Delayed transitions, promoted states and multistability in a pressure-driven nematic under an electric field
We consider the effects of an applied pressure gradient on the classical Freedericksz transition, finding a delayed transition, the promotion of particular director configurations and even pressure-induced multistability. Using the theoretical framework developed by Ericksen and Leslie, we find that the applied pressure gradient adapts the normal pitchfork bifurcation at critical applied voltage, leading to both a delayed bifurcation to higher voltages and a transformation from a supercritical to a subcritical bifurcation so that within a range of voltages there are at least two possible steady states. This range of voltages grows with increasing pressure gradient and eventually includes the zero voltage state so that, for sufficiently strong flow, there are at least two steady states at zero applied voltage. For sufficiently high pressure gradients, we also find that flow-alignment can create a completely new attracting steady state, one that is unstable without flow. We provide a flow-strength-electric field parameter plane that summarises the parameter ranges for which there are multiple steady states and suggest realistic mechanisms to move between these states, as well as an analytical model for the delayed Freedericksz transition effect. The novel steady states found in this work give the possibility of director and flow hysteresis in microfluidic devices.