On the propulsion of capsule-shaped organisms next to slippery rigid boundaries

Capsule-shaped bacteria glide mysteriously near the surface by creating waves in their bodies and secreting a trail of slime (non-Newtonian fluid) that permits them to move without flagella. We present a hybrid numerical study of a complex wavy undulating sheet gliding over Ellis slime. It is also assumed that there are slip effects at the bacterial surface and substrate. The equations that govern the slime flow are normalized using suitable dimensionless variables and then reduced via long wavelength and creeping flow assumption. The resulting DE is solved numerically. A root-finding is also utilized to compute flow rate, speed of glider, and energy losses for different rheological conditions. Additionally, streamlines and slime velocity profiles are also graphically presented.