| Liquid Crystalline Polymers have a wide variety of applications. They are not only interesting to the industrial world, but to the academic world as well. To take full advantage of these interesting materials, it is necessary to develop numerical algorithms that predict their behavior when subjected to processing flows. In the current work, an algorithm was developed that directly solves the full Doi-Marrucci-Greco (DMG) model for a 2D flow domain when subjected to simple shear flow. This algorithm is referred to as the direct solver. Due to the extremely high computational cost of implementing this direct solver, a Multi-Resolution based methodology was designed and proves to be a viable technique in reducing this cost. It also displays promise as a tool that could be applied to different complex fluids problems and perhaps beyond.;Simulations for two different Deborah numbers were performed. The Deborah number, De, gives a ratio of shear rate to rotational diffusion. First, for De = 0.5, the direct solver developed here displays dynamics that are very similar to results from the Bingham closure approximation technique recently published. What is shown in this work is that the dynamics of these flow problems are dependent on the size of the flow domain. For De = 2.0 we observe behavior in the direct solver results that are qualitatively different than those from the closure approximation. Sufficient testing is performed to show that the numerical tools developed here are not the cause for these differences. The discrepancies observed are attributed to the differences in the models. These results show great promise as they display that solving a high dimensional complex flow problem directly can be computationally realistic. |
