  The modelling of symmetric rigid dumbbell particles suspended in a Newtonian
fluid, as a model of a rigid-rod polymeric solution, has been accomplished
exclusively through the diffusion equation, which has been detailed elegantly
by Bird et al. [Chapter 14 of $Dynamics \ of \ Polymeric \ Liquids$, Vol 2, Ed
2, (1987)]. In this tutorial, a straightforward approach for modelling a
lopsided rigid dumbbell particle is presented by the Langevin analysis. The
connector force between the dumbbell beads is obtained through the rigidity
constraint of the center-to-center vector of the dumbbell using its Langevin
equation. By directly averaging via the Langevin equation, the evolution of the
center-to-center vector, and the configuration tensor are derived. The stress
expressions for the dumbbell from the Langevin equation, and the diffusion
equation for the orientation distribution function of the center-to-center
vector of the dumbbell are also derived, and the final expressions agree with
established results from other methods.
