How drops start sliding over solid surfaces

Abstract

It has been known for more than 200 years that the maximum static friction force between two solid surfaces is usually greater than the kinetic friction force. In contrast to solid-solid friction, there is a lack of understanding of liquid-solid friction, i.e. the forces that impede the lateral motion of a drop of liquid on a solid surface. Here, we report that the lateral adhesion force between a liquid drop and a solid can be divided into a static and a kinetic regime. This striking analogy with solid-solid friction is a generic phenomenon that holds for liquids of different polarities and surface tensions on smooth, rough and structured surfaces.When two solid objects are brought into contact, a threshold force FTHRD must be overcome in order for one of the objects to slide 1-3 . This phenomenon can be visualised in a typical classroom experiment where a solid block attached to a spring is pulled over a solid surface (Fig. 1a). The static force FS is applied to the stationary block and then increased until it exceeds FTHRD, upon which the block begins to slide. After that, a lower kinetic force FKIN is required to maintain the block's motion 3 . However, it is not clear whether these forces develop in a comparable manner when a drop of liquid resting on a solid surface starts to slide. This gap in our understanding is astonishing, given the fact that liquid drops are omnipresent in our lives and their motion is relevant for numerous applications, including microfluidics 4 , printing 5 , condensation 6,7 , and water collection 8,9 . Hence insight on the behaviour of drops that start sliding over solid surfaces is needed.A sessile drop of liquid is usually in molecular contact with the supporting solid surface. In contrast, two solid bodies are in direct contact only at asperities owing to surface roughness 10,11 . Thus, the real contact area of a solid-solid contact is much smaller than the apparent contact area. Consequently the sliding of drops might be fundamentally different.However, by simply observing a drop of water on a pivot window pane, we know that also sessile drops start sliding when a critical tilt angle is reached, i.e. when the gravitational force acting on the drop overcomes the lateral adhesion force. The question may therefore be raised whether a static and a kinetic regime are also present for sessile drops. The general questions is: How do drops start sliding over solid surfaces and how do the forces develop while the drops slide?

Origins of Extreme Liquid Repellency on Structured, Flat, and Lubricated Hydrophobic Surfaces

“…F d is taken to be the long-time average, once F t has reached a steady state. Typically, a larger force F peak is required to jump start the motion, reminiscent of the static and kinetic friction forces between two solid surfaces [37]. For a lotus-effect surface, this F peak ¼ 6.6 μN is sharp and distinct from the force F d ¼ 5.0 AE 0.2 μN required to maintain the motion.…”

“…In this study, to avoid the ambiguity in interpreting contact angle measurements, we measured F d for a droplet moving at controlled speed U directly using a cantilever force sensor (Fig. 2) [14,36,37]. The droplet was attached to a capillary tube, and the force F t ðtÞ acting on the droplet was inferred from the tube's deflection ΔxðtÞ: F ¼ kΔx, where k ¼ 5-25 mN=m for tube lengths L ¼ 6-9 cm.…”

Steerable Droplet Bouncing for Precise Materials Transportation

“…As the droplet horizontally rebounds and the system is vertically symmetric (the y-direction), we focus on the liquid behavior in the horizontal direction (the x-direction). So the lateral interaction force exerted from the solid to the liquid at the interface in stage I (F I ) can be expressed as [5,14,30,41,42] = + = cos cos c os cos I s d s rs Figure 3a schemes the typical liquid morphology of stage I.…”

“…Droplet manipulation is a ubiquitous phenomenon in various natural processes and biological processes such as selfcleaning, [1][2][3][4] drag reduction, [3,[5][6][7][8] and microfluidics. [9][10][11][12][13] As one of the key aspects for droplet manipulation, [7,[14][15][16][17][18] the directional transportation of liquid droplets has aroused great interest due to its importance in applications including water collecting, [19][20][21] anti-icing [16,22,23] and materials transportation.…”

“…[29] By introducing anisotropic microstructures, guided self-propelled leaping of droplet is realized on the superhydrophobic surface. [5,22,[30][31][32] However, due to the complexity in the interaction between the droplet and the solid, [33][34][35][36][37][38] the precise control of the lateral droplet movement, both in the direction and the quantity, remains a great challenge.Recently, the development of the surface wettability provides an efficient way to control the liquid behaviors. [5,22,[30][31][32] However, due to the complexity in the interaction between the droplet and the solid, [33][34][35][36][37][38] the precise control of the lateral droplet movement, both in the direction and the quantity, remains a great challenge.…”