Behavior of Solutions of Linear Macromolecules in Steady Shear Flow with Superposed Oscillations

Abstract

The rotational diffusion equation has been solved for a suspension of rigid dumbbells in a velocity field which is the superposition of steady shearing flow (large deformation) and an infinitesimal oscillatory motion (very small deformation). An expression is obtained for the associated shear stresses and the results are expressed in terms of a complex viscosity, appropriately modified for the superposed steady shearing flow. The rigid dumbbell model gives a maximum in the real part of the complex viscosity as well as negative values for the imaginary part at low frequencies. Such behavior has been observed experimentally. The elastic dumbbell model (two beads connected by a Hookean spring) does not give results which are qualitatively similar to the experimental data.