Lopsided Elastic Dumbbell Suspension

TL;DR

This paper derives a constitutive equation for suspensions of lopsided Hookean dumbbells, showing how results for symmetric dumbbells can be adapted by replacing friction coefficient terms.

Contribution

It introduces a modified constitutive equation for lopsided dumbbells, extending existing models for symmetric dumbbells to asymmetric bead sizes.

Findings

Derived the constitutive equation for lopsided dumbbells

Established the relation between symmetric and lopsided dumbbell results

Provided a simple substitution rule for existing models

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}{\zeta}$ with $\frac{1}{\zeta_1}+\frac{1}{\zeta_2}$, where ${\zeta}$, ${\zeta}_1$ and ${\zeta}_2$ are the bead friction coefficients for the symmetric dumbbell beads, and the first and second beads of the lopsided dumbbell respectively.