† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11472220 and 11872315).
Wetting states and processes attract plenty of interest of scientific and industrial societies. Air entrainment, i.e., wetting failure, on smooth plate in wetting process has been investigated carefully before. Liquid bath entries of “rough” silicon wafers are studied experimentally in the present work, and the air entrainment condition is analyzed specially with the lubrication theory. The roughness effects on the moving contact lines are therefore explored. The contact line pinning is found to be the main reason for the dynamically enhanced hydrophobicity of rough surface, which implies an effective microscopic contact angle of
Wetting phenomena and wetting processes are important for industry and in nature. Dropletʼs rolling on lotus leaf,[1] basilisk lizardʼs running on the surface of a pool,[2] shorebirdʼs drinking water,[3] etc., attract great interest of scientists. Meanwhile, by using the wetting mechanism, one can massively print functional material on soft substrates in electric industry,[4] control the small robot through “smart” liquid metal,[5] and control the mixing in droplets as chemical vessels.[6] However, in the framework of fluid mechanics, severe theoretical challenge arises in analyzing the (liquid–air–solid) contact line motion on a solid surface due to the deduced shear stress singularity.[7,8] The assumptions of precursor film, non-Newtonian, and liquid evaporation, etc., were therefore made.[8] Coupling with slip boundary condition, the lubrication model is developed into a powerful tool to describe the dynamics of a moving contact line.[9] Marchand et al.[10,11] found that it can well predict the air entrainment condition when a smooth plate enters into viscous liquids vertically. On the other hand, the wall heterogeneity has been found to play important roles in determining the wetting states of liquids on a solid wall so far,[12–14] thus exerting a subtle influence on the spreading outcomes of a droplet impact onto a wall,[15] etc. As is well known, the detailed investigations are still lacking, and one still has a great enthusiasm for knowing how to model a rough plate in wetting processes for practical purposes. In this paper, we conduct the experiments to explore the roughness effects on the moving contact line dynamics. Well controlled wall surfaces and liquids are adopted following the previous experimental and numerical attempts on this subject. An empirical simple model is subsequently proposed.
The experimental apparatus adopted in the present research is similar to that used by Marchand, Chan, and Snoeijer,[10,11] which is schematically depicted in Fig.
The “liquid-bath entry” processes of the plates were recorded by a MegaSpeed MS-75K camera at 2000 frames per second (Fig.
For the cases of a smooth solid surface plunging into a viscous liquid, Snoeijer et al.[10,11] analyzed the meniscus in the vicinity of the moving contact line by using the lubrication theory.[9] In the later publication, the author proved that the theory can be applied to the flows in large contact angle. The governing equation is as follows:
Snoeijerʼs model successfully captures the most prominent features of the experimental results.[10,11] It leads to a solution of
To characterize the roughness influence on wetting failure in detail, we try to model a rough surface with effective parameters for smooth surface. This idea is surely acceptable, since all theories for smooth surface are compared with (more or less) rough surface experiments. In Ref. [17], the authors found water entry cavity was induced easily as a rough hydrophilic sphere entered into water. They postulated that air was entrapped in the valley of the roughness when contact line advanced over the sphere surface. By using the Cassie–Baxter model,[12,14] a critical speed for splashing was estimated by following the Duezʼs procedure.[18] On the other hand, Qian and Wang[19] also derived an average value of the contact angle when the interface moves slowly on a chemically patterned surface, which was consistent with the scenario obtained from the Cassie–Baxter equation.
The geometry of the presented surface is regular enough and the corresponding effective contact angle under Cassie–Baxter (θ CB) or Wenzel (θ W) state could be obtained easily from the following equations[12,14]
It is well known that “mesa” defects cause contact angle hysteresis, which could also be explained as energy barrier through thermodynamics.[12,14] The energy barrier will be overcome by adjusting the interface such that the contact angle reaches a new value while the contact line is pinned on the defect. As depicted in Fig.
In the present paper, we conduct water entry experiments of rough plates to explore the dynamic process of contact lines moving over rough surfaces. The flow in the vicinity of the contact line is well described with the traditional lubrications theory. Unlike the equilibrium states, the dynamics of the moving contact line is governed greatly by local effect, namely pinning effect, rather than the temporal/spatial averages based on the thermodynamic approaches. The findings in our previous numerical simulations[20] are demonstrated. The experiments with various liquids and plate topographies show that the combination of local inclined angle of the valley and Youngʼs contact angle of the liquid (
We are grateful to Chan T S, Gao P and Thoraval M J for valuable discussion.
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