Microscopic Treatment of a Barrel Drop on Fibers and Nanofibers *

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle θ ₀which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of θ ₀and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane θ ₀-a, separated by two critical curves https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ3_4_0001.tif"/> ρ a v ∗ σ f f 3 . and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ3_4_0002.tif"/> a = a c 1 ( θ 0 ) [ a c ( θ 0 ) < a c ( θ 0 ) ] . In the first domain, below the curve a = a_c (θ ₀), the drop can have any height at its apex. In the second and third domains the values of h_m are limited; in the second domain (above the curve a = a _c1(θ ₀)) there is an upper limit of h, h_{m 1}, and the drops with h_m > h_{m 1}cannot exist, whereas in the third domain (between those curves) the drop can have values of h_m either smaller than h_{m 1}or larger than h_m2, where h_{m 2} > h_{m 1}is a second critical height. For sufficiently large fiber radii, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429401848/07e61596-d871-4168-9433-7efd43350ea8/content/equ3_4_0003.tif"/> R f ≥ 1 μm the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (θ ₀,a) on the θ ₀-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.

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Keywords: Contact angle; Barrel drop; Fiber; Microscopic theory