study on the hydrophobic property of shark-skin-inspired micro-riblets

Corresponding author: Danyang Zhao E-mail: [email protected]

Journal of Bionic Engineering 11 (2014) 296–302

Study on the Hydrophobic Property of Shark-Skin-Inspired Micro-Riblets

Danyang Zhao, Qianqian Tian, Minjie Wang, Yifei Jin Key Laboratory for Precision & Non-Traditional Machining Technology of Ministry of Education,

Dalian University of Technology, Dalian 116024, P. R. China

Abstract This paper aims to characterize the hydrophobic property of shark-skin-inspired riblets with potential engineering appli-

cations. Based on the hydrophobic theory, a new hydrophobic model which is consistent with the special structure of shark-skin-inspired micro-riblets was proposed. Then, the contact angles of different droplets were measured by optical contact angle measuring device on the shark-skin-inspired micro-riblets and the smooth surface, respectively. The results show that the surface of micro-riblets possesses obvious hydrophobicity, and the actual contact angles of different droplets residing on the riblets decrease with the increase in the droplet volume. According to the new hydrophobic model and the measurement of contact angle, it was found that the arrangement and structure of the shark-skin-inspired micro-riblets significantly affect the surface hydrophobic property. Using the new hydrophobic model, the prediction error of contact angle can be less than 3%compared with the measured one. The research on hydrophobic property of biomimetic micro-riblets is proved to be necessary and important to well explain drag reduction and microbe-resistant property of micro-riblets.

Keywords: hydrophobic property, micro-riblet, contact angle, shark skin Copyright © 2014, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60046-9

1 Introduction

Nature provides various examples of materials, surfaces and structures whose features can be replicated for practical applications[1]. Particularly, hydrophobic surfaces, due to their fabulous properties, such as self-cleaning, antifouling properties, water repellency and anti-corrosion, have a significant impact on many fields of science researches and practical applica-tions[2,3].

Such a well-known example is the ‘lotus effect’, which is defined as the self-cleaning paragon with highly super-hydrophobic property and anti-pollution ability like a lotus leaf[4,5]. The study of ‘lotus effect’ can go back to the work of Barthlott, who focused on inves-tigating leaf surfaces of 200 species. It was reported that the surface of plant is covered with wax and has the micro-scale papillae, resulting in the self-cleaning property[6,7]. Besides, the insects, cicada and termite, exhibit ordered hexagonal packed array structures on their wings surface. Watson et al. pointed out that the

wing structures with spacings, providing mechanical strength to prevent load failure under flight and/or aid in the aerodynamic efficiency of the insect, serve as an anti-reflective coating but may also act as a self-cleaning coating[8]. In view of the phenomenon, Wenzel[9,10], as well as Cassie and Baxter[11], proposed the model to interpret the hydrophobic phenomenon.

Another example, providing the ideal template or model for artificial application, is shark skin, which has been widely investigated for many years because of the drag reduction effect[12,13]. On the surface of shark skin, there are many micro-scales called dermal denticles. It was reported that the grooved scales can prevent the formation of vortices or keep the vortices off the surface, witch result in water moving easily over the shark skin[14,15]. Moreover, the structures can also protect skin surface from marine fouling and play a role in the de-fense against adhesion and growth of marine organ-isms[16]. It can be seen that the characteristics of shark skin are of great scientific and technological relevance. On the basis of the understanding of shark skin, a lot of

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studies and imitations of the grooved scales, which are referred to as ‘biomimetics’, have been carried out by researchers. For example, Speedo invented the swimsuit called ‘Fastskin’ which mimics the V-shape micro-scales of the shark skin and displays admired drag reduction[17]. Another commercial product ‘Sharklet’ is comprised of millions of tiny diamonds arranged in a distinct pattern that mimics the microbe-resistant property of shark skin. The study showed that it can defense against multiple strains of bacteria and keep surfaces clean[18,19]. Subse-quently, placoid-shaped, V-shaped, riblet-shaped, and ridge-shaped grooved surfaces, were investigated as the micro-grooved surfaces for the purpose of reducing pressure loss. The results show that these micro-grooved surfaces possess the drag reduction performance[20]. In addition, based on the quantitative analysis of feather structure of adult pigeons, novel biomimetic herring-bone riblets with narrow smooth edge were proposed to reduce surface drag[21]. Given that the influence of hy-drophobic property on the drag reduction and mi-crobe-resistant property, the research on hydrophobic property of biomimetic micro-structures is proved to be necessary and important. However, there are few reports concerning hydrophobic property of shark-skin-inspired micro-riblets yet.

