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Series Editor: R. Aims and Scope of the Series The purpose of this series is to focus on subjects in which fluid mechanics plays a fundamental role.

Bubbles, drops, and particles

A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity , i. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid.

Ketchup , for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard , [1] honey , [1] toothpaste , starch suspensions, corn starch , paint , blood , melted butter , and shampoo. Most commonly, the viscosity the gradual deformation by shear or tensile stresses of non-Newtonian fluids is dependent on shear rate or shear rate history.

Some non-Newtonian fluids with shear-independent viscosity, however, still exhibit normal stress-differences or other non-Newtonian behavior. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin , the constant of proportionality being the coefficient of viscosity.

In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different. The fluid can even exhibit time-dependent viscosity. Therefore, a constant coefficient of viscosity cannot be defined. Although the concept of viscosity is commonly used in fluid mechanics to characterize the shear properties of a fluid, it can be inadequate to describe non-Newtonian fluids.

They are best studied through several other rheological properties that relate stress and strain rate tensors under many different flow conditions—such as oscillatory shear or extensional flow—which are measured using different devices or rheometers. The properties are better studied using tensor -valued constitutive equations , which are common in the field of continuum mechanics.

The viscosity of a shear thickening fluid , or dilatant fluid, appears to increase when the shear rate increases. Corn starch suspended in water "oobleck", see below is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid. A familiar example of the opposite, a shear thinning fluid , or pseudoplastic fluid, is wall paint : The paint should flow readily off the brush when it is being applied to a surface but not drip excessively.

Note that all thixotropic fluids are extremely shear thinning, but they are significantly time dependent, whereas the colloidal "shear thinning" fluids respond instantaneously to changes in shear rate.

Thus, to avoid confusion, the latter classification is more clearly termed pseudoplastic. Another example of a shear thinning fluid is blood. This application is highly favoured within the body, as it allows the viscosity of blood to decrease with increased shear strain rate.

Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The surface of a Bingham plastic can hold peaks when it is still. By contrast Newtonian fluids have flat featureless surfaces when still. There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic.

An opposite case of this is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate thixotropic. Many common substances exhibit non-Newtonian flows.

These include: [6]. An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch e. Seuss book Bartholomew and the Oobleck. Because of its properties, oobleck is often used in demonstrations that exhibit its unusual behavior. A person may walk on a large tub of oobleck without sinking due to its shear thickening properties, as long as the individual moves quickly enough to provide enough force with each step to cause the thickening.

Also, if oobleck is placed on a large subwoofer driven at a sufficiently high volume, it will thicken and form standing waves in response to low frequency sound waves from the speaker. If a person were to punch or hit oobleck, it would thicken and act like a solid.

After the blow, the oobleck will go back to its thin liquid-like state. Flubber, also commonly known as slime, is a non-Newtonian fluid, easily made from polyvinyl alcohol —based glues such as white "school" glue and borax. It flows under low stresses but breaks under higher stresses and pressures.

This combination of fluid-like and solid-like properties makes it a Maxwell fluid. Its behaviour can also be described as being viscoplastic or gelatinous. Another example of this is chilled caramel ice cream topping so long as it incorporates hydrocolloids such as carrageenan and gellan gum. The sudden application of force —by stabbing the surface with a finger, for example, or rapidly inverting the container holding it—causes the fluid to behave like a solid rather than a liquid.

This is the " shear thickening " property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. Silly Putty is a silicone polymer based suspension which will flow, bounce, or break depending on strain rate. Plant resin is a viscoelastic solid polymer. When left in a container, it will flow slowly as a liquid to conform to the contours of its container.

If struck with greater force, however, it will shatter as a solid. Quicksand is a shear thinning non-Newtonian colloid that gains viscosity at rest. Quicksand's non-Newtonian properties can be observed when it experiences a slight shock for example, when someone walks on it or agitates it with a stick , shifting between its Gel and Sol phase and seemingly liquefying, causing objects on the surface of the quicksand to sink. Ketchup is a shear thinning fluid. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates.

Shaking an inverted bottle of ketchup can cause it to transition to a lower viscosity, resulting in a sudden gush of the shear thinned condiment. Such continuum models tend to be non-Newtonian, since the apparent viscosity of granular flows increases with pressure and decreases with shear rate. The main difference is the shearing stress and rate of shear. From Wikipedia, the free encyclopedia. Fluid that does not follow Newton's Law of Viscosity. Solid mechanics. Fluid mechanics. Surface tension Capillary action.

Main article: Flubber material. Main article: Silly Putty. Main article: Pitch resin. Main article: Quicksand. Scientific American. Springer handbook of experimental fluid mechanics.

Prentice Hall. Emulsions, Foams, and Suspensions: Fundamentals and Applications. Wiley VCH. Iowa State University Extension. The Rheology of Caramel PhD. University of Nottingham. Chemistry World. Royal Society of Chemistry. Branches of physics.

Pure Applied Engineering. Experimental Theoretical Computational. Relativistic mechanics Special General Nuclear physics Quantum mechanics Particle physics Atomic, molecular, and optical physics Atomic Molecular Modern optics Condensed matter physics. Astrophysics Atmospheric physics Biophysics Chemical physics Geophysics Materials science Mathematical physics Medical physics Quantum information science. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file.

