Page 247 - Bird R.B. Transport phenomena

Chapter 8

Polymeric Liquids

§8.1 Examples of the behavior of polymeric liquids

§8.2 Rheometry and material functions
§8.3 Non-Newtonian viscosity and the generalized Newtonian models
§8.4° Elasticity and the linear viscoelastic models
§8.5* The corotational derivatives and the nonlinear viscoelastic models
§8.6* Molecular theories for polymeric liquids

In the first seven chapters we have considered only Newtonian fluids. The relations be-
tween stresses and velocity gradients are described by Eq. 1.1-2 for simple shear flow
and by Eq. 1.2-6 (or Eq. 1.2-7) for arbitrary time-dependent flows. For the Newtonian
fluid, two material parameters are needed—the two coefficients of viscosity /x and к—
which depend on temperature, pressure, and composition, but not on the velocity gradi-
ents. All gases and all liquids composed of "small" molecules (up to molecular weights
of about 5000) are accurately described by the Newtonian fluid model.
There are many fluids that are not described by Eq. 1.2-6, and these are called non-
Newtonian fluids. These structurally complex fluids include polymer solutions, polymer
melts, soap solutions, suspensions, emulsions, pastes, and some biological fluids. In this
chapter we focus on polymeric liquids.
Because they contain high-molecular-weight molecules with many internal degrees
of freedom, polymer solutions and molten polymers have behavior qualitatively differ-
ent from that of Newtonian fluids. Their viscosities depend strongly on the velocity gra-
dients, and in addition they may display pronounced "elastic effects." Also in the steady
simple shear flow between two parallel plates, there are nonzero and unequal normal
stresses (т , т , and r ) that do not arise in Newtonian fluids. In §8.1 we describe some
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experiments that emphasize the differences between Newtonian and polymeric fluids.
In dealing with Newtonian fluids the science of the measurement of viscosity is
called viscometry, and in earlier chapters we have seen examples of simple flow systems
that can be used as viscometers (the circular tube, the cone-plate system, and coaxial cylin-
ders). To characterize non-Newtonian fluids we have to measure not only the viscosity,
but the normal stresses and the viscoelastic responses as well. The science of
measurement of these properties is called rheometry, and the instruments are called
rheometers. We treat this subject briefly in §8.2. The science of rheology includes all aspects
of the study of deformation and flow of non-Hookean solids and non-Newtonian liquids.
After the first two sections, which deal with experimental facts, we turn to the pre-
sentation of various non-Newtonian "models" (that is, empirical expressions for the
stress tensor) that are commonly used for describing polymeric liquids. In §8.3 we start
with the generalized Newtonian models, which are relatively simple, but which can describe
only the non-Newtonian viscosity (and not the viscoelastic effects). Then in §8.4 we give
examples of linear viscoelastic models, which can describe the viscoelastic responses, but

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