Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. For example, high-viscosity felsic magma will create a tall, steep stratovolcano, because it cannot flow far before it cools, while low-viscositymafic lava will create a wide, shallow-sloped shield volcano.
With the exception of superfluids, all real fluids have some resistance to stress and therefore are viscous. A fluid which has no resistance to shear stress is known as anideal fluid or inviscid fluid. In common usage, a liquid with the viscosity less than water is known as a mobile liquid, while a substance with a viscosity substantially greater than water is simply called a viscous liquid.
The SI unit of viscosity is the pascal second [Pa s], which has no special name. Despite its self-proclaimed title as an international system, the International System of Units has had very little international impact on viscosity. The pascal second is rarely used in scientific and technical publications today. The most common unit of viscosity is the dyne second per square centimeter[dyne s/cm2], which is given the name poise [P] after the French physiologist Jean Louis Poiseuille(1799-1869). Ten poise equal one pascal second [Pa s] making the centipoise [cP] andmillipascal second [mPa s] identical.
1 pascal second = 10 poise = 1,000 millipascal second
1 centipoise = 1 millipascal second
1 centipoise = 1 millipascal second
There are actually two quantities that are called viscosity. The quantity defined above is sometimes called dynamic viscosity, absolute viscosity, or simple viscosity to distinguish it from the other quantity, but is usually just called viscosity. The other quantity called kinematic viscosity (represented by the symbol ν "nu") is the ratio of the viscosity of a fluid to its density.
ν = η/ρ
Kinematic viscosity is a measure of the resistive flow of a fluid under the influence of gravity. It is frequently measured using a device called a capillary viscometer — basically a graduated can with a narrow tube at the bottom. When two fluids of equal volume are placed in identical capillary viscometers and allowed to flow under the influence of gravity, a viscous fluid takes longer than a less viscous fluid to flow through the tube. Capillary viscometers are discussed in more detail later in this section.
The SI unit of kinematic viscosity is the square meter per second [m2/s], which has no special name. This unit is so large that it is rarely used. A more common unit of kinematic viscosity is thesquare centimeter per second [cm2/s], which is given the name stokes [St] after the Irish mathematician and physicist George Gabriel Stokes (1819-1903). Even this unit is also a bit too large and so the most common unit is probably the square millimeter per second [mm2/s] orcentistokes [cSt].
1 m2/s = 10,000 cm2/s [stokes] = 1,000,000 mm2/s [centistokes]
1 cm2/s = 1 stokes
1 mm2/s = 1 centistokes
1 cm2/s = 1 stokes
1 mm2/s = 1 centistokes
Factors Affecting Viscosity
Viscosity is first and foremost a function of material. The viscosity of water at 20 ℃ is 1.0020 millipascal seconds (which is conveniently close to one by coincidence alone). Most ordinary liquids have viscosities on the order of 1 to 1000 mPa s, while gases have viscosities on the order of 1 to 10 μPa s. Pastes, gels, emulsions, and other complex liquids are harder to summarize. Some fats like butter or margarine are so viscous that they seem more like soft solids than like flowing liquids. Molten glass is extremely viscous and approaches infinite viscosity as it solidifies. Since this process is not as well defined as true freezing, some believe (incorrectly) that glass may still flow even after it has completely cooled, but this is not the case. At ordinary temperatures, glasses are as solid as true solids.
From everyday experience, it should be common knowledge that viscosity varies with temperature. Honey and syrups can be made to flow more readily when heated. Engine oil and hydraulic fluids thicken appreciably on cold days and significantly affect the performance of cars and other machinery during the winter months. In general, the viscosity of a simple liquiddecreases with increasing temperature (and vice versa). As temperature increases, the average speed of the molecules in a liquid increases and the amount of time they spend "in contact" with their nearest neighbors decreases. Thus, as temperature increases, the average intermolecular forces decrease. The exact manner in which the two quantities vary is nonlinear and changes abruptly when the liquid changes phase.
Viscosity is normally independent of pressure, but liquids under extreme pressure often experience an increase in viscosity. Since liquids are normally incompressible, an increase in pressure doesn't really bring the molecules significantly closer together. Simple models of molecular interactions won't work to explain this behavior and, to my knowledge, there is no generally accepted more complex model that does. The liquid phase is probably the least well understood of all the phases of matter.
While liquids get runnier as they get hotter, gases get thicker. (If one can imagine a "thick" gas.) The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at higher temperatures. Since most of the time the molecules in a gas are flying freely through the void, anything that increases the number of times one molecule is in contact with another will decrease the ability of the molecules as a whole to engage in the coordinated movement. The more these molecules collide with one another, the more disorganized their motion becomes. Physical models, advanced beyond the scope of this book, have been around for nearly a century that adequately explain the temperature dependence of viscosity in gases. Newer models do a better job than the older models. They also agree with the observation that the viscosity of gases is roughly independent of pressure and density. The gaseous phase is probably the best understood of all the phases of matter.
