Synonyms
Bingham fluids; Dilatant; Power law fluids; Pseudoplastic; Shear thinning
Definition
Viscosity is the physical property that characterizes the flow resistance of simple fluids. Newton’s law of viscosity defines the relationship between the shear stress and shear rate of a fluid subjected to a mechanical stress. The ratio of shear stress to shear rate is a constant, for a given temperature and pressure, and is defined as the viscosity or coefficient of viscosity. Newtonian fluids obey Newton’s law of viscosity. The viscosity is independent of the shear rate.
NonNewtonian fluids do not follow Newton’s law and, thus, their viscosity (ratio of shear stress to shear rate) is not constant and is dependent on the shear rate.
Dynamic viscosity is the coefficient of viscosity as defined in Newton’s law of viscosity. Kinematic viscosity is the dynamic viscosity divided by the density.
Scientific Fundamentals
The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another
The stress is proportional to the strain. These two laws set the boundary conditions for flow behavior of fluids. Fully viscous behavior is governed by Newton and fully elastic (solidlike) behavior by Hooke. Many fluids (e.g., industrial greases) will exhibit characteristics of both viscous and elastic behavior and are commonly referred to as viscoelastic fluids. Viscoelastic fluids are considered nonNewtonian fluids (257).
Units of Viscosity

In the SI system:

Stress = F/A = newton/m^{2} = Pascal (Pa)

Strain − distance moved/gap = m/m = dimensionless

Rate of strain = shear rate = strain/time = dimensionless/s = 1/s (s^{−1})

Viscosity = stress/shear rate =Pa/ (1/s) = Pas

In the cgs system:

Stress = F/A = dyne/cm^{2}

Strain − distance moved/gap = cm/cm = dimensionless

Rate of strain = shear rate = strain/time = dimensionless/s = 1/s (s^{−1})

Viscosity = stress/shear rate =dyne/cm^{2}/(1/s) = dyne s/cm^{2} = Poise
The common units used in lubrication are milli Pasec (mPas) and centipoise (cP).
Approximate viscosities of some common fluids at ambient conditions
Fluid 
Viscosity, mPas 

