Anisotropic Fluid Theory: A Different Approach to the Dumbbell Theory of Dilute Polymer Solutions

The continuum theory of anisotropic fluids, as developed by Ericksen and others, has been used to formulate an expression for the time derivative of the end-to-end vector of a linear macromolecule. When this expression is used in conjunction with the equation describing the distribution function for a dilute solution of dumbbell elements, the results exhibit important differences from the usual dumbbell theory. Presence of an additional term in the differential equation for the distribution function leads to the prediction of both a non-Newtonian viscosity and nonzero first and second normal stress differences in simple shearing flow. The normal stress differences are found to be of opposite sign, the secondary normal stress difference being negative. In small-amplitude oscillatory shear flow, and in pure deformational flow, the results are equivalent to those of the dumbbell theory. Expressions are presented for both stress and optical properties in an arbitrary homogeneous shear field.