A Theory for Ciliary Gliding in Freshwater Planarians

Abstract

Planarians' locomotion is called ciliary gliding: they secrete mucus on substrata, and glide there by beating ventral cilia in an antiplecticly metachronous manner. A mathematical model for this locomotion consists of the continuity of mass and the Brinkman's equation for the continuity of momentum in the periciliary layer. The reaction of the mucus layer is treated by the Maxwell constituent equation. The boundary layer developed on the back is analysed. The equation of motion, built up by these models, reveals that planarians attain the stable steady-state gliding at 4.7 mm/s by utilising 28 % of the full power of cilia.