A 2D numerical study of polar active liquid crystal flows in a cavity. (20th September 2017) - Yang, Xiaogang; Wang, Qi
Highlights: Study hydrodynamics of polar active liquid crystals in a cavity flow using a continuum model. Discover new emergent structures both in steady state and spatial-temporal patterns. Categorize the various patterns with respect to a set of model parameters. Discuss rheological signatures of the emergent structures. Abstract: We study systematically dynamics of polar active liquid crystals in a 2D cavity flow geometry using a continuum model based on the polarity vector. We devise a numerical scheme based on the projection method and discretized using finite difference methods to solve the model equations and to investigate various patterns and their dependence on the active stresses, the self-propelled speed, the geometry of the active liquid crystal molecule, and the imposed shear rate subject to physical boundary conditions. In addition to the already known 2D spatial temporal patterns obtained using periodic boundary conditions by various groups, we discover new emergent out-of-plane structures both in steady state and spatial-temporal patterns. We then qualitatively categorize the various patterns with respect to the active parameters as well as the geometric parameter of the active liquid crystal molecules into three types: spatially inhomogeneous steady state, periodic patterns, and irregularly oscillatory patterns in both space and time.