Viscosity (redirected from viscous)

viscosity, resistance of a fluid to flow. This resistance acts against the motion of any solid object through the fluid and also against motion of the fluid itself past stationary obstacles. Viscosity also acts internally on the fluid between slower and faster moving adjacent layers.

All fluids, i.e., all liquids and gases, exhibit viscosity to some degree. Viscosity may be thought of as fluid friction, just as the friction between two solids resists the motion of one over the other but also makes possible the acceleration of one relative to the other (e.g., the friction between the wheels of an automobile and a highway), so viscosity resists the motion of a solid through a fluid but also makes it possible for a propeller or other device to accelerate the solid through the fluid.

The Velocity Gradient

When a fluid is moving through a pipe or a solid object is moving through a fluid, the layer of fluid in contact with the sides of the pipe or the surface of the object tends to be in the same state of motion as the object with which it is in contact; that is, the layer of fluid along the side of the pipe is at rest, while that in contact with the moving object is carried along at the same velocity as the object. If the difference in velocity between the fluid at the sides of the pipe and that at the center, or between the moving object and the fluid through which it is moving, is not too great, then the fluid flows in continuous, smooth layers; that is, the flow is laminar.

The difference in velocity between adjacent layers of the fluid is known as a velocity gradient and is given by v/x, where v is the velocity difference and x is the distance between the layers. To keep one layer of fluid moving at a greater velocity than the adjacent layer, a force F is necessary, resulting in a shearing stress F/A, where A is the area of the surface in contact with the layer being moved.

The Coefficient of Viscosity

The ratio of the shearing stress to the velocity gradient is a measure of the viscosity of the fluid and is called the coefficient of viscosity η, or η=Fx/Av. The cgs unit for measuring the coefficient of viscosity is the poise. Experiments have shown that the coefficient of viscosity of liquids decreases with increasing temperature, while the coefficient of viscosity of gases increases with increasing temperature. In liquids an increase in temperature is associated with the weakening of bonds between molecules; since these bonds contribute to viscosity, the coefficient is decreased. On the other hand, intermolecular forces in gases are not as important a factor in viscosity as collisions between the molecules, and an increase in temperature increases the number of collisions, thus increasing the coefficient of viscosity. A striking result of the kinetic theory of gases is that the viscosity of a gas is independent of the density of a gas. Viscosity is the principal factor resisting motion in laminar flow. However, when the velocity has increased to the point at which the flow becomes turbulent, pressure differences resulting from eddy currents rather than viscosity provide the major resistance to motion.

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viscosity

Resistance of a fluid to a change in shape, or movement of neighbouring portions relative to one another. Viscosity denotes opposition to flow. It may also be thought of as internal friction between the molecules. Viscosity is a major factor in determining the forces that must be overcome when fluids are used in lubrication or transported in pipelines. It also determines the liquid flow in spraying, injection molding, and surface coating. The viscosity of liquids decreases rapidly with an increase in temperature, while that of gases increases with an increase in temperature. The SI unit for viscosity is the newton-second per square metre (N-s/m²).

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Viscosity

The material property that measures a fluid's resistance to flowing. For example, water flows from a tilted jar more quickly and easily than honey does. Honey is more viscous than water, so although gravity creates nearly the same stresses in honey and water, the more viscous fluid flows more slowly.

The viscosity can be measured where the fluid of interest is sheared between two flat plates which are parallel to one another (see illustration). This is known as planar Couette flow. The shear stress is the ratio of the tangential force F needed to maintain the moving plate at a constant velocity V to the plate area A. The shear flow created between the plates has the velocity profile given by Eq. (1),

(1) 

where v_x is the velocity parallel to the plates at a perpendicular distance y above the stationary plate. The coefficient γ ˙, called the velocity gradient or shear rate, is given by V/δ, where δ is the distance between the plates. It is expected that the shear stress increases with increasing shear rate but that the ratio of these two quantities depends only on the fluid between the plates. This ratio is used to define the shear viscosity, &eegr;, as in Eq. (2).

(2) 

The shear viscosity may depend on temperature, pressure, and shear rate.

Planar Couette flow

Isaac Newton is credited with first suggesting a model for the viscous property of fluids in 1687. Newton proposed that the resistance to flow caused by viscosity is proportional to the velocity at which the parts of the fluid are being separated from one another because of the flow. Although Newton's law of viscosity is an empirical idealization, many fluids, such as low-molecular-weight liquids and dilute gases, are well characterized by it over a large range of conditions. However, many other fluids, such as polymer solution and melts, blood, ink, liquid crystals, and colloidal suspensions, are not described well by Newton's law. Such fluids are referred to as non-newtonian.

For planar Couette flow, Newton's law of viscosity is given mathematically by

(3) 

Eq. (3), where is the shear stress, and μ, a function of temperature and pressure, is the coefficient of viscosity or simply the viscosity. Therefore, by comparing Eqs. (2) and (3) the shear viscosity is equal to the coefficient of viscosity (that is, η = μ) for a newtonian fluid. Because of this re­lation the shear viscosity is also often referred to as the viscosity. However, it should be clear that the two quantities are not equivalent; μ is a newtonian-model parameter, which varies only with temperature and pressure, while &eegr; is a more general material property which may vary nonlinearly with shear rate. See Fluid flow, Newtonian fluid

Viscosity conversions

Unit	poise	cp	Pa · s	m/(ft · s)	lbf · s/ft2
1 poise*	1	100	0.1	6.72 × 10-2	2.089 ×10-3
1 centipoise	0.01	1	0.001	6.72 × 10-4	2.089 × 10-5
1 pascal-second†	10	1000	1	0.672	2.089 × 10-2
1 lbm/(ft · s)	14.88	1488	1.488	1	3.108 × 10-2
1 lbf · s/ft2	478.8	4.788 × 104	47.88	32.17	1
*1 poise = 1 dyne · s/cm2 = 1 g/(cm · s). †1 Pa · s = 1 kg/(m · s).

From Eqs. (2) and (3), the units of viscosity are given by force per area per inverse time. If in planar Couette flow, for example, 1 dyne of tangential force is applied for every 1 cm² area of plate to create a velocity gradient of 1 s^-1, then the fluid between the plates has a viscosity of 1 poise (=1 dyne · s/cm²). Several viscosity units are in common use (see table). Comparison of the viscosities of different fluids demonstrates some general trends. For example, the viscosity of gases is generally much less than that of liquids. Whereas gases tend to become more viscous as temperature is increased, the opposite is true of liquids. Other data also show that increasing pressure tends to increase the viscosity of dense gases, but pressure has only a small effect on the viscosity of dilute gases and liquids.

Whereas dilute gas molecules interact primarily in pairs as they collide, molecules in the liquid phase are in continuous interaction with many neighboring molecules. The concepts of velocity and mean free path have little meaning for liquids. It is clear, however, that increasing temperature increases the mobility of molecules, thus allowing neighboring molecules to more easily overcome energy barriers and slip past one another. Such arguments lead to an exponential relation for the dependence of viscosity on temperature.

Many non-newtonian fluids not only exhibit a viscosity which depends on shear rate (pseudoplastic or dilantant) but also exhibit elastic properties. These viscoelastic fluids require a large number of strain-rate-dependent material properties in addition to the shear viscosity to characterize them. The situation can become more complex when the material properties are time dependent (thixotropic or rheopectic). Fluids that are nonhomogeneous or nonisotropic require even more sophisticated analysis. The field of rheology attempts to deal with these complexities. See Rheology