Showing papers in "Annual Review of Fluid Mechanics in 1979"

On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines

Abstract: A contact line is formed at the intersection of two immiscible fluids and a solid. That the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field is demonstrated by the behavior of two immiscible fluids in a capillary. It is well known that the height to which a column of liquid will rise in a vertical circular capillary with small radius, a, whose lower end is placed into a bath, is given by (2(j/apg) cos (), where (j is the surface tension of the air/liquid interface, f) is the static contact angle as measured from the liquid side of the contact line, p is the density, and g is the magnitude of the accelera­ tion due to gravity.! Thus, depending on the value of the contact angle, e, which is a direct consequence of the molecular interactions among the three materials at the contact line, the height can take on any value within the interval [ 2(J/apg, 2(J/apg]. In a sense, the influence of the contact angle is indirect: the contact angle, in capillaries with small radii, controls the radius of curvature of the meniscus which, in turn, regulates the pressure in the liquid under the meniscus. It is this pressure that determines the height of the column. In a similar manner, the dynamic contact angle can influence the rate of displacement of tbe meniscus through the capillary. The pressure drop

Drop Formation in a Circular Liquid Jet

Abstract: Several recent developments in ink-jet printing have motivated numerous scientists to investigate the details of the breakup process of liquid jets emanating from nozzles. The entire January 1977 issue of the IBM Journal of Research and Development was devoted to ink-jet printing technology, and several of the papers were concerned with drop formation. The main concern is the control of the relatively small drops called "spherules" by Rayleigh (1896, p. 366) and "satellite drops" in the recent literature. These small drops form when thin ligaments separate from the main drops at both ends (see Figure 1). In the ink-jet printer the main drops are supplied with a predetermined electrical charge as they detach from the liquid column. They are then deflected to a desired location by appropriately charged downstream capacitor plates. When the satellite drops occur they receive a relatively large charge-to-mass ratio and their resulting large deflection causes printer malfunctions. The understanding of the drop-formation process is crucial to the control and elimination of the satellite-drop problem. This article is primarily restricted to a review of those investigations that bear on this rather narrow but very difficult aspect of jet breakup. For a detailed description of the classical work on the linear capillary instability of jets the reader is referred to Rayleigh (1896, §361) and Chandrasekhar (1961, §111). A more recent review can be found in McCarthy & Molloy (1974). Only a brief summary of this classical work, as is required for background, is presented here. The early experiments ofSavart(1833) and Magnus (1855) demonstrated that a liquid jet emanating from a circular nozzle could be made to breakup in a regular manner by supplying a steady vibration to the source tank or nozzle. Rayleigh (1879) studied the linear stability of an infinitely

Wakes in Stratified Fluids

Abstract: In this article we review research activities concerning wakes generated by moving bodies in stratified fluids. A wake is defined to be the non­ propagating disturbance produced by a moving body, and thus research activities concerning internal waves generated by a moving body are not included. Wakes have been of interest to many fluid dynamicists and engineers because they are a basic flow phenomenon associated with fluid flowing over an obstacle or with the movement of a natural or man-made body. The wake flow depends strongly on the Reynolds number RD == VoDjv, which is defined as the ratio of the inertia force to the viscous force. Here U 0 is the body speed, D is the characteristic length, e.g. the diameter of a cylinder or a sphere, and v is the kinematic viscosity of the fluid. For small Reynolds numbers, the viscous force dominates the inertia force and the wake is laminar. As the Reynolds number increases, the wake becomes unstable and a regular flow pattern, such as Karman's vortex street in the wake of a cylinder, can be observed. At still higher Reynolds numbers, the flow pattern becomes irregular and a turbulent flow is formed. Books written by Townsend (1956), Hinze (1959), and Schlichting ( 1960) can be referred to for further information about wakes. When the fluid is stratified thermally or with foreign additives, such as salt, a gravitational force, in addition to inertia and viscous forces, is exerted on the flow. A stratified fluid occurs very commonly in the

