Mechanisms of drag reduction of superhydrophobic surfaces in a turbulent boundary layer flow

Jingxian Zhang1, Haiping Tian2, Zhaohui Yao1*, Pengfei Hao1, Nan Jiang2

1Department of Engineering Mechanics, Tsinghua University, P.R. China

2School of Mechanical Engineering, Tianjin University, P.R. China

Submitted to Experiments in Fluids

"Supplementary materials"

*Corresponding Author:Dr. Zhaohui Yao

Department of Engineering Mechanics, Tsinghua University, P.R. China

Tel.: +86-10-627-72558, E-mail:

The superhydrophobic surface used in our experiment is very similar to the superhydrophobic surface (SH-2) used in Aljallisetal.PoF2013. The two superhydrophobicsurfaces were both prepared by a spray coating method, using the product of Ross Nanotechnology Company. The morphologies of the two surfaces were shown and compared in Fig. S1, examined by scanning electron microscope (SEM).As shown in Fig. S1, the random distribution of the nano particles and the size of the nano particles are quite similar for the two surfaces.

Suface used in our experimentSH-2 coating in Aljallis et al.

Fig.S1 Scanning electron microscope (SEM) images of the surface morphology of the two superhydrophobic surfaces of the one used in our experiment [(a), (c)] and SH-2 in Aljallis et al [(b), (d)].

The contact angles of the superhydrophobic surface used in our experiment were measured and compared with the data of SH-2 coating used in Aljallis et al., shown in Table S1.

Table S1 Contact angle measurement data

Surface type / Initial contact angle (o) / Advancing contact angle (o) / Receding contact angle (o)
Suface used in our experiment / 160.0±0.5 / 161.9±0.8 / 158.9±0.9
SH-2 coating in Aljallis et al. / 161.6±0.5 / 164.3±4 / 158.9±1.5

Considering the similar morphology and properties of the surfaces in our experiment and in Aljallis et al., it is interesting to compare the drag reduction of the two surfaces. In our experiment, the drag reduction is estimated by the friction velocities, which can be expressed as

(S1)

where , are the wall shear stress values for the smooth and superhydrophobic surfaces, respectively, and , are their friction velocities.

In Aljallis et al., the drag reduction is calculated by the measured drag force. Drag reductions at different ReL (the Reynoldsnumbersbasedontheplatelength) in our experiment and in Aljallis et al. (SH-2) are shown in Fig. S2.

Fig.S2Drag reductions of SH-2 in Aljallis et al. (■) and in our experiment (○) at different ReL.

Although measured using different methods, our results agree well with Aljallisetal.’s(2013) at similar ReL. The drag reductionsat two similar ReLare listed in Table S2.

Table S2Comparison of the drag reduction

Our Experiment / Results of SH-2 coating
in Aljallis et al.
Drag Reduction / 20.7% / 24.1% / 20.4% / 24.1%

In Aljallis et al., the drag reducing effect was weakened or even disappeared at higher ReL, which can be regarded as results of the removal of the entrapped air layer from the surface by high shear rate. However, Limited by the pump used in our experiment,results for higher ReL were not obtained. The air layer was present during ourcurrent experiment.

It would be interesting to study the case in which the air layer is removed from the surface and we will investigate this in the future, using a high-power pump.