Stages That Lead to Drop Depinning and Onset of Motion

Abstract

In this paper, we consider drops that are subjected to a gradually increasing lateral force and follow the stages of the motion of the drops. We show that the first time a drop slides as a whole is when the receding edge of the drop is pulled by the advancing edge (the advancing edge drags the receding edge). The generality of this phenomenon includes sessile and pendant drops and spans over various chemically and topographically different cases. Because this observation is true for both pendant and sessile cases, we exclude hydrostatic pressure as its reason. Instead, we explain it in terms of the wetting adaptation and interfacial modulus, that is, the difference in the energies of the solid interface at the advancing and receding edges. At the receding edge, a slight motion exposes to the air a recently wetted solid surface whose molecules had reoriented to the liquid and will take time to reorient back to the air. This results in a high surface energy at the solid–air interface which pulls on the triple line, that is, inhibits the motion of the receding edge. On the other hand, at the advancing edge, a slight advancement does not change the nature of the solid interfacial molecules outside the drop, and the advancing side’s sliding can continue. Moreover, the solid molecules under the drop at the advancing edge take time to reorient, and hence, their configuration is not yet adapted for the liquid and therefore not adapted for retention of the advancing edge. Therefore, in sliding-drop experiments, the advancing edge moves before the receding one, typically a few times before the receding edge moves. For the same reason, the last motion of the receding edge usually happens as a result of the advancing edge pulling on it.

Does the Roll-off Angle Depend on Work of Adhesion?

“…Our results indicate little or no dependence of the roll-off angle on the work of adhesion, for a set of structurally similar surfaces displaying a uniformly low contact-angle hysteresis with hexadecane. These results are consistent with the semi-empirical expectation provided by the Furmidge equation, as well as by more recent thermodynamic analyses. ,− ,− The ∼15% variation in the work of adhesion reflects a ∼100% variation in contact angle for these samples, and although the latter only gains thermodynamic significance as its cosine, the angle itself clearly affects the perception of experimentalists and is often quoted without reference to the cosine. The average roll-off angle for all of these samples of 2.1° and an average hysteresis of 2 ± 1° were observed for all the samples.…”

“…All measurements were made using a Ramé-Hart NRL model 100 goniometer, and samples were titled by manipulation of the four screws holding the rectangular stage (Scheme S1). ,− ,− ,,, These screws are located at the center-edge of each side, with the two in line with the optical path of observation fixed ( y -axis), and the two aligned in the perpendicular direction ( x -axis) adjusted using longer screws. These adjustments allowed a see-saw movement of the stage pivoted at its center.…”

“…For most of our samples, the onset of motion at a given inclination was typically noticed within about 3–5 s. The samples were then tilted in the opposite direction and checked for droplet movement at the same critical angle of inclination. Using the terminology in ref , we designate the onset of motion as the “transition to motion stage,” when the entire drop moves. For a given sample, the variation of the tilt angle was within ±0.2° when motion was observed on the same drop as it was tilted in the opposite direction.…”

“…Hence, at the inclination angle α where movement commences, the component of the gravitational force acting along the direction of motion is set equal to the effective drag on the droplet. This approach can be traced in various forms back to the works of Jamin, West, Yarnold, MacDougall and Ockrent, and Frenkel; more recent and theoretically grounded treatments are provided in the works of Bikerman, Marmur, de Gennes, Tadmor, and others. − …”

Mucus-Inspired Tribology, a Sticky Yet Flowing Hydrogel

“…As time progresses, the lateral force, f ∥ , required to slide the gel on the surface decreases, while that needed to slide water increases with time. The reduction of f ∥ of the gel with t still signifies an increase in the solid−gel interfacial energy, γ SL , 35 while the increase of f ∥ for water signifies a decrease in the solid−water interfacial energy γ SW . (Considering Young's equation, γ LV cosθ = γ SV − γ SL , none of the other interfacial energies can change.)…”