In this work, based on the fundamental hydropho-bic model, a new hydrophobic model which is consistent with the special structure of shark-skin-inspired mi-cro-riblets was proposed. It was investigated how the riblet’s size and arrangement affect the wetting behavior of micro-patterned surface. Then, the contact angles of different droplets were measured by optical contact angle measuring device on the shark-skin-inspired mi-cro-riblets and the smooth surface, respectively. In ad-dition, the hydrophobic mechanism of shark- skin-in-spired micro-riblets was also analyzed and discussed in the paper.

2 Hydrophobic theory

When a liquid droplet resides on the solid surface, the included angle between the tangent of liquid-vapor interface and the tangent of solid-liquid interface is re-ferred as the contact angle. It is well-known that the contact angle in practice is influenced by both surface chemistry and roughness. The contact angle of a droplet residing on the solid surface increases up to 90˚ or larger, namely, achieving a hydrophobic state.

2.1 Hydrophobic models The contact angle of a droplet residing on the ide-

ally flat surface can be given by Young’s equation[22] in the form

cos ,SV SL LVγ γ γ θ= + (1)

where θ is the intrinsic contact angle; and SVγ , SLγ , LVγ , are the surface tensions of solid-vapor, solid-liquid, and liquid-vapor interfaces, respectively.

However, relation between the apparent contact angle on a rough surface and surface tensions is not consistent with Young’s equation. Based on thermody-namics, a new formula which is similar to Young’s equation can be gained as[22]

cos ( ) / .r SV SL LVrθ γ γ γ= − (2)

Combining Eq. (1) and Eq. (2), the apparent contact angle is given as

cos cos ,r rθ θ= (3)

where rθ is the apparent contact angle, and r is the sur-face roughness defined as the ratio of actual area to the projected area. The new formula is Wenzel’s model, and the diagram[22] of Wenzel approach is shown in Fig. 1a.

Unlike the homogeneous wetting (Wenzel’s model), heterogeneous wetting as shown in Fig. 1b is the other wetting state in which a liquid droplet is residing on a composite surface. The Cassie’s model considers the synthetic effect of each acting phase resulting in contact angle. Especially, for the composite surface of solid and air, the liquid droplet has an apparent contact angle which is given as[22]

1 1 2 2cos cos cos ,r f fθ θ θ= + (4)

where f1 is the coefficient of solid surface being in touch with the liquid droplet; f2 is the coefficient of air being in touch with the liquid droplet (f1 + f2 =1); θ1 is the

(a) (b) Fig. 1 Diagrams of the homogeneous wetting (a) and the het-erogeneous wetting (b).

Journal of Bionic Engineering (2014) Vol.11 No.2 298

intrinsic contact angle of a drop residing on the solid surface; and θ2 is the intrinsic contact angle of a drop residing on the air. It is well-known that the intrinsic contact angle of a drop residing on the air is 180˚, namely, θ2 = 180˚. As a result, the apparent contact angle of a liquid droplet residing on the composite surface can be given as[22]

1 1 2cos cos ,r f fθ θ= − (5)

1 1 1cos cos 1.r f fθ θ= + − (6)

2.2 Hydrophobic model of shark-skin-inspired mi-cro-riblets Shark skin is composed of many small scales ar-

ranged in an interlocking array. The micro morphology of surface taken by scanning electron microscope is shown in Fig. 2. On the surface of real shark skin, there is a space between two adjacent scales. Based on the micro-structures of real shark skin, the idealized and normalized shark-skin-inspired micro-riblets, as shown in Fig. 3, were proposed for the large-area fabrication. In order to study the hydrophobic property of the shark-skin-inspired micro-riblets, the influences of scale arrangement and micro-riblets’ structure on the apparent contact angle were analyzed.

(1) The scale arrangement is considered inde-pendently. As shown in Fig. 4, the coefficient of solid surface being in touch with the liquid droplet f1 is given as

1

( )2 ,

2

a d na df

mn m

++

= = (7)

where a, d, m and n is the longest riblet size, the shortest riblet size, vertical spacing and horizontal spacing be-tween two scales, respectively. According to the Cassie’s model, the apparent contact angle of the liquid droplet residing on the composite surface can be given as

1 1cos cos 1,2 2r

a d a dm m

θ θ+ += + − (8)

where θr1 is the theoretical apparent contact angle. Ac-cording to the analysis above, the longer the vertical spacing is, the larger the theoretical contact angle θr1 is. Meanwhile, the shorter the length of the riblet presents, the larger the theoretical contact angle θr1 is. In other words, the hydrophobicity will increase.

