Pulsatile flows of Leslie–Ericksen liquid crystals

Abstract

Capillary pulsatile flows of calamitic (rod-like) and discotic nematic liquid crystals are analyzed using the Leslie–Ericksen equations for low-molar mass liquid crystals, using computational, analytical, and scaling methods. The dependence of flow-enhancement and power requirement on frequency, amplitude, pressure drop wave-form, molecular geometry is characterized. The unique roles of orientation-dependent local viscosity and backflow (orientation-driven flow) on flow-enhancement and power requirement are elucidated. The local viscosity effect is shown to be a significant factor in flow-enhancement at all pressure drops, but only affects power requirement at higher pressure drops. Backflow has weak effects on flow-enhancement and large effects on power requirements at low average pressure drops. Amplitude, frequency, and molecular geometry effects are clearly manifested through viscosity and backflow. A detailed comparison with predictions for power law fluids shows a clear correspondence between these non-Newtonian fluids and nematic liquid crystals. The unique distinguishing feature of pulsatile flows of liquid crystals is found to be backflow, such that power increases with increasing frequency, a featured that does not exist in other non-Newtonian fluids due to lack of a strong flow driven by restructuring/re-orientation processes. Future use of these new results may include measurements of viscoelastic parameters that control backflow.