arXiv subjects
Publications and source records attributed to Alan Jeffrey Giacomin.
The novelty of this work is that it takes a result of macromolecular theory that is not objective, and fixes it. To do so we use an objective vorticity tensor to obtain a fully frame invariant form of the classical constitutive equation for FENE dumbbell fluids obtained within the conceptual framework of kinetic theory for polymer solutions. The influence of such an objective formulation is discussed for steady shear flows.
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.