Three-dimensional computational model of multiphase flow driven by a bed of active cilia

Micro-scale physiological fluid propulsion is often accomplished with arrays of beating cilia. It is well-known that cilia can spontaneously coordinate their beat patterns to form metachronal waves. While it is generally agreed upon that metachronal waves arise largely due to hydrodynamic coupling, their effects on fluid propulsion are not thoroughly explored. There are presently complex, nonlinear models where cilia motion mimics their internal mechanisms; however these models are often computationally challenging and expensive to perform. We therefore present a simplified computational model of a cilia array with the ability to spontaneously produce metachronal waves. Each cilium is modeled as a one-dimensional elastic structure immersed in a stratified, two-fluid configuration. This model is used to simulate in vitro artificial cilia. Our model treats the upper fluid as a high-viscosity Newtonian fluid. Our model shows that, in the presence of surface tension between the lower and upper fluid layers, the fluid velocity component perpendicular to the interface is suppressed. This suppression prevents the interface from deforming, leading to increased fluid flow along the cilia array and enhancing fluid transport. Conversely, in the absence of surface tension, the fluid velocity component perpendicular to the interface is unsuppressed. The interface becomes severely deformed, enlarging the fluid interface area, thus potentially enhancing diffusive mixing. We finally present a phase-space plot of viscosity ratio against surface tension, showing conditions under which fluid transport or mixing is enhanced.