Author
Osborne Reynolds
Other affiliations: University of Cambridge, Owens Community College, Victoria University, Australia
Bio: Osborne Reynolds is an academic researcher from Queens College. The author has contributed to research in topics: Equations of motion & Viscous liquid. The author has an hindex of 16, co-authored 38 publications receiving 6041 citations. Previous affiliations of Osborne Reynolds include University of Cambridge & Owens Community College.
Papers
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TL;DR: In this article, it was shown that the general character of the motion of fluids in contact with solid surfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid.
Abstract: 1. Objects and results of the investigation.—The results of this investigation have both a practical and a philosophical aspect. In their practical aspect they relate to the law of resistance to the motion of water in pipes, which appears in a new form, the law for all velocities and all diameters being represented by an equation of two terms. In their philosophical aspect these results relate to the fundamental principles of fluid motion; inasmuch as they afford for the case of pipes a definite verification of two principles, which are— that the general character of the motion of fluids in contact with solid surfaces depends on the relation between a physical constant of the fluid and the product of the linear dimensions of the space occupied by the fluid and the velocity.
1,820 citations
TL;DR: In this paper, the authors considered the boundary or surface actions of fluids and proposed a theoretical treatment of the physical actions of oils and other viscous fluids to diminish friction and wear between solid surfaces.
Abstract: 1. Lubrication, or the action of oils and other viscous fluids to diminish friction and wear between solid surfaces, does not appear to have hitherto formed a subject for theoretical treatment. Such treatment may have been prevented by the obscurity of the physical actions involved, which belong to a class as yet but little known, namely, the boundary or surface actions of fluids; but the absence of such treatment has also been owing to the want of any general laws discovered by experiment. The subject is of such fundamental importance in practical mechanics, and the opportunities for observation are so frequent, that it may well be a matter of surprise that any general laws should have for so long escaped detection.
1,636 citations
TL;DR: In this paper, the authors compare the results of a singular solution of Navier's equations of motion of viscous fluid with the results obtained from many experiments, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved.
Abstract: 1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.
1,409 citations
TL;DR: In this paper, the action of oils and other viscous fluids to diminish friction and wear between solid surfaces is treated as a subject for theoretical treatment, and the absence of such treatment has also been owing to the want of any general laws revealed by experiment.
Abstract: Lubrication, or the action of oils and other viscous fluids to diminish friction and wear between solid surfaces, does not appear to have hitherto formed a subject for theoretical treatment. Such treatment may have been prevented by the obscurity of the physical actions involved, which belong to a class as yet but little known, namely, the boundary or surface actions of fluids; but the absence of such treatment has also been owing to the want of any general laws revealed by experiment. The subject is of such fundamental importance in practical mechanics, and the opportunities of observation so frequent, that it may well be a matter of surprise that any general laws should have for so long escaped detection.
547 citations
Journal Article•
TL;DR: In this article, it was shown that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a coefficient depending on the physical state of the fluid.
Abstract: 1. TtH equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form, so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier* seems to have first introduced in 1822, and which were much studied by Cauchyt and Poisson+) were finally shown by St Venant? and Sir Gabriel Stokesll, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a coefficient depending on the physical state of the fluid.
136 citations
Cited by
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TL;DR: The Navier-Stokes equations are well-known to be a good model for turbulence as discussed by the authors, and the results of well over a century of increasingly sophisticated experiments are available at our disposal.
Abstract: It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical
3,721 citations
TL;DR: In this article, 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.
Abstract: 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.
2,689 citations
Book•
01 Oct 2006
TL;DR: Compounding, Contemporary, andProcess Chemistry in the Pharmaceutical Industry: Characterization and Function, Volume 19.
Abstract: Contributors to Volume 19Contents of Other VolumesBlow-Fill-Seal Aseptic ProcessingDeborah J. JonesCompounding, ContemporaryLoyd V. Allen, Jr.Drug Delivery-Oral Colon SpecificVincent H. L. Lee and Suman K. MukherjeeThe European Agency for the Evaluation of Medicinal Product (EMEA)David JacobsHarmonization-CompendiaLee. T. Grady and Jerome A. HalperinInhalation, Dry PowderLynn Van Campen and Geraldine VenthoyeLiquid Crystals in Drug DeliveryChristel C. Mueller-GoymannMedication Errors: A New Challenge for the Pharmaceutical IndustryDiane R. CousinsMucoadhesive Hydrogels in Drug DeliveryHans E. Junginger, Maya Thanou, and J. Coos VerhoefPeptides and Proteins: Buccal AbsorptionHemant H. Alur, and Thomas P. Johnston, and Ashim K. MitraPharmaceutical Quality Assurance Microbiology LaboratoriesAnthony M. CundellProcess Chemistry in the Pharmaceutical IndustryKumar G. Gadamasetti and Ambarish K. SinghRadiolabeling of Pharmaceutical Aerosols and Gamma Scintigraphic Imaging for Lung DepositionHak-Kim ChanSuper Disintegrants: Characterization and FunctionLarry L. Augsburger, Albert W. Brzeczko, Umang Shah, and Huijeong A. HahmIndex to Volume 20
2,683 citations