Assessing fluid transport in the periciliary layer through distinct measures of mixing

The mucociliary escalator in the respiratory system can become impaired due to disease and change morphologically, affecting fluid transport. In our study, we focus on flow only in the periciliary layer of the upper respiratory mucosal layer and calculate several distinct mixing measures (the mixing number, the finite-time Lyapunov exponent (FTLE) field, and the multiscale mix norm) to assess whether chaotic advection exists. We aim to visualize the mixing process over time and quantify the effect of selected parameters (beat frequency, domain length, height, metachronal wavelength, and inter-cilium spacing) on the flow field. The backward image trace methodology allows us to generate high-resolution visual maps of scalar transport in the periciliary layer. These compelling images, which provide a clear representation of the mixing process, are then analyzed heuristically by calculating the FTLE field of the flow. Then, we discuss our findings on the potential for chaotic advection by calculating both the mixing number and the multiscale mix-norm of the passive advection of a scalar. Interestingly, we see the emergence of two areas where mixing occurs at dissimilar rates. These two areas can be delineated using the FTLE field and are quantitatively evaluated using the mix norm. Finally, we present differences in the mixed state for various configuration parameters between a single cilium and a cilium patch.