23-07-2012, 12:19 PM
Rheology of Fluids
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For most fluids, viscosity is not a constant but varies with the shear rate. Such fluids are called rate dependent. To check
for rate dependent effects, a fluid is tested for shear stress or viscosity at a number of shear rates on the same viscometer.
From this data the rheological constants from the Bingham and Power Law Models can be obtained or when this data is
plotted the result is called a viscosity profile. A few examples are shown below.
In a few systems, such as in water and oils, the shear stress and shear rate are in direct proportion. Such fluids have a
constant viscosity. They are termed Newtonian after Newton, who first postulated their existence.
Most polymers are pseudoplastic. In this case, increased shear rate causes a progressive decrease in viscosity and inversely
a decrease in shear rate will result in an increase in viscosity due to alignment of the long polymer chains along the flow
lines. A few rare concentrated suspensions have been found to be dilatent. These fluids increase in viscosity with
increasing shear. Some fluids have a certain critical shear stress that must be exceeded before flow can begin. This critical
shear stress is called the "yield value". If the fluid has essentially Newtonian flow after the yield value is exceeded, it is
called a Bingham Plastic fluid. This model has been used extensively for circulating fluids in the oil industry. Another
model that has gained acceptance for pseudoplastic fluids is the Ostwald-deWaele-Nutting or Power Law model. If the
fluid has a yield value and also follows the pseudoplastic model, it is referred to as an Ellis fluid and can be described by a
simplified Hershel-Bulkley model. The Power Law and Hershel-Bulkley model have often been used to describe polymer
solutions.
Viscoelasticity
The distinction between solid and liquid materials is not as clear as the preceding would indicate. Most materials have
some solid like character as well as some viscous properties. It is easy to visualize the appearance differences between
viscous liquids and gelled or cross-linked solids. These fluids are characterized by taking the viscosity of liquids and the
gel strength of solids. Many different viscometers and gel testers are sold, depending on the industry. A problem arises
when one tries to characterize a fluid that behaves like both a viscous liquid and a gel. Such fluids are called viscoelastic
fluids. They can be pumped easily (although they have the appearance of a viscous liquid), but they are able to suspend
small solid particles indefinitely (so have the characteristic of an elastic solid). In fact, molten polymers are viscoelastic to
different degrees.
A way of quantifying the viscoelastic properties of materials is by measurement of their elastic modulus and viscous
modulus. It is convenient to think of these as vector quantities located 90 degrees apart. Vector quantities have a magnitude
(which is indicated by the length of the vector) as well as a direction. When the rheology is measured with a viscometer in
steady shear, only the resultant vector of the viscous and elastic modulus is measured, this is usually called the shear stress.
Shear stress divided by the shear rate is called complex viscosity.