Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 35

1g = cm s

2

30mm = s

105 dyne
cm 2

10 2 2 P τ lower 5 3 : 5 3

10mm 5

0 : 0105Pa 5 0 :

1P 2

Although the shear forces have the same magnitude, their directions are opposite. The force
on the top plate is acting in the negative x-direction, while the force on the bottom plate is
acting in the positive x-direction. Remember the sign convention for stress that was discussed in
section 2.5 .

2.8 FLUID MOTIONS

Most fluids, under normal conditions can be considered Newtonian fluids. A
Newtonian fluid is classified by a constant dynamic viscosity under any shear rate. Similar
to a purely elastic material, these fluids have a linear relationship between shear stress and
shear rate. However, many fluids do not exhibit Newtonian properties and, therefore, are
termed “Non-Newtonian” fluids ( Figure 2.20 ). For example, ketchup will flow out of the
bottle very slowly with only the gravitational force pulling it. However, if you squeeze the
bottle slightly, the ketchup will flow out of the bottle more quickly. This is an example of a
shear-thinning fluid (also termed “pseudoplastic”). These fluids have a larger dynamic vis-
cosity at low shear rates and a lower dynamic viscosity at high shear rates. Another non-
Newtonian fluid is a sand

water mixture. When there is a large volume of water with a
small amount of sand, this fluid will have a lower viscosity. Under a low shear rate, this
mixture behaves as water. As the shear rate increases, water will flow out of the mixture,
leaving a similar quantity of sand and water. This mixture will have a larger viscosity
(at the higher shear rate). At some time, most of the water will be removed from the mix-
ture, and it will become very difficult to make this fluid flow. Although, under these large
stresses, the fluid will marginally deform because the resistance against motion is
extremely large. This type of fluid is a shear-thickening fluid (also termed “dilatant”). To
describe these fluids, the shear stress shear rate relationship becomes

n

y 1 @

v y
@

@ v x

@

τ 5 k ð 2 : 34 Þ

xy

x

FIGURE 2.20

Shear stress, τ Relationship between shear stress

and shear rate for Newtonian and non-Newtonian
fluids. Newtonian fluids have a constant viscosity as
a function of shear rate. Non-Newtonian fluids have a
non-constant viscosity.

Bingham plastic

Pseudoplastic
Dilatant

τ y

Newtonian

Shear rate, du
dy