Macroscopic thin liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. In this review a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations. As a result of this long-wave theory, a mathematical system is obtained that does not have the mathematical complexity of the original free-boundary problem but does preserve many of the important features of its physics. The basics of the long-wave theory are explained. If, in addition, the Reynolds number of the flow is not too large, the analogy with Reynolds's theory of lubrication can be drawn. A general nonlinear evolution equation or equations are then derived and various particular cases are considered. Each case contains a discussion of the linear stability properties of the base-state solutions and of the nonlinear spatiotemporal evolution of the interface (and other scalar variables, such as temperature or solute concentration). The cases reducing to a single highly nonlinear evolution equation are first examined. These include: (a) films with constant interfacial shear stress and constant surface tension, (b) films with constant surface tension and gravity only, (c) films with van der Waals (long-range molecular) forces and constant surface tension only, (d) films with thermocapillarity, surface tension, and body force only, (e) films with temperature-dependent physical properties, (f) evaporating/condensing films, (g) films on a thick substrate, (h) films on a horizontal cylinder, and (i) films on a rotating disc. The dynamics of the films with a spatial dependence of the base-state solution are then studied. These include the examples of nonuniform temperature or heat flux at liquid-solid boundaries. Problems which reduce to a set of nonlinear evolution equations are considered next. Those include (a) the dynamics of free liquid films, (b) bounded films with interfacial viscosity, and (c) dynamics of soluble and insoluble surfactants in bounded and free films. The spreading of drops on a solid surface and moving contact lines, including effects of heat and mass transport and van der Waals attractions, are then addressed. Several related topics such as falling films and sheets and Hele-Shaw flows are also briefly discussed. The results discussed give motivation for the development of careful experiments which can be used to test the theories and exhibit new phenomena.

Long-scale evolution of thin liquid films

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

/pdf/the-physics-of-wind-blown-sand-and-dust-4ggy9vm6xy.pdf

The physics of wind-blown sand and dust

The viscous gravity current that results when fluid flows along a rigid horizontal surface below fluid of lesser density is analysed using a lubrication-theory approximation. It is shown that the effect on the gravity current of the motion in the upper fluid can be expressed as a condition of zero shear on the unknown upper surface of the gravity current. With the supposition that the volume of heavy fluid increases with time like F, where a is a constant, a similarity solution to the governing nonlinear partial differential equations is obtained, which describes the shape and rate of propagation of the current. The viscous theory is shown to be valid for t & t, when a -c a, and for t -4 t, when a > a,, where t, is the transition time at which the inertial and viscous forces are equal, with a, = $ for a two-dimensional current and a, = 3 for an axisymmetric current. The solutions confirm the functional forms for the spreading relationships determined for a = 1 in the preceding paper by Didden & Maxworthy (1982), as well as evaluating the multiplicative factors appearing in the relationships. The relationships compare very well with experimental measurements of the axisymmetric spreading of silicone oils into air for a = 0 and 1. There is also very good agreement between the theoretical predictions and the measurements of the axisymmetric spreading of salt water into fresh water reported by Didden & Maxworthy and by Britter (1979). The predicted multiplicative constant is within 10 Yo of that measured by Didden & Maxworthy for the spreading of salt water into fresh water in a channel.

/pdf/the-propagation-of-two-dimensional-and-axisymmetric-viscous-1ybbc4dya0.pdf

The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface

Background—The goal of this statement is to review available literature and to put forth a scientific statement on the current practice of fetal cardiac medicine, including the diagnosis and manage...

/pdf/diagnosis-and-treatment-of-fetal-cardiac-disease-a-1komqhwbxf.pdf

Diagnosis and Treatment of Fetal Cardiac Disease A Scientific Statement From the American Heart Association

The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.

Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows

Foreword Steve Thorpe Preface 1. The nature of gravity currents 2. Atmospheric gravity currents 3. Sea-breeze fronts 4. Gravity currents in satellite imagery 5. Fronts and topography 6. Environmental problems: atmosphere 7. Gravity currents in rivers, lakes and the ocean 8. Industrial problems with gravity currents: oceanography 9. Avalanches 10. Volcanic gravity currents 11. The anatomy of a gravity current 12. Spread of dense fluid 13. Ambient stratification 14. Ambient turbulence 15. Viscous gravity currents 16. Suspension flows 17. Gravity currents on a rotating earth 18. Numerical models of gravity currents Index.

Gravity Currents: In the Environment and the Laboratory

Experimental results for the release of a fixed volume of one homogeneous fluid into another of slightly different density are presented, From these results and those obtained by previous experiments, it is argued that the resulting gravity current can pass through three states. There is first a slumping phase, during which the current is retarded by the counterflow in the fluidinto which it is issuing. The current remains in this slumping phase until the depth ratio of current to intruded fluid is reduced to less than about 0,075. This may be followed by a (previously investigated) purely inertial phase, wherein the buoyancy force of the intruding fluid is balanced by the inertial force. Motion in the surrounding fluid plays a negligible role in this phase. There then follows a viscous phase, wherein the buoyancy force is balanced by viscous forces. It is argued and confirmed by experiment that the inertial phase is absent if viscous effects become important before the slumping phase has been completed. R’elationships between spreading distance and time for each phase are obtained for all three phases for both two-dimensional and axisymmetric geometries. Some consequences of the retardation of the gravity current during the slumping phase are discussed.

/pdf/the-slumping-of-gravity-currents-f0dbs0r0s9.pdf

The slumping of gravity currents

Foreword Preface 1. The sea breeze 2. Formation of the sea breeze 3. Sea-breeze fronts 4. Sea-breeze forecasting 5. Other local winds 6. Air quality 7. Sea breeze interactions 8. Life and the sea breeze 9. Sports 10. Technology: field measurements of the sea-breeze 11. Laboratory measurements 12. Theoretical models References Index.

Sea Breeze and Local Winds

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases: an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t−1/3 (where t is the time measured from release) The experiments reported herein were designed to emphasize the inviscid motion From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop Otherwise, the disturbance is a long wave of depression Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions of the ratio of the initial heavy fluid depth to the total fluid depth These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083002979

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

A gravity current, or "density current," is the flow of one fluid within another caused by the density difference between the fluids The difference in specific weight that provides the driving force may be due to dissolved or suspended material or to temperature differences Gravity currents are primarily horizontal, occurring as either top or bottom boundary currents, or as intrusions at some intermediate level The fluids are usually miscible and the mixing that results can play an important part in the dynamics of the flow Since gravity currents are formed in many different natural situations and may also be man-made, knowledge of their properties is of importance in many scientific disciplines In the atmosphere, thunderstorm outflows and sea-breeze fronts are gravity currents of relatively cold dense air Atmospheric-suspension gravity currents include avalanches of airborne snow particles, also fiery avalanches and base surges formed from gases and solids issuing from volcanic eruptions Gravity currents have important applications in aircraft safety, atmo­ spheric pollution, entomology and pest control, and especially in dense-gas technology Industrial accidents in which gravity currents may be formed include the spread of a dense gas from an accidental release In the ocean, gravity currents are driven by salinity and temperature inhomogeneities, or as turbidity currents whose density derives from sus­ pended mud or silt Lines of foam and debris on the ocean surface may indicate the front of a gravity current, frequently brought about by tidal processes The latter also affect the behavior of gravity currents such as river plumes at the surface and salt wedges on a river bed The important problems related to oil spillage on the sea have been the subject of a review paper in this series (Hoult 1972)

J. E. Simpson

Papers

Gravity Currents: In the Environment and the Laboratory

The slumping of gravity currents

Sea Breeze and Local Winds

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

Gravity currents in the laboratory, atmosphere, and ocean