Page 60 - Instrumentation Reference Book 3E

easurement of viscosit

K. WALTERS and W. M. JONES

2.4 Introduction these simple Newtonian fluids. It is now common
knowledge, however, that most fluid-like ma-
In the Principia published in 1687. Sir Isaac New- terials have a much more complex behavior, and
ton postulated that “the resistance which arises this is characterized by the adjective “non-New-
from the lack of slipperiness of the parts of the tonian.” The most common expression of non-
liquid, other things being equal, is proportional Newtonian behavior is that the viscosity is now
to the velocity with which parts of the liquid are dependent on the shear rate 7, and it is usual to
separated from one another” (see Figure 2.1). refer to the apparent viscosity q(y) of such fluids,
This ‘‘lack of slipperiness” is what we now call where, for the motion of Figure 2.1,
viscosity. The motion in Figure 2.1 is referred to
as steady simple shear flow and if 7 is the relevant 7- = rl(Y)Y (2.2)
shear stress producing the motion and is the In the next section, we shall argue that the con-
velocity gradient (7 = Uild), we have cept of viscosity is intimately related to the flow
field under investigation (e.g., whether it is steady
7 = q;! (2.1) simple shear flow or not) and in many cases it is
7 is sometimes called the coefficient of viscosity, more appropriate and convenient to define an
but it is now more commonly referred to simply extensional viscosity q5 corresponding to a steady
as the viscosity. An instrument designed to meas- uniaxial extensional flow. Now, although there is
ure viscosity is called a viscometer. A viscometer a simple relation between the (extensional) vis-
is a special type of rheometer (defined as an cosity qc and the (shear) viscosity 7 in the case of
ins1.rument for measuring rheological properties) Newtonian liquids (in fact, 11;: = 3q for Newton-
which is limited to the measurement of viscosity. ian liquids) such is not the case in general for
The SI units of viscosity ,are the pascal non-Newtonian liquids, and this has been one of
second = 1 Nsm-’(= 1 kgm-ls- and NsT-’). the motivations behind the emergence of a num-
The c.g.s. unit is the poise (= 0.1 kgm-ls- ) or ber of extensional viscometers in recent years (see
the poiseciille (= 1 Nsm-’). The units of kin- Section 2.5).
ematic viscosity v ( =q/p, where p is the density) Most fluids of industrial importance can be
are m’s-’. The c.g.s. unit is the stokes (St) and classified as non-Newtonian: liquid detergents,
1 cst = IO -6m’s-’. multigrade oils, paints, printing inks, and molten
For simple liquids like water, the viscosity can plastics are obvious examples (see: for example,
depend on the pressure and temperature, but not Walters (1980)), and no chapter on “the measure-
on the velocity gradient (Le., shear rate). If such ment of viscosity” would be complete without a
materials satisfy certain further formal require- full discussion of the application of viscometry to
ments (e.g., that they are inelastic), they are these complex fluids. This will necessitate an
referred to as Newtonian viscous fluids. Most initial discussion of such important concepts as
viscometers were originally designed to study yield stress and thixotropy (which are intimately
related to the concept of viscosity), and this is
undertaken in the next section.

U
2.2 Newtonian and non-
Newtonian behavior
For Newtonian liquids, there is a linear relation
between shear stress 7- and shear rate ;/. For most
non-Newtonian materials, the shear-thinning
Figure 2.1 Newton’s postulate. behavior shown schematically in Figure 2.2