Spontaneous flow in active nematics: Effects induced by annular confinement

Within the framework of continuum mechanics for materials with relaxation, this study investigates activity-induced laminar flow in an active nematic confined within an annular domain. Subsequent to the formulation of the problem as a nonlinear boundary value problem, a bifurcation analysis of the governing equation demonstrates that the critical threshold for the initiation of spontaneous flow is dependent on the aspect ratio (thickness-to-radius) of the domain. The influence of domain curvature is twofold: firstly, it facilitates the inception of spontaneous motion by reducing the critical threshold; secondly, it resolves the indeterminacy inherent in the planar geometry, wherein, at an equivalent critical threshold, two distinct flow configurations may manifest: a unidirectional flow or a configuration exhibiting two counter-propagating bands. In the annular geometry, the double-band configuration, characterized by a thicker inner layer, exhibits the lowest activation threshold. With an augmentation of either activity or curvature, the principal motion transitions towards a predominantly unidirectional flow, accompanied by a narrow counter-rotating band adjacent to the outer boundary, aligning with experimental observations of confined bacterial colonies.