Page 29 - Fluid mechanics, heat transfer, and mass transfer

FLUID MECHANICS BASICS
6
& Any fluid that does not obey the Newtonian relation- . What are shear thinning and shear thickening fluids?
ship between the shear stress and shear rate is called & The slope of the shear stress versus shear rate curve
non-Newtonian. The subject of rheology is devoted will not be constant as we change the shear rate.
to the study of the behavior of such fluids. High When the viscosity decreases with increasing shear
molecular weight liquids that include polymer melts rate, the fluid is called shear thinning. However, the
and solutions of polymers, as well as liquids in which rate of increase is less than linear as shown in
fine particles are suspended (slurries and pastes), are Figure 1.1.
usually non-Newtonian. Fluids such as water, etha- & Where the viscosity increases as the fluid is subjected
nol, and benzene and air and all gases are Newtonian.
to a higher shear rate, the fluid is called shear
Also, low molecular weight liquids and solutions of
thickening. For a shear thickening fluid, t increases
low molecular weight substances in liquids are usu-
faster than linearly with increasing g. Shear thinning
ally Newtonian. Some examples are aqueous solu-
behavior is more common than shear thickening
tions of sugar or salt.
behavior.
. What are broad classes of non-Newtonian fluids?
. What are pseudoplastic fluids?
& Non-Newtonian fluids can be divided into two broad
& Shear thinning fluids are called pseudoplastic fluids.
categories on the basis of their shear stress/shear rate
& Apparent viscosity for these fluids decreases with
behavior: those whose shear stress is independent of
increasing shear rate, butinitial viscosity may be high
time or duration of shear (time-independent) and
enough to prevent start of flow.
those whose shear stress depends on time or duration
& Most shear thinning fluids behave in a Newtonian
of shear (time-dependent).
manner (i.e., their viscosity is independent of g)at
. How is a power law fluid characterized?
very high and very low shear rates.
& A power law fluid exhibits the following nonlinear
& Pseudoplastics do not have a yield value.
relationship between shear stress and shear rate:
& Examples of shear thinning fluids are polymer melts
0
0 n
t ¼ K g : ð1:7Þ such as molten polystyrene, polymer solutions such
as polyethylene oxide in water, emulsions, molten
0
& When n ¼ 1, the fluid is Newtonian.
sulfur, molasses, greases, starch suspensions, paper
& Apparent viscosity for a power law fluid under shear
pulp, biological fluids, soaps, detergent slurries,
conditions is toothpaste, cosmetics and some pharmaceuticals,
and inks and paints.
0
0 n 1
a
m ¼ t=g ¼ K g : ð1:8Þ
. Give examples of shear thickening fluids.
0
& When n < 1, m a decreases with increasing g, and the & Some examples of shear thickening fluids are corn-
fluid is called shear thinning or pseudoplastic. starch, pastes, slurries of clay and titanium dioxide,
& When n > 1, m a increases with increasing g, and the wet beach sand and sand-filled emulsions, sugar,
0
fluid is called shear thickening or dilatant. paper coatings, pigment–vehicle suspensions such

Shear rate versus shear stress diagrams for Newtonian and non-Newtonian fluids.
FIGURE 1.1