Viscoelasticity - Orthopaedic Biomaterials in Research and Practice - page 92

Viscoelasticity of fluids

Fluids, as well as solids, exhibit viscoelastic stress-strain behavior. This
is easiest to characterize in shear, as in a shear viscometer, as shown in
Figure 4.15. In this device, a fluid is placed in the annular space between
the inner (rotating) and outer (fixed) cones. A device is provided to mea-
sure the torque applied to the outer cone by the fluid, and the inner cone
is driven at ever-increasing speeds (producing increasing shear strain
rates in the fluid). The force on the outer cone may be expressed, as a
function of geometry, as a viscosity, v , expressed in SI units of pascal-
seconds (Pa*s). A more common unit is the centipoise with 1000 cen-
tipoise = 1 Pa*s. Since energy is continuously dissipated, care must be
taken to keep the temperature of the fluid from increasing.
There are three types of behavior of v as a function of shear strain rate
(Figure 4.15). If v is constant with shear strain rate, the fluid is said to be
Newtonian. Then we can write:

s

σε =⋅ v

where ε s is the shear strain rate. Many fluids, such as water and blood
plasma, are Newtonian.
If v either increases or decreases with shear strain rate, the fluid is said
to be non-Newtonian. In particular, if v decreases with increasing shear
strain rate, the fluid is said to be strain thinning or thixotropic. Tomato
ketchup, non-drip paint, and normal synovial fluid are all thixotropic.
Thixotropy is reversible, but hysteresis heating effects (which generally
reduce v , until cooling occurs) may interfere with recovery of viscosity.
If v increases with increasing strain rate, the fluid is said to be dilatant.
Fluids possess modest unrelaxed shear, tensile, and compressive
moduli. However, the value of their relaxed shear and tensile moduli is
zero; this is an alternative way of defining the fluid state.

100

Rotating
cone

10

Synovial
fluid Te st

fluid

(Normal) *

1

Fixed
cup

Synovial
fluid (RA) *

0.1

Torque
trans-
ducer

0.01

Water (25˚C) = 0.0009 Pa*S

1 0 1 10 2 10 3 10 4

Viscometer (cone type)

Strain rate (LOG) (S -1 )

FIGUre 4.15 the viscometer and some results. (reprinted from
Tribology of Natural and Artificial Joints , dumbledon, J.h., Copyright
1981, with permission from elsevier.)