Bi-Gaussian Stratified Wetting Model on Rough Surfaces
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Subscriber access provided by Imperial College London | Library New Concepts at the Interface: Novel Viewpoints and Interpretations, Theory and Computations Bi-Gaussian Stratified Wetting Model on Rough Surfaces Songtao Hu, Tom Reddyhoff, Debashis Puhan, Sorin-Cristian Vladescu, Weifeng Huang, Xi Shi, Daniele Dini, and Zhike Peng Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00107 • Publication Date (Web): 04 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019 Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. 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Page 1 of 25 Langmuir 1 2 3 4 Bi-Gaussian Stratified Wetting Model on Rough Surfaces 5 6 7 Songtao Hu,† Tom Reddyhoff,‡ Debashis Puhan,‡ Sorin-Cristian Vladescu,‡ Weifeng Huang,§ Xi Shi,*,† 8 Daniele Dini,‡ Zhike Peng† 9 10 11 †State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 12 200240, China 13 ‡ 14 Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK 15 §State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China 16 17 18 ABSTRACT: Wetting mechanisms on rough surfaces were understood from either a monolayer or a 19 multiscale perspective. However, it has recently been shown that the bi-Gaussian stratified nature of real 20 surfaces should be accounted for when modelling mechanisms of lubrication, sealing, contact, friction, 21 acoustic emission, and manufacture. In this work, a model combining Wenzel and Cassie theories was 22 23 put forward to predict the static contact angle of a droplet on a bi-Gaussian stratified surface. The model 24 was initially applied to numerically simulated surfaces, and subsequently demonstrated on hydrophilic 25 steel and hydrophobic self-assembled monolayer specimens with preset bi-Gaussian stratified 26 27 topographies. In the Wenzel state, both the upper and the lower surface components are fully wetted. In 28 the Cassie state, the upper component is still completely wetted while the lower component serves as gas 29 traps and reservoirs. By this model, wetting evolution was assessed, and the existence of different wetting 30 31 states and potential state transitions was predicted. 32 33 ■ INTRODUCTION 34 Wetting behavior occurs when a solid-gas interface transfers into a solid-liquid interface on a solid, and 35 36 it indicates the ability of the solid surface to accommodate and maintain permanent contact with the 37 liquid. Controlling the wettability of a solid is a research area of intense focus, which has resulted in a 38 significant number of applications including self-cleaning1,2, anti-icing3,4, antifogging5,6, antireflection7,8, 39 40 friction reduction9,10, etc. It is therefore of utmost importance to understand the intrinsic wetting 41 mechanism that occurs. Since Young introduced the theoretical modelling of static contact angle (CA, 42 serving as a key wetting index) on an ideal smooth surface, it has become well known that the roughness 43 44 of a surface can induce a significant effect on its wettability. Two famous hypotheses have been proposed 45 to explain the wetting mechanism of a rough surface. In the Wenzel11 case (see Figure S3a), the liquid 46 completely fills the valleys of a rough surface. The roughness extends the solid area in comparison to the 47 projected one, enhancing the intrinsic wettability of the solid (a hydrophilic surface turns into a more 48 49 hydrophilic one, while a hydrophobic surface becomes more hydrophobic). In the Cassie12 case (see 50 Figure S3b), gas is trapped into the valleys underneath the liquid, transforming the surface from a 51 continuous solid-liquid interface into a composite one consisting of solid-liquid and gas-liquid interfaces. 52 53 To date, these two theoretical models have been widely used to capture CAs on rough surfaces, however 54 these studies have been limited to scenarios of either a monolayer13−18 or a multiscale (fractal, 55 hierarchical)1925 topography. 56 57 In fact, most researchers have focused exclusively on either a Gaussian or a non-Gaussian 58 distribution of topographical heights from the view of monolayer point, overlooking the real-life case of 59 a bi-Gaussian stratified property (see Figure 1a) long-termly covered by the non-Gaussian one. As 60 ACS Paragon Plus Environment Langmuir Page 2 of 25 1 2 3 schematically illustrated in Figure 1b, a bi-Gaussian stratified surface consists of a large roughness-scale 4 5 Gaussian surface (lower component) and another Gaussian surface at a small roughness scale (upper 6 component), where the lower height is maintained on each node when combining the two components. 7 In contrast with a multiscale property emphasizing the properties (e.g., self-similarity, self-affinity) 8 exhibited by a rough surface at different scales, the bi-Gaussian one displays its two components in a 9 10 stratified (following a selective superposition rather than a direct superposition as depicted in Figure 1b) 11 formation at the same scale. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Figure 1. Topography of a bi-Gaussian stratified surface (a) and its schematic in a profile formation (b). 33 34 The bi-Gaussian stratified property of a rough surface was initially observed on automotive cylinder 35 36 liners through a two-stage manufacturing process (plateau honing),26 and was then extended to model 37 surfaces modified by a material wear.27 Notably, the bi-Gaussian stratified property should be 38 differentiated from the mother non-Gaussian property in three ways: (1) The bi-Gaussian stratified 39 40 surface can arise from a multi-stage subtractive manufacturing process,28 indicating its widespread 41 applicability. Moreover, an active service usually induces a material wear as similar to the multi-stage 42 subtractive manufacturing process,29 thus extending the applicability. (2) The mechanism of forming the 43 44 two components is clearly associated with specific actions. Namely, the lower component is produced 45 by the early manufacturing process or is the original unused surface, while the upper component is 46 generated by the following manufacturing stage or the material wear. (3) The functional performance of 47 the two components is clearly defined in comparison to a conventional monolayer surface. For instance, 48 49 in the tribological field, the upper component plays a predominant role in load bearing and wear 50 resistance, and the lower component acts as lubricant reservoirs and debris traps. 51 By reviewing the most relevant studies in the area of surface roughness, it becomes evident that the 52 53 bi-Gaussian stratified perspective has exhibited an excellent capability in revealing the mechanisms in 54 terms of lubrication, sealing, asperity contact, friction, acoustic emission, and manufacture.28−30 However, 55 to our knowledge, it has not yet been employed to analyze the wetting mechanism of rough surfaces. In 56 57 this paper, a model combining Wenzel and Cassie theories was established to predict the static CA of a 58 droplet on a bi-Gaussian stratified surface (see section “Theoretical Model”). In particular, the model 59 contains two special cases, i.e., Wenzel and Cassie states. In section “Model Demonstration”, the model 60 ACS Paragon Plus Environment Page 3 of 25 Langmuir 1 2 3 was initially investigated on numerically simulated bi-Gaussian stratified surfaces, and subsequently 4 5 demonstrated on hydrophilic steel specimens and hydrophobic self-assembled monolayer (SAM) coated 6 specimens with prescribed bi-Gaussian stratified topographies. Furthermore, the model was used to 7 explain and predict the existence of different wetting states and potential state transitions from a bi- 8 Gaussian stratified viewpoint (see section “Discussion”). 9 10 11 ■ MODEL 12 In the Wenzel model, the CA can be described as11 13 14 15 cos * r cos , (1a) 16 17 * 18 where is the apparent CA of a droplet on a rough surface, and is the intrinsic CA on an ideal smooth 19 surface modelled by the well-known Young equation. Herein, r is the ratio of the real area to the projected 20 one, acting as the roughness factor used to assess the area extension. As the value of r is always greater 21 than 1, the intrinsic wettability of a solid will be enhanced according to the Wenzel model. When the 22 23 liquid droplet is located on a heterogeneous solid surface, the reduced Cassie model can be applied12 24 25 * cos f cos f 1 , (1b) 26 27 28 where f is the fraction of the solid-liquid interface.