Simultaneous observation of asymmetric speed-dependent capillary force hysteresis and slow relaxation of a suddenly stopped moving contact line

Abstract

We report direct atomic-force-microscope measurements of capillary force hysteresis (CFH) and relaxation of a circular moving contact line (CL) formed on a long micron-sized hydrophobic fiber intersecting a liquid-air interface. By using eight different liquid interfaces with varying solid-liquid molecular interactions, we find a universal behavior of the asymmetric speed dependence of CFH and CL relaxation. A unified model based on force-assisted barrier crossing is used to connect the mesoscopic measurements of CFH and CL relaxation with the energy barrier height E_{b} and size λ associated with the surface defects. The experiment demonstrates that the CL pinning (relaxation) and depinning dynamics are closely related and can be described by a common microscopic framework.

Effective boundary conditions for dynamic contact angle hysteresis on chemically inhomogeneous surfaces

“…Moreover, the dynamic behaviours fit well with the experiments for all the four cases, i.e. the water-air, octanol-air, decane-air and FC77-air systems (Guan et al 2016b).…”

“…To compare with the experiments, we use the reduced model (2.24) which is an approximation for the problem in Guan et al (2016b). The radius of the fibre is r 0 = 1.1 μm which is consistent with the experiment.…”

“…Many interesting phenomena are observed in the experiments. It is found that the dependence of the advancing and receding contact angles on the fibre velocity is not unified (see figure 6 in Guan et al 2016b). In some cases (e.g.…”

“…The dimensionless wall velocity is represented by v = μu wall /γ , where the fibre speed |u wall | is suggested by the experiments as 2 μm s −1 , 5 μm s −1 , 20 μm s −1 and 50 μm s −1 . We refer to table 1 of Guan et al (2016b) for the material properties, especially the surface tension γ and the viscosity μ. Since the capillary lengths of the materials under consideration have the range 0.86-2.71 mm, we choose it to be l c = 1mm.…”

“…If the length scale D is small or the contact line friction ξ is large, it is possible that Re is still small even when the contact line slips on the substrate. For example, in the experiments of Guan et al (2016b), the Reynolds numbers Re are in the range [0, 0.14]. In this case, the inertial effect is not important and the system can be well approximated by Stokes flows.…”