Introduction of fluid mechanics
01 Jan 1993-pp 15-49
TL;DR: A fluid is a substance in which the constituent molecules are free to move relative to each other, and in a solid, the relative positions of molecules remain essentially fixed under non-destructive conditions of temperature and pressure.
Abstract: A fluid is a substance in which the constituent molecules are free to move relative to each other Conversely, in a solid, the relative positions of molecules remain essentially fixed under non-destructive conditions of temperature and pressure While these definitions classify matter into fluids and solids, the fluids subdivide further into liquid and gases
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TL;DR: A review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena as mentioned in this paper.
Abstract: Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.
4,044 citations
TL;DR: In this article, a review of microfiltration is presented, focusing on the formation of cakes, the behavior of suspension flows and particle transport in simple geometry ducts, and the formation and behavior of fouling layers including those resulting from macromolecules, colloids and particles.
1,317 citations
TL;DR: In this article, the use of acoustic fields, principally ultrasonics, for application in microfluidics is reviewed, and the abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques.
Abstract: This article reviews acoustic microfiuidics: the use of acoustic fields, principally ultrasonics, for application in microfiuidics. Although acoustics is a classical field, its promising, and indeed perplexing, capabilities in powerfully manipulating both fluids and particles within those fluids on the microscale to nanoscale has revived interest in it. The bewildering state of the literature and ample jargon from decades of research is reorganized and presented in the context of models derived from first principles. This hopefully will make the area accessible for researchers with experience in materials science, fluid mechanics, or dynamics. The abundance of interesting phenomena arising from nonlinear interactions in ultrasound that easily appear at these small scales is considered, especially in surface acoustic wave devices that are simple to fabricate with planar lithography techniques common in microfluidics, along with the many applications in microfluidics and nanofluidics that appear through the literature.
975 citations
Cites methods from "Introduction of fluid mechanics"
...In the fluid medium, using conservation of mass, momentum, and energy in the typical way [via Batchelor (1967), for example] results in a set of governing equations appropriate for analysis (Nyborg, 1965; Morse and Ingard, 1968; Bradley, 1996; Doinikov, 1996; Howe, 2007): @ f @t þ r ð fuÞ ¼ 0;…...
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...In the fluid medium, using conservation of mass, momentum, and energy in the typical way [via Batchelor (1967), for example] results in a set of governing equations appropriate for analysis (Nyborg, 1965; Morse and Ingard, 1968; Bradley, 1996; Doinikov, 1996; Howe, 2007):...
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TL;DR: The improvements and the new techniques proposed in the last decade are analyzed in depth and compared in order to highlight the qualities and defects of each.
Abstract: In this paper, the authors present an extended survey on the evolution and the modern approaches in the thermal analysis of electrical machines. The improvements and the new techniques proposed in the last decade are analyzed in depth and compared in order to highlight the qualities and defects of each. In particular, thermal analysis based on lumped-parameter thermal network, finite-element analysis, and computational fluid dynamics are considered in this paper. In addition, an overview of the problems linked to the thermal parameter determination and computation is proposed and discussed. Taking into account the aims of this paper, a detailed list of books and papers is reported in the references to help researchers interested in these topics.
823 citations
TL;DR: In this article, the authors describe the results of a numerical investigation of the dynamics of breakup of streams of immiscible fluids in the confined geometry of a microfluidic T-junction.
Abstract: We describe the results of a numerical investigation of the dynamics of breakup of streams of immiscible fluids in the confined geometry of a microfluidic T-junction. We identify three distinct regimes of formation of droplets: squeezing, dripping and jetting, providing a unifying picture of emulsification processes typical for microfluidic systems. The squeezing mechanism of breakup is particular to microfluidic systems, since the physical confinement of the fluids has pronounced effects on the interfacial dynamics. In this regime, the breakup process is driven chiefly by the buildup of pressure upstream of an emerging droplet and both the dynamics of breakup and the scaling of the sizes of droplets are influenced only very weakly by the value of the capillary number. The dripping regime, while apparently homologous to the unbounded case, is also significantly influenced by the constrained geometry; these effects modify the scaling law for the size of the droplets derived from the balance of interfacial and viscous stresses. Finally, the jetting regime sets in only at very high flow rates, or with low interfacial tension, i.e. higher values of the capillary number, similar to the unbounded case.
610 citations
Cites background from "Introduction of fluid mechanics"
...Because the drag force exerted on the droplet depends only very weakly on the viscosity of the droplet, within the shear-driven regime, the viscosity of the dispersed phase does not influence the size of droplets appreciably (e.g. see discussion of flow past a drop in Batchelor 1967)....
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...see discussion of flow past a drop in Batchelor 1967). This effect has been confirmed experimentally by Cramer, Fischer & Windhab (2004). Qualitatively, the rate-of-flow-controlled breakup (Garstecki et al....
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References
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01 Feb 1939
1,652 citations
Book•
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01 Jan 1970
TL;DR: In this article, the authors present fundamental concepts and principles governing fluids in motion problems, including the Momentum Equation (ME) and the Laminar Flow between Solid Boundaries (LFL) problems.
Abstract: Contents Preface to the eighth edition 1 Fundamental Concepts Problems 2 Fluid Statics Problems 3 The Principles Governing Fluids in Motion Problems 4 The Momentum Equation 5. Physical Similarity and Dimensional Analysis Problems 6 Laminar Flow between Solid Boundaries Problems 7 Flow and Losses in Pipes and Fittings Problems 8 Boundary Layers, Wakes and other Shear Layers Problems 9 The flow of an Inviscid Fluid Problems 10 Flow with a Free Surface Problems 11 Compressible Flow of Gases Problems 12 Unsteady Flow Problems 13 Fluid Machines Problems Appendix 1 Units and Conversion Factors Appendix 2 Physical Constants and Properties of Fluids Appendix 3 Tables of Gas Flow Functions Appendix 4 Algebraic Symbols Answers to Problems Index
1,242 citations
TL;DR: Nikuradse as discussed by the authors showed that the resistance law of the Karman-Prandtl theory for smooth surfaces was satisfactorily satisfied with respect to the size of roughness grains.
Abstract: Nikuradse (1933; Prandtl 1933), experimenting with pipes roughened internally by a uniform layer of sand, found that such pipes were indistinguishable from perfectly smooth ones, provided that the pressure gradient was less than that given by pV*k / μ = 4, where V = √( T / p ), T = shear stress at wall, p = density of fluid, μ , —- viscosity of fluid, k = diameter of roughness grains. With lesser flows neither the resistance nor the distribution of velocity was measurably influenced by the size of the roughness grains, and the observed resistance law was satisfactorily of the type required by the Karman-Prandtl theory for smooth surfaces. This law is usually expressed in the following form:
658 citations
Book•
01 Jan 1965
TL;DR: Properties of fluids fluid statics basis of fluid flow energy considerations in steady flow momentum and forces in fluid flow similitude and dimensional analysis steady incompressible flow in pressure conduits forces on immersed bodies steady flow in open channels fluid measurements unsteady-flow problems steady flow of compressible fluids idea/flow maths hydraulic machinary - pumps hydraulic machinery - turbines
Abstract: Properties of fluids fluid statics basis of fluid flow energy considerations in steady flow momentum and forces in fluid flow similitude and dimensional analysis steady incompressible flow in pressure conduits forces on immersed bodies steady flow in open channels fluid measurements unsteady-flow problems steady flow of compressible fluids idea/flow maths hydraulic machinary - pumps hydraulic machinary - turbines.
633 citations