Fluid transport by a single active filament in a three-dimensional two-phase flow

Micro-scale cilia play a vital role in mucociliary clearance (MCC) in the human respiratory airways. In this numerical study, we examine fluid transport driven by the active beating of a single filament immersed in a three-dimensional two-phase flow. The cilium is modeled as an elastic filament actuated by a time-varying basal angle. The two-phase flow is resolved using the Shan-Chen model in a lattice Boltzmann solver, while the two-way coupling between the filament and the fluid is treated by the immersed boundary method. Pathological conditions such as cystic fibrosis and chronic obstructive pulmonary disease are associated with drastic alterations of MCC properties, including changes in periciliary layer (PCL) thickness and the viscosity ratio between the PCL and the mucus layer (ML). Here, we systematically investigate the effects of these parameters, along with filament bending stiffness, on the beating pattern and fluid transport. Within the parameter ranges investigated, a moderate PCL thickness and viscosity ratio, together with high bending stiffness, tend to yield higher net flow rate and transport efficiency. The underlying hydrodynamic mechanisms are characterized through analyses of the beating pattern, filament dynamics, energy partition, and flow-field evolution. Two competing mechanisms are identified: the drag-elastic force balance and the viscous diffusion of momentum. Furthermore, quantitative relationships are established between flow rate and beating pattern, expressed in terms of tip amplitude and beating asymmetry.