Motion of asymmetric objects through soft lubricated tubes

The motion of tightly fitting objects through soft narrow tubes is a scenario that commonly arises in physiological processes. One example is that of avian egg laying, where it has been observed across species that eggs move through the oviduct pointy-end first, even though they are often 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 for small speeds, 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 grows with the square root of this slope, while also depending on the translation velocity, the elastic properties of the tube and the viscosity of the lubricant. 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.