynamically smooth and rough surfaces may be extended to three-dimensional diffusion of vapour over an evaporating area.
Abstract: In view of the practical significance in dynamical meteorology of the problem of evaporation from areas of finite lateral extent, it is a matter of fundamental importance to test as fully as possible the applicability of the hypothetical three-dimensional model of turbulence which was introduced by the author in 1947. The present paper describes in detail the manner in which the two-dimensional system developed by O. G. Sutton, K. L. Calder and E. L. Deacon for flow over aerodynamically smooth and rough surfaces may be extended to three-dimensional diffusion of vapour over an evaporating area. The agreement obtained between theory and experiment is good at points over the area. This agreement indicates that the assumed law, introduced by the author to give the variation of the coefficient of lateral diffusivity with height above the surface, may be used satisfactorily in evaporation problems as long as attention is confined to points not too far outside the boundaries of the area. The complicated mathematical relationship previously obtained for the vapour distribution vertically above the down-wind edge of a parabolic strip is reduced to a much simpler one. This serves to bring out explicitly the relationship between the effects of the two- and three-dimensional theoretical systems of turbulent transfer at points on the central axis of the area.
3 citations