Lopsided Elastic Dumbbell Suspension

Abstract

We derive the constitutive equation for a suspension of lopsided Hookean dumbbells. By lopsided, we mean that one bead is larger than the other. We find that all results derived for symmetric Hookean dumbbells can be taken over for lopsided ones by replacing$\frac{2}{\hat{I}}\P$ with $\frac{1}{\hat{I}{\P }_1}+\frac{1}{\hat{I}{\P }_2}$, where $\hat{I}\P$, $\hat{I}{\P }_1$ and $\hat{I}{\P }_2$ are the bead friction coefficients for the symmetric dumbbell beads, and the first and second beads of the lopsided dumbbell respectively.