Air 
.001 
Water 
1 
Milk 
10 
Olive oil 
100 
Engine oil 
1,000 
Honey 
10,000 
Key Applications
Newtonian Fluids
In general, most additives used in the lubrication industry would affect the absolute value of the viscosity of the formulation but not the Newtonian behavior (454,348). Common dispersants and detergents used in engine oil formulations, for example, will raise the viscosity of the formulation due to their own higher viscosities. However, the formulation will still obey Newton’s law and follow Newtonian fluid behavior.
NonNewtonian Fluids
Many fluids do not obey Newton’s law of viscosity (349). The viscosity will vary with shear rate and a single measurement is not sufficient to characterize the flow properties of the fluid. Other factors that may affect flow properties include pressure and temperature.
Polymeric additives are the most common cause of nonNewtonian behavior in fully formulated lubricating oils (131,164). The major factors affecting this flow behavior are the molecular weight and concentration of the polymer (625). Polymer morphology is a minor factor affecting the nonNewtonian behavior. The higher the molecular weight and the higher the concentration, the more pronounced the nonNewtonian behavior of the fluid. These effects relate to new, unused lubrication formulations.
As oils age in service and become used, other factors can cause them to take on more nonNewtonian characteristics even at the lower shear rates. These factors include contamination particles, soot/sludge from incomplete combustion, and oxidation by products and particles. Some of the factors that can determine the degree of non–Newtonian behavior include particle size, shape and distribution, volume fraction of particles, electrostatic charges on particles, and steric effects, among others. The more the particles can interact with one another, the greater the likelihood of nonNewtonian behavior.
NonNewtonian Fluid Models
(Note: Figure 4 refers to shear thinning as power law, whereas shear thickening also can be described by power law. The figure can also show typical thixotropic behavior.)
n = 1 
This reduces to Newton’s law and the constant is the viscosity 
\( {\text{Viscosity }} = {\text{ stress}}/{\text{shear rate}} \)  
n < 1 
The fluid is shear thinning with the viscosity decreasing with shear rate. This is the most common type of behavior for nonNewtonian fluids. Shear thinning is the predominant phenomena associated with polymer solution flow behavior. 
\( \eqalign{ {\text{Viscosity }} = {\text{ stress}}/{\hbox{shear rate }} = {\text{ constant}}^*{\left( {\text{shear rate}} \right)^{\text{n}}}/{\text{shear rate}} \cr { } = {\text{constant }}/{\left( {\text{shear rate}} \right)^{{{\text{n}}  {1}}}}} \)  
n > 1 
The fluid is dilatant or rheopectic, with the viscosity increasing with shear rate 
\( \eqalign{ {\text{Viscosity }} = {\text{ stress}}/{\hbox{shear rate }} = {\text{ constant}}^*{\left( {\text{shear rate}} \right)^{\text{n}}}/{\text{shear rate}} \cr = {\text{ constant }}^*{\left( {\text{shear rate}} \right)^{{{\text{n}}  {1}}}}} \) 
This is generally unusual behavior and is not observed often. Highly loaded particle systems (75+%) tend to show an increase in viscosity as the shear rate increases.
This describes a fluid with a yield stress (constant a) followed by a power law term. If n = 1, then this describes a Bingham fluid. This reduces to a Newtonian fluid for n = 1 and constant a (yield stress) = 0.
The cross model is a fourparameter model and describes the general non–Newtonian viscosity versus shear rate curve of Fig. 3. It includes a zero shear viscosity, infinite shear viscosity and power law, and shear thinning terms.
Temporary and Permanent Viscosity Shear Loss
The change in viscosity with shear rate for nonNewtonian fluids (shear thinning) is termed temporary shear loss (454). It is temporary in the sense that, as the shear rate increases and decreases, the viscosity is totally recoverable. The decrease in viscosity is temporary at the high shear rates and the viscosity recovers as the shear rate is decreased. Permanent shear loss occurs when physical changes occur to the fluid, causing a permanent change in the viscosity. A polymercontaining fluid will show shear thinning character, as discussed above. If this fluid is mechanically sheared such that the polymer chains are broken, then this effectively reduces the molecular weight of the polymer. The fluid will still be nonNewtonian in behavior but the absolute value of the viscosity will be decreased by a certain amount. This permanent decrease in viscosity across shear rates is called permanent viscosity shear loss or permanent shear loss.
Thixotropic fluids show a decrease in viscosity over time, irrespective of the shear rate.
Viscosity Measurement
Viscosity can be measured by a number of techniques that yield a single value (165). This is perfectly appropriate and valid for Newtonian fluids. NonNewtonian fluids need to be measured under varying stress or shear rate to yield shear stress versus shear rate data to obtain the real behavior of the system. NonNewtonian fluid viscosities must be compared at equivalent shear rates to be meaningful. The glass capillary tube is a common technique used in lubrication to measure viscosity. The stress is applied by gravitational force and thus the shear rate tends to be low for this type of measurement. As discussed above, many polymercontaining lubrication fluids are shear thinning but only at very high shear rates. The shears rates of the capillary instrument are in the range of the low shear Newtonian region and thus the fluids will behave as Newtonian fluids.
The capillary method generates viscosity termed kinematic viscosity. The units of kinematic viscosity are centistokes (cSt) and the conversion to dynamic viscosity is \( {\text{cSt}} = {\text{cP}} \) divided by density.
A variety of highpressure capillary (271) and rotational instruments (453) are used to measure the viscosity versus shear rate behavior of nonNewtonian fluids. These include cone and plate and concentric cylinder type systems. The rotational systems use a mechanical force and operate in one of two ways: (1) the mechanical force is applied (stress) and resulting speed of rotation is measured (shear rate) or (2) speed of rotation is set and the force required to maintain speed is measured.
CrossReferences
Lubrication with a Newtonian Fluid
Lubrication with a NonNewtonian Fluid
Rheological Measurement Methods and Equipment