Roberto Camassa

Department of Mathematics
University of North Carolina

Abstract.Understanding and modeling how human lungs function is in large part based on the hydrodynamics of the mucus fluid layers that coat lung airways. In healthy subjects, the beating of cilia is the primary method of moving mucus. With the aim of establishing a quantitative benchmark of how cilia motion propels the surrounding fluid, we study the idealized situation of one rod spinning in a fluid obeying the Stokes approximation, the appropriate limit for a Newtonian fluid with typical dimensions and time scales of cilia dynamics. New approximate -- for cylindrical rods pinned to a flat plane boundary, and exact -- for ellipsoidal rods freely spinning around their center -- solutions for the fluid motion will be presented and compared with the experimental data collected with spinning magnetic nano-rods in water. In particular, analytical results where the influence of Brownian perturbations is taken into account will be compared with some preliminary data from an experiment scaled-up by dynamical similarity to macroscopic (table-top) dimensions.