| Abstract
| - The existence and shape of a cylindrical (infinitely long) liquid drop on a fiber of arbitrary radius are examinedusing a microscopic approach based on the interaction potentials between the molecules of the system. Adifferential equation for the drop profile was derived by the variational minimization of the total potentialenergy by taking into account the structuring of the liquid near the fiber. This equation was solved by quadrature,and the existence conditions and the shape of the drop were examined as functions of the radius of the fiber,microscopic contact angle θ0, which the actual drop profile makes with the fiber, and a certain parameter, a,which depends on the interaction potential parameters. Angle θ0 is defined in the nanoscale range near theleading edge where the interactions between the liquid and solid are strong. It differs from the macroscopicallymeasured wetting angle (θm) that represents the extrapolation of the profile outside the range of liquid−solidinteraction to the solid surface. Expressions for both θ0 and θm are established in the paper. For any givenfiber radius, the range of drop existence involves two domains in the plane θ0 − a, separated by a criticalcurve a = ac(θ0). In the first domain, below the curve a = ac(θ0), the drop always exists and can have anyheight, hm. In the second domain, above the curve a = ac(θ0), there is an upper limit of h, hm1, such that dropswith hm> hm1 cannot exist. The shape of the drop depends on whether the point (θ0, a) on the θ0 − a planeis far from the critical curve or near to it. In the first case, the drop profile has generally a circular shape, withthe center of the circle not located on the fiber axis, whereas in the second case the shape is “quasi planar”,that is, most of the drop profile lies on a circle concentric with the fiber profile. Comparing the potentialenergies of a cylindrical drop on a fiber and a film of uniform thickness covering the fiber and having thesame volume as the drop, the energetically preferred configuration was determined for various conditions.Considering the cylindrical drop as a limiting case of a clam-shell one, and the film as a limiting case of abarrel drop, the obtained analytical results could be employed to examine the barrel-drop−clam-shell-droptransformation (roll-up transition).
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