The line friction parameter allows us to define the characteristic velocity of “slip” on the tip of the structures as σ/μ f for a relatively small impact speed. Here, we postulate that the impact velocity V 0 determines the characteristic speed of “leaping”. In this work, we investigate the same microstructured surface as studied in ref (64), but now for impacting drops, which introduces the impact velocity V 0 as an additional parameter. (64) Therefore, the spreading can be symmetric for the hydrophobic asymmetric microstructures. Then, the spreading in both directions is expected to follow the same mechanisms: the combination of “stick” and “leap”. We also note that for hydrophobic asymmetric microstructures, pinning may occur in the direction against the inclination as well. Here, we assume a length scale separation between the droplet size and the microstructures so that the spreading mechanisms can be considered local at the contact line. In the direction with the inclination (indicated by the blue arrow in Figure 2a), the contact line motion could be explained by a combination of “slip”, “stick”, and “leap” the contact line is pinned at the acute corner of the surface microstructures and the average spreading velocity is set by a combination of the capillary spreading on the flat fraction of the surface and “leaping” of the contact line to the next rise of the surface after the pinning. The spreading in the direction against the inclination (indicated by the red arrow in Figure 2a) was driven by the slip mechanism, i.e., a so-called “capillary spreading” driven by uncompensated Young’s force. In our previous work, (64) the spontaneous spreading of a droplet on hydrophilic slanted microstructures (see the inset in Figure 2a) was explained by mechanisms referred to as “slip”, “stick”, and “leap”. (46,47) See the recent reviews (48,49) for discussions of these and other possibilities. Under different circumstances, the moving contact line can be treated as a thermally activated process, which is the basis for the molecular kinetic theory (MKT). Assuming a microscopic cutoff region where fluid slip is allowed, (45) the dissipation due to slip and viscous friction in the vicinity of the contact line can be viewed as a local dissipation. This dissipation is expected from fundamental principles of thermodynamics, and it can have different molecular or hydrodynamic origins. 4.71, p 860) introduced a local dissipation proportional to μ f U 2 near the moving contact line, where U is the contact line speed and μ f is a “simple friction coefficient” with the same dimensions as viscosity (denoted η l in de Gennes’ original paper). When a moving contact line exhibits a dynamic contact angle different from the static value, we expect a local dissipation at the contact line. When Ca f ≫ 1, the geometric details of nonsmooth surfaces play little role. We show that when Ca f ≪ 1, the droplet impact is asymmetric the contact line speed in the direction against the inclination of the ridges is set by line friction, whereas in the direction with inclination, the contact line is pinned at acute corners of the ridges. The line-friction capillary number Ca f = μ f V 0/σ (where μ f, V 0, and σ are the line friction, impact velocity, and surface tension, respectively) is defined as a measure of the importance of the topology of surface textures for the dynamics of droplet impact. We found that the difference between impact velocity and the capillary speed on a solid surface is a key factor of spreading asymmetry, where the capillary speed is determined by the friction at a moving three-phase contact line. Here, we experimentally study drops impacting at low velocities onto surfaces textured with asymmetric (tilted) ridges. However, it is not clear how details of pores, roughness, and texture on the solid surface influence the initial stages of the impact dynamics. The impact of liquid drops on a rigid surface is central in cleaning, cooling, and coating processes in both nature and industrial applications.
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