Mathematical modeling of a hydrophilic cylinder floating on water

In this paper, a hydrostatic model of the surface profile anchored to the upper edge of a vertical cylinder is proposed to explain why coins can float on water surface. The sharp edge of a cylinder is thus modeled as a round smooth surface on which the contact line may be anchored at a position according to the weight of the cylinder. The mathematical model of the surface profile is established based on the hydrostatics and a third order ordinary differential equation is resulted. Numerical solution of the model demonstrates under practical conditions the existence of the surface profiles that provide reasonable uplifting force at the contact line so that the force is available for floating coins on water surface. The proposed model explains the obviously enlarged apparent contact angle and the edge effect in the literature. The numerical simulation is found in very good agreement with the experimental data in the literature.

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► Floating coins are well explained by mathematical modeling.
► The edge effect and its singularity are phenomena complied with physical laws.
► An illusion of sharp edge originates from a round corner with small radius.
► The hydrostatic model agrees well with the experimental data.