Biomedical Engineering Reference
In-Depth Information
Solid
Fluid
FIGURE 4.34
(Left) A solid material resists applied external shear stress (solid vectors) via internally generated
reaction shear stress (dashed vectors). (Right) A fluid subjected to applied shear stress is unable to resist and
instead flows (dashed lines).
the solid via internally generated reaction forces, depicted by the dashed arrows. When
applied to a fluid (right panel), the fluid cannot resist the applied shear but rather flows.
The applied shear forces lead to shear stresses, force per area, and the measure of flow
can be quantified by the resulting shear strain rate. In essence, the harder one pushes on
a fluid (higher shear stress), the faster the fluid flows (higher shear strain rate). The relation-
ship between shear stress, t, and shear strain rate,
g, is the fluid's viscosity, m. Viscosity is
_
sometimes written as
in biomedical applications. As shown in Figure 4.35, many fluids,
including water, are characterized by a constant, linear viscosity and are called Newtonian.
Others possess nonlinear shear stress-strain rate relations, and are non-Newtonian fluids.
For example, fluids that behave more viscously as shear strain rate increases are called
dilatant, or shear thickening. One example of dilatant behavior is Dow Corning 3179 dilat-
ant compound, a silicone polymer commonly known as “Silly Putty.” When pulled slowly,
this fluid stretches (plastic deformation); when pulled quickly, it behaves as a solid and
fractures. Fluids that appear less viscous with higher shear strain rates are called pseudo-
plastic, or shear thinning. For example, no-drip latex paint flows when applied with a brush
or roller that provides shear stress, but it does not flow after application.
Bingham Plastic
Casson Equation
Dilatant
Newtonian
Pseudoplastic
τ
0
•
Shear Strain Rate
γ
FIGURE 4.35
Newtonian fluids exhibit a constant viscositym ¼ t=g, arising from the linear relation between
shear stress and shear strain rate. Non-Newtonian fluids are nonlinear. Blood is often characterized with a Casson
equation but under many conditions may be described as Newtonian.
