Figure 6 shows the cavitation volume Vc in terms of the inverse Euler number , a dimensionless number that is independent of the viscosity of the system. The ratio between the pressure gradient and the kinetic energy per volume is decisive for the development of a cavitating volume, as captured distinctly in Fig. 6. Independent of the model system cavitation occurs at the same Euler number . When cavitation first occurs in the experiments we find that is within similar order of magnitude as the simulations.
Dependence of the cavitation volume on the inverse Euler number for the nematic LC (red circle) and isotropic LC (blue square).
Full size image
Figure 7 maps the local nematic order parameter over the range of flow regimes considered here. The flow field reorients the nematic director from homeotropic (on the surfaces) to flow-aligned orientation (in the flowing matrix). Topological defects arise in the director field, close to the top and the bottom walls, where the cylindrical pillar intersects the channel surfaces (Fig. 7a). The singular defect loops are formed due to the homeotropic anchoring, both on the channel surfaces and on the pillar, and are consistent with the defect topology discussed in ref. 49. It is evident from Fig. 7d that over the x–y plane, located at the channel half depth (z=0), no defect is visible. The director field remains stable for small Er. However, for Er≥675 a single loop around the pillar stabilizes in the x–y mid-plane. The loop is deformed and extended towards the downstream direction along with the flow, shown in Fig. 7b,e. Additionally, there is a growing region of flow alignment behind the cylindrical pillar in the downstream T5 Fluorescent Lamp direction. Upon increasing Er one can see that the loop becomes stretched further downstream (see Fig. 7c). However, the overall defect topology, especially downstream behind the pillar, is increasingly smeared, possibly due to the appearance of the vapour phase at high Ericksen numbers (Fig. 7f). Changing the surface anchoring from homeotropic to planar did not produce any qualitative change in our results. This agrees well with the experiments, where too we have observed that cavitation in nematic phase was independent of the nature of the surface anchoring.