Particle Transport by Cilia Arrays in Parallel-Wall Channels

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Cilia are thin hair-like organelles projecting from a cell body, which are found in many unicellular and multicellular organisms. Individual cilia in ciliary arrays often coordinate their motion, leading to formation of metachronal waves that can propel a uni- cellular organism in a fluid or generate particle and fluid transport along a cellular layer. For example, clean-up functions in living organs are carried out by coordinated oscillations in cilia carpets. Numerous mathematical models and simulations have been developed to investigate the mechanism of metachronal wave formation and cilia dynamics. However, much less is known about particle transport by cilia, which is an interesting and important re- search topic. This thesis aims to use a simplified rower model of the arrays of hydrodynamically coupled cilia to investigate particle transport by metachronal waves. In circular rower models cilia are represented by spherical beads (rowers) moving on prescribed trajectories that mimic the motion of cilia tips. Such models have been successful in explaining the cilia beating coordination and the mechanism of propagation of metachronal waves but the problem of particle transport has not been addressed. Here, a circular rower model that includes hydrodynamic interactions between the rowers and free particles in a parallel-wall channel has been implemented to investigate this problem. Accurate incorporation of hydrodynamic interactions into the model is essential for quantifying particle transport. In our model, metachronal waves are generated by placing consecutive rowers at a constant phase difference in the initial configuration. Various system parameters, such as the wavelength and direction of the metachronal wave, particle position with respect to a rower array, and the channel width, affect the transport rate. In this thesis, a large set of numerical simulations has been performed and analyzed to understand how the transport in cilia arrays depends on these parameters. The results obtained explain how fast (or slow) a particle can be transported by a cilia array and how this transport is affected by the hydrodynamic interactions and by changes of system parameters. Some cases of interesting behavior of both the rower arrays and transported particles have been elucidated, including looped particle trajectories (associated with backflow patterns) and instabilities in cilia array motion. Our results are not only relevant for understanding particle transport by cilia arrays in vivo but can also be used in the development of artificial microfluidic cilia systems for biomedical applications.

Embargo status: Restricted until 09/2025. To request the author grant access, click on the PDF link to the left.

Cilia, Rower array, Metachronal wave, Hydrodynamic Interaction, Free particle