(2) The micro-riblets’ structure is taken into con-

sideration independently. As shown in Fig. 5, the com-posite surface being in touch with the liquid droplet is

Fig. 2 SEM image of shark skin surface.

Fig. 3 Shark-skin-inspired micro-riblets.

a d

n

m

Fig. 4 The scale arrangement of shark-skin-inspired micro-riblets.

h

Fig. 5 Schematic of water droplet residing on the shark-skin- inspired micro-riblets.


composed of solid and air. Simultaneously, the solid surface being in touch with liquid droplet achieves the homogeneous wetting state. Therefore, combining Eq. (3) and Eq. (6), the apparent contact angle can be gained as

2 1cos cos 1,r s srθ ϕ θ ϕ= + − (9)

where θr2 is the theoretical apparent contact angle with the micro-riblets’ structure which is taken into consid-eration independently; φs is the coefficient of solid sur-face being in touch with the liquid droplet, φs = l/f; and r is the surface roughness defined as the actual area A1 of micro-riblets divided by the projected area A2.

The actual area A1 of micro-riblets between two ribs can be calculated by

22

1 2 .2 2 2f x yA h x y c

⎛ ⎞⎛ ⎞⎜ ⎟= − − + + +⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ (10)

The projected area of micro-riblets between two ribs can be calculated by

2 ,A fc= (11)

where c is the length of micro-riblets. Therefore, r can be calculated by

2 2( ) 4,

f x y h x yr

f− − + + +

= (12)

where l, h, f, x and y are the rib width of the solid-liquid interface, the depth of riblets, riblet spacing, the width of two riblet tops, and the width of two riblet bottom, re-spectively.

(3) Taking the scale arrangement and micro-riblets’ structure into comprehensive consideration, the apparent contact angle θr can be gained from Eq. (13).

3 Measurement of contact angle

The apparent contact angles of liquid droplets re-siding on the biomimetic film and smooth film were measured by optical contact angle measuring device, respectively. As shown in Fig. 6, the biomimetic film bought from Sharklet Company has simplified shark-skin-inspired micro-riblets. Firstly, the biomi-metic film and smooth film were degreased over 3 min

in the alkaline degreasing agent at 50 ˚C. Then, the two degreased films were rinsed with the deionized water to remove residual chemicals adhering to the films and blow-dried subsequently through nitrogen gas. Simul-taneously, the micro-needle of the instrument was rinsed with the deionized water and blow-dried through nitro-gen gas. The biomimetic film and the smooth film were put on the center of the measuring platform, and the water droplet was dripped onto the films through the micro-needle. The volumes of water droplets were 3 μL, 4 μL, 4.5 μL, 5 μL and 5.5 μL, respectively. Finally, the standard sessile drop method was adopted for the measurement.

4 Results and discussion

As shown in Fig. 7, it was found obviously that the apparent contact angles of water droplets residing on the biomimetic film were larger than those of water droplets residing on smooth film. Through the analysis of hy-drophobic model of shark-skin-inspired micro-riblets, it was shown that the solid-liquid interface was changed by the scale arrangement and the wettability of the liquid on the riblets was weakened. Simultaneously, due to the micro-riblets’ structure, there was available air trapped on the bottom of riblets so that the solid-liquid interface was changed to the composite interface of solid-liquid interface and air-liquid interface. Therefore, it can be concluded that the surface with shark-skin-inspired mi-cro-riblets was more beneficial in enhancing the hy-drophobic property than the smooth surface.

Fig. 6 SEM image of the biomimetic film.

2 2

1( ) 4

cos cos 1,2 2r

f x y h x y a d l a d lf m f m f

θ θ− − + + + + +

= + − (13)


(a)

(c)

(e)

(g) (h)

(i) (j)

(f)

(d)

(b)

Fig. 7 The apparent contact angles taken at 3 μL, 4 μL, 4.5 μL, 5 μL, 5.5 μL of water droplets residing on the smooth film as shown in (a), (c), (e), (g), (i), respectively and the apparent contact angles taken at 3 μL, 4 μL, 4.5 μL, 5 μL, 5.5 μL of water droplets residing on the biomimetic film as shown in (b), (d), (f), (h), (j) respectively.


