Asymmetric and Speed-Dependent Capillary Force Hysteresis and Relaxation of a Suddenly Stopped Moving Contact Line

Abstract

We report on 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 water-air interface. The measured CFH and CL relaxation show a strong asymmetric speed dependence in the advancing and receding directions. A unified model based on force-assisted barrier crossing is utilized to find the underlying energy barrier Eb and size λ associated with the defects on the fiber surface. The experiment demonstrates that the pinning (relaxation) and depinning dynamics of the CL can be described by a common microscopic framework, and the advancing and receding CLs are influenced by two different sets of relatively wetting and nonwetting defects on the fiber surface.

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

“…(i) For the water-air interface, the u dependence of its CFH is asymmetric with the effect on the receding CL being much larger than that on the advancing CL, as discussed in Ref. [23]. (ii) For the octanol-air interface, on the other hand, the u dependence of its CFH is more symmetric with the effects in the advancing and receding directions being almost the same.…”

“…Details about the experimental apparatus and procedures as well as AFM operation have been described elsewhere [18,23], and here we mention only some key points.…”

“…Some of the derivations to be given below have already been discussed in Ref. [23]. We include them here to fully explain the physical underpinning of the model.…”

“…where the sign of f i is defined as f i 0 for θ i 90 • and f i > 0 for θ i > 90 • . In a recent letter [23], we reported an experimental study of capillary force hysteresis (CFH) observed on a hydrophobic fiber surface intersecting a water-air interface. In the experiment, the glass fiber was coated with a monolayer of Trichloro(1H,1H,2H,2H-perfluorooctyl) silane (FTS), and AFM was used to measure the advancing force f a (= − πdγ cos θ a ) when the fiber was pushed downward and the receding force f r (= − πdγ cos θ r ) when the fiber was pulled upward.…”

Modified Wenzel and Cassie Equations for Wetting on Rough Surfaces

“…Secondly, the equation is derived from a stationary wetting problem. It might need to be adapted for dynamic problems where the apparent contact angle also depends on velocity [13,21].…”