  A dilute polymer solution is modeled as a suspension of non-interacting
Hookean dumbbells and the effect of excluded volume is taken into account by
incorporating a narrow Gaussian repulsive potential between the beads of each
dumbbell. The narrow Gaussian potential is a means of regularising a
delta-function potential---it tends to the delta-function potential in the
limit of the width parameter going to zero. Exact predictions of viscometric
functions in simple shear flow are obtained with the help of a retarded motion
expansion and by Brownian dynamics simulations. It is shown that for relatively
small non-zero values of the width parameter, the presence of excluded volume
causes a swelling of the dumbbell at equilibrium, and shear thinning in simple
shear flow. On the other hand, a delta function excluded volume potential does
not lead to either swelling or to shear thinning. Approximate viscometric
functions, obtained by assuming that the bead-connector vector is described by
a Gaussian non-equilibrium distribution function, are found to be accurate
above a threshold value of the width parameter, for a given value of the
strength of excluded volume interaction. A first order perturbation expansion
reveals that the Gaussian approximation is exact to first order in the strength
of excluded volume interaction. The predictions of an alternative quadratic
excluded volume potential suggested earlier by Fixman (J. Chem. Phys., 1966,
45, 785; 793) are also compared with those of the narrow Gaussian potential.