In Fig. 8, the actual contact angles of different

droplets residing on the biomimetic film decrease with the increase in the droplet volume. Jiang[22] studied the energy variation of droplet on the substrate, and reported the energy equation at equilibrium as

2/3 1/32/33

(1 cos ) (2 cos ) ,9π r r

LV

GV

θ θγ

= − + (14)

where G is the gravity of the drop and V is the volume of the drop. From Eq. (14), it was found that the contact angle of droplet varies inversely with the droplet volume. The contact angle of a droplet residing on rough surface can be expressed in two ways. One is the contact angle

crθ which is consistent with the Cassie equation, and the

other is the contact angle wrθ which is consistent with

the Wenzel equation. The theoretical contact angle at equilibrium corresponds with the inequality:

w cr r rθ θ θ< < . As the volume of a droplet increases, the

liquid droplet residing on the rough surface is close to the Wenzel model by gravity. As shown in Eq. (13), the theoretical contact angle θr will decrease with the in-creasing riblet width of the solid-liquid interface l. It can be seen that there is a good consistency between the variation tendency of the theoretical contact angle and the variation tendency of actual contact angle.

To study the effects of the scale arrangement and micro-riblets’ structure on hydrophobicity, the values of riblet sizes, a, d, m, n, x, y, f and h, were measured 5 times by scanning electron microscope. The average values of a, d, m, n, x, y, f and h were 16.9 μm, 4.7 μm, 12.0 μm, 24.4 μm, 0.9 μm, 1.1 μm, 4.1 μm and 2.0 μm, respectively. The values of theoretical apparent contact angle were calculated by Eqs. (8), (9) and (13) and summarized in Table 1. From Table 1, the intrinsic contact angle θ of a volume of 3 μL of water droplet is 75.1˚, while the theoretical contact angle θr1 considering the scale arrangement independently and the theoretical contact angle θr2 regarding the micro-riblets’ structure independently are 82.4˚ and 99.4˚, respectively. Con-sidering both scale arrangement and micro-riblets’ structure, the theoretical contact angle θr is 103.6˚. By using the new hydrophobic model, the prediction error of contact angle can be less than 3% compared with the measured one, which demonstrates that the proposed hydrophobic model of shark-skin-inspired micro-riblets is effective and accurate. Due to both the calculation

Con

tact

ang

le (˚

)

Fig. 8 Relationship between contact angle and droplet volume.

Table 1 The contact angles of different droplets

Droplet volume

(μL)

Intrinsic contact angle

(˚)

Rib width l (μm)

θr1 (˚)

θr2 (˚)

Theoretical contact angle

(˚)

Actual contact angle

(˚)

Error(%)

3.0 75.1 2.4 82.4 99.4 103.6 103.9 0.3

4.0 75.0 2.6 82.3 95.3 100.6 102.9 1.3

4.5 74.2 2.8 81.6 90.4 96.6 99.0 2.5

5.0 75.9 3.0 83.1 88.3 95.0 97.8 2.9

5.5 75.6 3.3 82.8 82.0 88.6 89.2 0.7

error through Eq. (13) and the measurement errors of contact angles of different droplets, the prediction error will be different from the droplet volumes, as shown in Table 1. Meanwhile, during the experiment, because of the measurement errors of riblets’ sizes and approxima-tion errors of average values, the prediction error cannot be avoided. The results further showed that the scale arrangement and micro-riblets’ structure play a critical role in the hydrophobic property of micro-riblets.

5 Conclusion

A new hydrophobic model which is consistent with the special structure of shark-skin-inspired micro-riblets was proposed according to the hydrophobic theory. It was found that the hydrophobic property of shark-skin-inspired micro-riblets was affected by the scale arrangement and micro-riblets’ structure. The solid-liquid interface was changed by the scale ar-rangement and the wettability of the liquid on the riblets was weakened. Simultaneously, due to the micro-riblets’ structure, there was available air trapped on the bottom of riblets so that the solid-liquid interface turned into composite interface of solid-liquid interface and


air-liquid interface. By using the proposed hydrophobic model, the prediction error of contact angle can be less than 3% compared with the measured one, which dem-onstrates that the proposed hydrophobic model of shark-skin-inspired micro-riblets is effective and accu-rate.

Acknowledgment This work was supported by the National Natural

Science Foundation of China (NSFC), NO. 51275071.

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