Download as PDF Printable version. Wikimedia Commons. Laws Conservations Mass Momentum Energy. Clausius—Duhem entropy. Rheology Viscoelasticity Rheometry Rheometer. Electrorheological Magnetorheological Ferrofluids. Kelvin material , Maxwell material. Some lubricants , whipped cream , Silly Putty. Time-dependent viscosity. Apparent viscosity increases with duration of stress. Synovial fluid , printer ink , gypsum paste. Apparent viscosity decreases with duration of stress [2].

Yogurt , peanut butter , xanthan gum solutions, aqueous iron oxide gels, gelatin gels, pectin gels, hydrogenated castor oil , some clays including bentonite , and montmorillonite , carbon black suspension in molten tire rubber, some drilling muds , many paints , many floc suspensions, many colloidal suspensions.

Shear thickening dilatant. Apparent viscosity increases with increased stress [3]. Suspensions of corn starch in water oobleck.

Apparent viscosity decreases with increased stress [4] [5].

Dynamics of Bubbles, Drops and Rigid Particles (1999) Springer - Z. Zapryanov, S. Tabakova

The dynamic behaviors of gas-liquid two-phase flow were simulated in a lab-scale intermittent bubble column by Euler-Euler two-fluid model coupled with the PBM population balance model using two different liquid phases, i. When non-Newtonian fluid was used during intermittent aeration, some interesting results were obtained. Two symmetric vortexes existed in the time-averaged flow field; the vertical time-averaged velocity of the liquid phase decreased with increasing anaerobic time; the average gas holdup distribution was like a trapezoid with long upper side and short lower side and affected by the dynamic viscosity of the liquid phase. Compared with non-Newtonian fluid, the use of Newtonian fluid as the liquid phase led to a more complicated time-averaged flow field structure and vertical time-averaged velocity distribution, higher average gas holdup, and the asymmetric column-shaped gas holdup distribution with increasing anaerobic time. For different liquid phases, the instantaneous flow field, instantaneous vertical velocity, and instantaneous gas holdup distribution all periodically changed with anaerobic time; however, different from Newtonian liquid phase, non-Newtonian liquid phase had no periodic oscillating instantaneous horizontal velocity. As an aeration reactor, the bubble column is widely used for study on wastewater treatment because of its low price, easy transport, and high mass transfer characteristics [ 1 — 4 ].

Arnipally, Sumanth Kumar, and Ergun Kuru. The objective of this paper is to determine how fluid shear viscosity and elasticity might influence the particle-settling velocity, and even more so to answer the question of which one of these two rheological properties is more dominant in controlling the particle-settling velocity when viscoelastic drilling fluids are used. The settling velocities of spherical particles diameters: 1. The shear-viscosity and elasticity characteristics of test fluids were determined by performing shear-viscosity and frequency-sweep oscillatory measurements, respectively. The first set of fluids had almost identical shear-viscosity characteristics while showing significantly different elastic properties quantified in terms of relaxation time.

Either your web browser doesn't support Javascript or it is currently turned off. In the latter case, please turn on Javascript support in your web browser and reload this page. Free to read. An experimental study is performed to measure the terminal settling velocities of spherical particles in surfactant based shear thinning viscoelastic VES fluids. VES fluids over a wide range of rheological properties are prepared and rheologically characterized. The rheological characterization involves steady shear-viscosity and dynamic oscillatory-shear measurements to quantify the viscous and elastic properties respectively. The settling velocities under unbounded conditions are measured in beakers having diameters at least 25x the diameter of particles.

In part, the writing of this book was inspired by the work of W.L. Wilkinson: fluid decreases from 0 to 1 with increasing shear rate. Chhabra, R.P., Bubbles, Drops and Particles in non-Newtonian Fluids, CRC Press, Boca Raton.

Viscoelastic and shear-thinning effects of aqueous exopolymer solution on disk and sphere settling

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. In this study, xanthan gum is used as a model exopolymer to demonstrate potential effects of non-Newtonian properties of natural aquatic systems on settling dynamics of particles.

A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity , i. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup , for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard , [1] honey , [1] toothpaste , starch suspensions, corn starch , paint , blood , melted butter , and shampoo.

International Journal of Chemical Engineering

ОНА ОТБРОСИТ АНБ НАЗАД НА ДЕСЯТИЛЕТИЯ. Сьюзан как во сне читала и перечитывала эти строки. Затем дрожащими руками открыла следующее сообщение. ТО: NDAKOTAARA. ANON. ORG FROM: ETDOSHISHA. EDU МЕНЯЮЩИЙСЯ ОТКРЫТЫЙ ТЕКСТ ДЕЙСТВУЕТ.

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Фонтейн долго молчал.

 Танкадо успел отдать его за мгновение до смерти. Все были в растерянности. - Ключ… - Ее передернуло.  - Коммандер Стратмор отправил кого-то в Испанию с заданием найти ключ. - И что? - воскликнул Джабба.

 Трансляция началась, - объявил агент Смит. Это было похоже на старое кино. Кадр казался неестественно вытянутым по вертикали и неустойчивым, как бывает при дрожащем объективе, - это было результатом удаления кадров, процесса, сокращающего видеозапись вдвое и экономящего время. Объектив, скользнув по огромной площади, показал полукруглый вход в севильский парк Аюнтамьенто. На переднем плане возникли деревья.

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 Все совсем не так, как вы подумали. Если бы вы только… - Доброй ночи, сэр.  - Кассирша опустила металлическую шторку и скрылась в служебной комнате.