Direct Measurement of Friction of a Fluctuating Contact Line

Abstract

We report a direct measurement of the friction coefficient of a fluctuating (and slipping) contact line using a thin vertical glass fiber of diameter d with one end glued onto a cantilever beam and the other end touching a liquid-air interface. By measuring the broadening of the resonant peak of the cantilever system with varying liquid viscosity , we find the friction coefficient of the contact line has a universal form, c ' 0:8d, independent of the liquid-solid contact angle. The obtained scaling law is further supported by the numerical simulation based on the phase field model under the generalized Navier boundary conditions. What happens near a contact line, where a liquid interface between two (immiscible) fluids intersects with a solid surface is a fundamental issue in fluid dynamics and is also a concern of many industrial processes ranging from spreading of droplets, lubricants, and coatings to the extraction of oil from sandstone by injecting water or gas [1]. While considerable progress has been made recently in controlling the wettability of various textured solid surfaces [2] and in understanding the energetics associated with deformable soft substrates [3][4][5], our fundamental understanding of the dynamics of the contact line still remains very limited [1,6]. Like the static problem [3][4][5], the motion of the contact line is also a singular problem; it is incompatible with the nonslip boundary condition and would lead to unphysical infinite dissipation [7]. Over the years there have been many ad hoc models and proposals aimed at resolving the incompatibility issue [1,2,6], but none of the theoretical ideas has been experimentally confirmed.As illustrated in the inset of Fig. 1, a moving contact line (MCL) involves fluid motion (i) at a small distance a ($ 1 nm) in the immediate vicinity of the contact line, in which molecular interactions between the liquid and solid are important, and (ii) in the ''outer region'' of meso-or macroscopic size ', in which classical hydrodynamics are applicable. To avoid the dissipation divergence of MCL, de Gennes et al. [8] introduced the cutoff length a and calculated the hydrodynamic friction coefficient w in regime (ii) away from the contact line,for liquids with a small contact angle . In the above, d is the contact line length, and is the fluid viscosity. The value of w becomes very large for liquids with small and even becomes divergent when ¼ 0 .Most experiments on MCL were conducted in regime (ii) [9][10][11], because direct observation of the fluid motion in regime (i) (& 1 m) is difficult with the conventional optical methods. While these measurements provided useful information about the MCL dynamics at large distances, direct comparison of the experimental results with the microscopic models is not possible. This is because all the theories predicted the same flow field to the leading order [1,12,13]. As a result, our current understanding of the contact line dynamics in regime (i) relies mainly on the results from molecular dynamic (MD) simulations ...

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