Fluid Dynamics of Flow Driven by Nodal Cilia Precessing Non-circular Cones

Abstract

Nodal cilia play an important role in the left-right symmetry breaking at the early stage of the mammal embryos and show an apparent rotational motion. This study is about the flow induced by cilia sweeping out circular/elliptical cones above a no-slip plane in the low Reynolds number regime. Using the regularized Stokeslet method, we examine the properties of flows generated by a single cilium and multiple cilia, especially two cilia, which are assumed to be anchored to the embryonic heart wall. For a short-term Lagrangian fluid tracer trajectory, epicycles are presented as a nodal cilium precesses in either a circular cone or a non-circular cone shape. For the long-term behavior, the trajectory is periodic around both the circular and elliptical cones. Compared to the circular cone cases, the vertical variances are enhanced in elliptical cone cases. Besides tracer trajectories, fluid velocity elds are presented to demonstrate the flow structure. When two cilia are considered in the system, the flow structure is analyzed for the dierent phase angles and relative orientation of the elliptical cones.