The Visco-elastic Properties of Network Structure III. Normal Stress Effect (Weissenberg Effect)

A statistical mechanical theory of the so-called Weissenberg effect (or, normal stress effect) is presented. We adopt the weakly coupled rubber-like network model which we have formulated and applied to investigate the shearing and the tensile viscosity of concentrated solutions of linear high polymers. When the elastico-viscous liquid is compelled to stationary shearing flow, our theory shows that an additional normal tension arises in the direction of flow owing to the orientation of the network structure in addition to the usual shearing stress. Furthermore if the fluid is in a concentric circular motion with the angular velocity gradient in the radial or the axial direction, each doughnut-shaped piece along a flow line behaves as a streched rubber loop due to the said additional tension. As the result the inner bulk of the liquid is squeezed. The pressure increases as one approaches to the rotational axis. Such pressure distribution is calculated for the instruments of three types, i.e., the coaxial cylinder, the parallel plate and cone and plate instrument. The results are at least qualitatively in good agreement with various experimental results reported by Roberts. Philippoff. Rivlin. Kurata, Kotaka and Tamura and others.