Dimensional analysis and the validation by molecular dynamics simulation of polymer melt flow

As well known, in the simulation process of wind tunnel, as long as the Reynolds number is kept constant, a small-sized model wing can be used to simulate a large-sized real wing and obtain similar flow fields. We draw inspiration from it that in the flow of viscoelastic fluid, such as the process of polymer melt injection, the mold corresponds to a wind tunnel, and there is also a flow field. Since the polymer melt is a viscoelastic fluid and is different from air, there should be another physical quantity corresponding to the Reynolds number. By dimensional analysis, we find that it is the Weissenberg number, $Wi$ $(=v\tau /z)$. If $Wi$ remains constant, changing the injection speed $v$, changing the relaxation time of the polypropylene melt $\tau$, or changing the size of the mold $z$ will result in a similar geometric shape of the flow field. In fact, changing the size of the mold in polymer processing is not an easy task. Therefore, we first conduct mesoscopic scale dimensional analysis and then perform mesoscopic scale molecular dynamics simulation. The simulation results verify the conclusion of the dimensional analysis, so we have reason to believe that the conclusion is correct at the macroscopic scale, and we expect to verify it in the future by changing the mold size and injection speed. In the future, we will use this method to understand the flow of polymer melt in the mold, which may enhance our understanding of melt flow instability within the mold.