In this study, we present a free-boundary problem for an active liquid crystal starting with the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor and then derive from it the Eriksen model for an active polar gel and scalar order parameter to analyse the rich defect structure observed in applications such as the adenosinetriphosphate-driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin-film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. As an example we derive the explicit solution for an active gel confined to a channel, which has discontinuous director profile leading to a bidirectional flow structure generated by the active terms.
Keywords: active matter; asymptotic analysis; liquid crystals.