Polymer Physics

wheregis the shear deformation ratio,g^0 is the shear rate. Accordingly, the equation
of motion for the Newtonian fluid can be obtained as

s¼g^0 (7.3)

This equation is similar to the second Newton’s law (total forces proportional to
the acceleration rate), because the shear rate reflects the acceleration rate generated
by the shear stress.
The second approach to realize laminar flow is theelongationalorextensional
flow. In this approach, the flow velocity changes along the flow directionx,as
illustrated in Fig.7.3. The longitudinal velocity gradient can be generated either by
the change in the diameter of the tube, or by the deformation under the external
pulling force. The tensile stress

s

f

A

¼e

dv

dx

(7.4)

Fig. 7.1 Illustration of the profiles of flow velocities in (a) Couette flow and (b) Poiseuille flow,
respectively

Fig. 7.2 Illustration of the definition to the Newtonian fluid in the shear flow field.fis the shear
force, andAis the shear area

7.1 Introduction to Rheology 129