Since viscosity is so dependent on temperature, it shouldn't never be stated without it.
How does temperature effect viscosity of liquids?
-As the temperature of the liquid fluid increases its viscosity decreases. In the liquids the cohesive forces between the molecules predominates the molecular momentum transfer between the molecules, mainly because the molecules are closely packed (it is this reason that liquids have lesser volume than gases.
-The viscosity of the gases increases as the temperature of the gas increases. The reason behind this is again the movement of the molecules and the forces between them. In the gases the cohesive forces between the molecules is lesser, while molecular momentum transfer is high. As the temperature of the gas is increased the molecular momentum transfer rate increases further which increases the viscosity of the gas.
-The viscosity of the gases increases as the temperature of the gas increases. The reason behind this is again the movement of the molecules and the forces between them. In the gases the cohesive forces between the molecules is lesser, while molecular momentum transfer is high. As the temperature of the gas is increased the molecular momentum transfer rate increases further which increases the viscosity of the gas.
CApillary viscometer
The the mathematical expression describing the flow of fluids in circular tubes was determined by the French physician and physiologist Jean Louis Marie Poiseuille (1799–1869). Since it was also discovered independently by the German hydraulic engineer Gotthilf Hagen (1797–1884), it should be properly known as the Hagen-Poiseuille equation, but it is usually just calledPoiseuille's equation. I will not derive it here. (Please don't ask me to.) For non-turbulent, non-pulsatile fluid flow through a uniform straight pipe, the volume flow rate (φ) is …
- directly proportional to the pressure difference (ΔP) between the ends of the tube,
- inversely proportional to the length (ℓ) of the tube,
- inversely proportional to the viscosity (η) of the fluid, and
- proportional to the fourth power of the radius (r4) of the tube.
| φ = | πΔPr4 |
| 8ηℓ |
falling sphere
The mathematical expression describing the viscous drag force on a sphere was determined by the British physicist George Gabriel Stokes (1819–1903). I will not derive it here. (Once again, don't ask.)
R = 6πηrv
The formula for the buoyant force on a sphere is accredited to the Greek engineer Archimedesa.k.a. Αρχιμήδης (287–212 BCE), but equations weren't invented back then.
B = ρfluidgVdisplaced
The formula for weight had to be invented by someone, but I don't know who.
W = mg = ρobjectgVobject
Let's combine all these things together for a sphere falling in a fluid. Weight goes down, buoyancy goes up, drag goes up. After awhile, the sphere will fall with constant velocity. When it does, all these forces cancel. When a sphere is falling through a fluid it is completely submerged, so there is only one volume to talk about — the volume of a sphere. Let's work through this.
| B | + | R | = | W | |||
| ρfluidgV | + | 6πηrv | = | ρobjectgV | |||
| 6πηrv | = | (ρobject − ρfluid)gV | |||||
| 6πηrv | = | Δρg | 4 | πr3 | |||
| 3 | |||||||
And here we are.
| η = | 2Δρgr2 |
| 9v |
Drop a sphere into a liquid. If you know the size and density of the sphere and the density of the liquid, you can determine the viscosity of the liquid. If you don't know the density of the fluid you can determine the kinematic viscosity. If you don't know the density of the sphere, but you know its mass and radius, well then you do know its density. Why are you talking to me? Go back several chapters and get yourself some education.
Viscosity of Solids
On the basis that all solids such as granite flow in response to small shear stress, some researchers have contended that substances known as amorphous solids, such as glass and many polymers, may be considered to have viscosity. This has led some to the view that solids are simply "liquids" with a very high viscosity, typically greater than 1012 Pa·s. This position is often adopted by supporters of the widely held misconception that glass flow can be observed in old buildings. This distortion is the result of the undeveloped glass making process of earlier eras, and not due to the viscosity of glass.
However, others argue that solids are, in general, elastic for small stresses while fluids are not. Even if solids flow at higher stresses, they are characterized by their low-stress behavior. This distinction is muddled if measurements are continued over long time periods, such as the pitch drop experiment. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the term viscosity is sometimes used for solid materials, for example Maxwell materials, to describe the relationship between stress and the rate of change of strain, rather than rate of shear.
These distinctions may be largely resolved by considering the constitutive equations of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called viscoelastic. In geology, earth materials that exhibit viscous deformation at least three times greater than their elastic deformation are sometimes called rheids.
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