Dynamic flotation conditions for elongated cylinders on liquid surfaces

Hypothesis: Although the static flotation of elongated cylinders is well understood, their flotation behavior under dynamic conditions after contacting a liquid surface, such as in situations experienced by water-walking insects, still need to be revealed. Methodology: The motion of elongated horizontal cylinders after zero-velocity contact with a liquid surface is considered, and the motion equation of the cylinder is established and solved to obtain the dynamic flotation conditions. Findings: The limiting density ratios for the dynamic flotation of elongated cylinders with different Bond numbers and contact angles are determined. The results show that although increasing the hydrophobicity promotes floatability of the elongated cylinders, there is little effect for contact angles >120°. Based on the energy balance, an asymptotic formula for the limiting density ratio is proposed, which agrees well with the theoretical results. Unlike small spheres, all elongated cylinders with contact angles >0° are observed to exhibit floatability after contacting a liquid surface. In addition, we found that elongated hydrophilic cylinders exhibit better floatability compared to small hydrophilic spheres with the same contact angle and Bond number, which assists small insects float and survive in various water environments.