Propulsion of asymmetric bodies through soft lubricated tubes

The motion of tightly fitting objects through soft tubes is a scenario that frequently arises in physiological processes. An example is that of avian egg laying, where observations across avian species suggest that eggs move through the oviduct pointy-end first, even though they are usually then laid blunt-end first. We investigate the mechanistic implications of this observation by considering the motion of fore-aft asymmetric intruders moving through lubricated elastic tubes. Using asymptotic theory, we find that the thickness of the lubricating fluid layer scales inversely with the square root of the slope of the intruder surface near its nose, in the direction of motion. Consequently, the force required to drive motion scales with the square root of this slope, and also depends on the translation velocity, the viscosity of the lubricant and the elasticity of the tube walls. Our findings show that asymmetric objects are more efficiently moved pointy-end-first through lubricated soft tubes, suggesting a mechanistic rationalization for the observed orientation of eggs moving in avian oviducts.