Fluid Mechanics
Nettie Rosier
Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach.[2] Particle image velocimetry, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to some aspects of geophysics and astrophysics (for example, in understanding plate tectonics and anomalies in the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields.
An inviscid fluid has no viscosity, ν = 0 \displaystyle \nu =0 . In practice, an inviscid flow is an idealization, one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of superfluidity. Otherwise, fluids are generally viscous, a property that is often most important within a boundary layer near a solid surface,[22] where the flow must match onto the no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer.
For a Newtonian fluid, the viscosity, by definition, depends only on temperature, not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress (in Cartesian coordinates) is
where κ \displaystyle \kappa is the second viscosity coefficient (or bulk viscosity). If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic.
The Cardiovascular Fluid Mechanics (CFM) Laboratory at Georgia Tech has been one of the pioneering laboratories in the world studying the function and mechanics of heart valves and other complex cardiac defects.
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Innovations in fluid mechanics have been leading to better food since ancient history, while creativity in cooking has inspired fundamental breakthroughs in science. This review addresses how recent advances in hydrodynamics are changing food science and the culinary arts and, reciprocally, how the surprising phenomena that arise in the kitchen are leading to new discoveries across the disciplines, including molecular gastronomy, rheology, soft matter, biophysics, medicine, and nanotechnology. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, an introduction and its connections to food are provided, followed by a discussion of how science could be made more accessible and inclusive. The state-of-the-art knowledge is then assessed, the open problems, along with the likely directions for future research and indeed future dishes. New ideas in science and gastronomy are growing rapidly side by side.
Turbulent pipe flow. (a) Drawings showing (i) laminar pipe flow, (ii) turbulent flow, and (iii) turbulent flow observed under the stroboscopic illumination achieved with an electric spark, thereby revealing that the structure of the flow comprises eddies and vortices. From [826]. (b) Spacetime diagram from a numerical simulation at Re=2300 showing the process of turbulent puff splitting. (c) Visualization of puff splitting in a cross section of the pipe. Time increases in the snapshots from bottom to top. (b),(c) From [46].
Wine aeration. (a) Oxygen injection using the Venturi effect. The wine moves down into a narrow funnel by gravity. In the funnel the liquid accelerates, which lowers the pressure relative to the surrounding atmosphere, as described by the Bernoulli principle [Eq. (6)]. Hence, air bubbles are drawn in, which aerates the wine. (b) Wine decanter. By pouring and swirling the liquid around, ripples form that mix oxygen in efficiently. Section 9e addresses thin-film instability. (a),(b) Courtesy Vintorio Wine Accessories.
Jets in the kitchen sink. (a) Example of the Rayleigh-Plateau instability, where a thin jet from a faucet breaks into droplets. From Niklas Morberg. (b) A circular hydraulic jump forms when a thicker liquid jet impinges on a planar surface. (c) A triangular hydraulic jump, seen from below through a glass plate. The impinging jet is the black center region, and the jump line is the triangular black line surrounding it. An additional roller structure, marked with a dye, extends from the jump line to the outer radius. In the corner region, the dyed fluid is expelled in radial jets. (b),(c) From [643].
Laser tomography of champagne glasses. (a) Natural, random effervescence in an untreated glass. Inset: growth of bubbles as they rise. (b) Stabilized eddies in a surface-treated glass. (a),(b) Courtesy of Grard Liger-Belair. (c) Counterrotating convection cells self-organize at the air-champagne interface. From [80].
Examples of complex rheological behavior of fluids. (a) People walking over a swimming pool full of oobleck, a mixture of cornstarch and water. From Ion Furjanic, [1017]. (b) Thixotropic fluids become thinner with time when they are sheared and solidify again at rest. Classic examples are paint and sandwich spread. (c) Whipped cream is an example of a Bingham plastic, which can be squeezed out like a fluid, but then turns solid in the absence of stresses. From Wikimedia Commons. (d) The Weissenberg rod climbing effect seen in a 2% solution of high molecular weight polyacrylamide. From Wikimedia Commons. (e) A sandwich cookie is mounted on a rheometer, where one wafer is rotated relative to the other. Hence, the properties of the creme between the wafers are measured. Courtesy of Crystal E. Owens.
Rayleigh-Bnard convection. (a) Rising plumes in a pot of water heated from below, visible because the refractive index changes with temperature differences. (b) Contrast-enhanced magnification. (c) Side view of mushroomlike plumes in a high-viscosity fluid. The green line at the bottom is the boundary layer. (d) Top view of dendritic line plumes. (c),(d) From [794]. (e) Temperature field in a simulation of Rayleigh-Bnard convection at Ra=5000 and Pr=0.7. From [293]. (f) Vortex structures in a coffee cup with milk at the bottom, which gets displaced by cold plumes that sink down from the evaporating interface. Inset: IR thermograph showing convection cells of colder (downwelling) and warmer (upwelling) regions. From [1023].
Double-diffusive convection phenomena. (a) Cocktail with blue salt fingers, produced by warmer salty water resting on colder fresh water of a higher density. Courtesy of Matteo Cantiello (Flatiron Institute). (b) Layered caff latte. Black arrows were added to highlight the layer boundaries. Adapted from [1049].
Buoyancy-driven plumes. (a) Flows developing over an espresso cup visualized with schlieren imaging. The largest amount of fluid displacement is observed on the sides and above the cup. From [162]. (b) Plume around a hot teakettle captured with schlieren imaging. From [878].
Microbial dynamics and food safety. (a) Time lapse of an E. coli bacterium performing oscillatory rheotaxis, with fluorescently labeled flagella to reveal its reorientation with respect to the flow (large arrow, pointing down). From [654]. (b) Working principle of an optofluidic pathogen detector. When E. coli binds to Y-shaped monoclonal antibodies, it induces a shift in refractive index that can be detected with an optical sensor. From [956].
Granular matter. (a) In a pile of grains, the motion is quantified by the rate of strain ϵ using spatially resolved diffusing wave spectroscopy. From [236]. (b) Rice sculpture. From [778]. (c) The velocity field of grains flowing in a 2D hopper is measured by direct particle tracking. The seven particles that are marked form a jamming arch, shown in the inset. (d) Force chains in a jammed state, visualized using photoelastic particles that show intensity fringes under stress, highlighted in the inset. From [928]. (e) The Brazil nut effect, with 8 mm black (small) glass beads and 15 mm green (gray, large) polypropylene beads. Evolution in time from left to right. From [142].
Coffee brewing. (a) Schematic of percolation in an espresso machine basket. A pressure differential pushes water down through the pore spaces. Courtesy of Christopher H. Hendon. Inset: espresso drops by photographer theferdi. (b) Diagram of a French press. The water moves up around the coffee grounds (upward arrows) by applying a constant gravitational force on the plunger (downward arrows). From [999]. (c) Cappuccino with latte art in the shape of a phoenix. From [438].
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