Instabilities in active nematic liquid crystals subject to an applied orienting field #

Ijuptil Joseph Kwajighu, Ijuptil Joseph K, Nigel J Mottram, Katarzyna N Kowal, Joseph R L Cousins

10:50 Tuesday in 3E11.

Part of the Liquid crystals and transport models session.

Abstract #

Motivated by applications of active liquid crystals in the design of sensors and various biological processes, we present a theoretical and computational study involving the mathematical modelling of active nematics using an adapted form of the Ericksen-Leslie equations. The forces the active agents exert on their surroundings lead to the generation of local stresses, proportional to the orientational order. These stresses are incorporated via an activity parameter term, which is negative for contractile agents (pullers) and positive for extensile agents (pushers). We consider the effect of a combination of activity and orienting field on active nematics with a director confined between two parallel plates in a 1D geometry, subject to either planar or homeotropic anchoring conditions and no-slip conditions on the boundaries of the channel. We first solve the system analytically by linearising around a uniform director that is aligned with the anchoring conditions. The behaviour is characterised by a critical parameter, below which the system exhibits a no-flow state with no director distortion or unstable state for contractile active agents and a stable state for extensile active agents. However, when the activity is above the critical activity, the system generates flow thereby causing director distortion for the contractile active agents. In the presence of an orienting field, the system becomes stable for the extensile active agents whenever the activity parameter value is greater than zero and the orienting field is below a critical value, and unstable otherwise.

To explore the nonlinear behaviour of the system at later times, we solve the full system numerically using finite difference methods. Our results show that the system exhibits three solution states: symmetric distorted, antisymmetric distorted, and uniform states. The zero solution corresponds to a uniform alignment of the director normal to the direction of the shear flow in the system. For field strengths greater than a critical value, the “uniform state is replaced by the even solution. Interestingly, the critical activity changes as we increase the magnitude of the orienting field. For odd solutions, there is a reorientation in the middle of the layer with high elastic energy. For low magnitude activity, the director angle in the middle of the layer prefers to align at π/2. However, increasing the activity decreases the director angle at the middle of the layer. This indicates that the activity is reducing the distortion and eventually the activity overrides the field giving rise to the solution with odd symmetry. Our results have potential applications for designing sensors and in improving our understanding of many biological processes such as biofilm formation and morphogenesis.