Cavitation in Bearings

Abstract: Cavitation is the disruption of what would otherwise be a continuous liquid phase by the presence of a gas or vapour or both. The phenomenon has been examined by scientists and engineers for a century or more, and although this review concentrates on cavitation in bearings, there have been many studies outside the field of lubrication. Most of these have been concerned with aqueous systems, and the erosive damage to surfaces bounding a cavitating flow has received much attention. Com­ ponents that have proved susceptible to cavitation erosion damage include pump impellers, valves, marine propelle rs, pipes, and cylinder liners. Another nont ribologi cal problem

Model equations of nonlinear acoustics

Abstract: Over the past twenty-five years , nonlinear acoustics has developed into a vigorous and distinctive branch of science. The subject covers a wide range of topics, including steady finite-amplitude waves in supersonic aerodynamics, weak-shock theory, unsteady finite-amplitude waves in gases, liquids, and solids, bubble dynamics and cavitation in liquids, and phonon interactions and the quantum acoustics of solids. Practical applications are on the increase: the steady wave systems of supersonic projectiles; the nonlinear parametric sonar array devised by Westervelt (1963) for the production of a highly directional low-frequency beam in water or air; the damaging effects of cavitation and bubble implosion on ship structures in water and on nuclear reactors cooled by liquid sodium; and the use of ultrasonics in biomedical and engineering non­ destructive testing. These are all well-known examples, though they hardly exhaust the possibilities . A series of eight (as of 1978) international symposia in the USA, Europe, and the USSR has greatly stimulated work in many aspects of nonlinear acoustics

Air flow and sound generation in musical wind instruments

Abstract: Over the past two decades or so, interest in musical acoustics appears to have been increasing rapidly We now have available several collections of reprinted technical articles (Hutchins 1975, 1976, Kent 1977), together with a large number of textbooks, of which those most suitable for citation in this review are by Olson (1967), Backus (1969), Nederveen (1969), and Benade (1976) The mathematical foundations of the subject were laid primarily by Lord Rayleigh (1896) and are well treated in such standard texts as Morse (1948) and Morse & Ingard (1968) This review covers a much more restricted field than this preliminary bibliography might suggest Among all the varieties of musical instruments I concentrate on those capable of producing a steady sound that is maintained by a flow of air, and even within this family I am interested not so much in the design and behavior of the instrument as a whole but rather in the details of the air flow that are responsible for the actual tone production Although musical instruments function as closely integrated systems, it is convenient and indeed almost essential for their analysis to consider them in terms of at least two interacting subsystems, as shown in Figure 1 The first of these is the primary resonant system, which consists of a column of air, confined by rigid walls of more or less complex shape and having one or more openings Such a system is generally not far from linear in its behavior and it can be treated, at least in principle, by the classical methods of acoustics The second subsystem is the airdriven generator that excites the primary resonator This subsystem is generally

Numerical Solution of Compressible Viscous Flows

Abstract: The presented review is concerned with the problem of calculating compressible viscous flows. Basic numerical considerations and problems associated with calculating viscous flows are examined and current numerical approaches toward the solution of the Navier-Stokes equations are discussed. It is pointed out that the numerical solution of the full time-dependent equations for turbulent flow is not practical with present computers. Therefore, turbulence effects must be accounted for by modeling. Developments related to turbulence modeling are described. In connection with a discussion of numerical methods for solving viscous flow equations, attention is given to numerical domains of dependence of typical explicit and implicit methods, the diffusion problem, the convection-diffusion problem, and the split-hybrid method.

Ship Boundary Layers

Abstract: In calculating boundary layers, whether two-dimensional, axisymmetric, or fully three-dimensional, one begins with an assumed or measured pressure distribution on a body and solves sets of approximate equations, proceeding in a generally downstream direction until the boundary layer becomes so thick that the mathematical model is no longer valid and needs to be modified, or until flow separation occurs. This brief statement has already referred to five problems, the resolution of which seems to be much more difficult for the three-dimensional case, and especially for ship forms. These problems are the determination of the pressure distribution on the given body, the selection of the governing equations, a procedure for their solution, their modification when the boundary layer becomes thick, and the prediction of vortex generation and flow separation. .