In this final section we calculate the viscosity of a dilute
polymer solution. Shear flows, for which the velocity components are given
by

(6.48) |

are commonly used for studying viscoelastic properties. If the shear rates are small enough, the stress tensor depends linearly on and can be written as

where

An important special case is a stepwise shear flow, which is switched on at *t*=0:

where is called the shear rate and is the Heaviside function ( for

The limit must be taken because during the early stages elastic stresses are built up.

The calculation now consists of two steps. First we shall bring Eq. (5.64) into a form applicable to the present case. In the second step we shall formulate the Langevin approach of section 6.3 in the case when the system is under shear, and calculate the stress tensor.