Back-flow and flow-alignment in pulsatile flows of Leslie-Ericksen liquid crystals

Analytical solutions to the capillary pulsatile flow of Leslie-Ericksen liquid crystals under small pressure drops are presented, when the imposed small pressure drop contains a steady and a time-periodic contribution. The results show that pulsatile flows initiate periodic backflows (reorientation-induced flow) which are directly linked to flow-alignment characteristics of the material. The experimentally measurable power requirement (flow rate x pressure drop) is shown to be well suited to quantify back-flows and flow-alignment material properties. The analysis reveals that power requirements deviate from the Newtonian limit when the frequency of the oscillating pressure drop is close to the splay orientation diffusivity, and backflows become significant. In the terminal zone (small frequencies) the response is Newtonian and the power requirement is a quadratic function of amplitude. At large frequencies, the amplitude of back-flow effects saturates and the power requirement is proportional to the square of the alignment viscosity coefficient alpha(3). An experimental procedure to measure the flow-alignment viscosity coefficient alpha(3) is formulated, based on large frequency measurements, and a formula derived from the close-form solution to the Leslie-Ericksen equations for capillary pulsatile flows.