Plastron morphology and drag of a superhydrophobic surface in turbulent regime

The relationship between the state of the plastron, slip velocity, and drag of a superhydrophobic surface in contact with a turbulent boundary layer was investigated. The experiments were carried out using a body of revolution which was spray coated with a superhydrophobic layer and tested in a water tunnel at velocities ranging from 0.98 to 2.92 m/s (Reynolds number from $5.0\times {10}^5$ to $1.5\times {10}^6$ based on the length of the model). Visualization of the plastron and particle-tracking velocimetry (PTV) of the near-wall boundary layer was carried out using a long-range microscope with backlight illumination. The model was also equipped with a load cell to simultaneously measure the drag force. The load measurement showed a 36.4% reduction in drag at the lowest Re of $5.0\times {10}^5$, which decreased to 5.6% at the highest Re of $1.5\times {10}^6$. The microscopic PTV showed an increase in the slip velocity from 0.131 to 0.602 m/s, and a relatively constant slip length (85–66 μm) over the superhydrophobic surface (SHS) as Re increased from $5.0\times {10}^5$ to $1.5\times {10}^6$. The wall-normal gradient of mean velocity in the linear viscous sublayer showed smaller viscous wall shear stress over the SHS compared with the smooth baseline surface for Re smaller than $1.0\times {10}^6$. At a larger Re of $1.2\times {10}^6$, drag reduction diminished with an increase of relative roughness. The visualizations of the surface showed frequent appearance of a full air plastron with average thickness of $\sim 10\mu \mathrm{m}$ at the two lowest Re of $5.0\times {10}^5$ and $7.0\times {10}^5$. The air-water interface of the plastron had a transient behavior due to low-wave-number ripples, which leads to thickness variation. This full plastron was essential for obtaining a considerable drag reduction ($>16\%$). At the three higher Re with smaller drag reduction ($<8\%$), the plastron demonstrated isolated menisci of air, pinned between the tip and the valley of large roughness protrusions.

Figure 1

A schematic view of the high-speed water loop showing the two levels of the facility, the settling chamber, flow straighteners, and the test section (the schematic is adapted from Ref. [21]).

Figure 2

(a) The assembled model showing the general dimensions and the start (point A) and end (point B) of the SHS module. (b) An exploded view of the model displaying the three main sections of the modular design: leading edge, central body, and the cylindrical body. The $x\text{−}y$ coordinate system is centered at the upstream edge of the field of view of the measurement system.

Figure 3

(a) A schematic of the shadow-based long-range micro-PTV setup. The camera is placed in front of the diffused light source to record the shadow of the tracer particles, surface roughness, and any air layer or bubble over the surface. (b) A photo of the experimental setup showing the model and the long-range microscope. The silvery color of the cylindrical section indicates presence of plastron over the SHS.

Figure 4

A sample image recorded using the long-range microscope with backlight illumination. The image is enhanced for particle detection by subtracting the local minimum and normalization over a kernel of $7\times 7$ pixels. The tracer parties are visible as the black dots, while the surface texture of the SHS is also visible at the bottom of the image. The velocity of the detected particle pairs is indicated with vectors. Only particle images smaller than 10 pix are used for tracking to avoid out-of-focus particle images.

Figure 5

Wall detection over the baseline smooth surface. (a) Micro-PTV image of the near wall over the smooth surface showing the interface of the solid (dark) and the liquid phase (bright). (b) The profile of wall normal distance $y$ versus light intensity ($I$, in counts) averaged in the streamwise direction ($x$). (c) The profile of wall-normal gradient of the average light intensity, $\partial I/\partial y$. The location of the peak of $\partial I/\partial y$ is selected as the wall location $\left(y=0\right)$.

Figure 6

The procedure for detection of the silhouette of the SHS formed by the water-air and water-solid interfaces. (a) A sample image of the SHS at $\mathrm{Re}=5.0\times {10}^5$ with the detected silhouette. The location of the average roughness height $\left(y=0\right)$ and the 95% cumulative distribution of the roughness height ($y_{95}$) is also shown. (b) The histogram and (c) the cumulative distribution of the roughness heights for the ensemble of data collected at $\mathrm{Re}=5.0\times {10}^5$.

Figure 7

Estimation of the thickness of the air layer from a sample image at $\mathrm{Re}=5.0\times {10}^5$. (a) The reference image with the minimum air within the ensemble of data as evident by the exposed surface roughness. The surface is expected to still hold small bubbles in its micropores and cavities. (b) A sample image with a large amount of surface air forming a flat air-water interface (i.e., full plastron). (c) The image obtained by subtraction image (b) from image (a) to visualize the thickness of air layer in image (b).

Figure 8

Average drag coefficient ($C_D$) based on load-cell measurement versus Re for the smooth baseline surface and the SHS. The error bars show the standard deviation of data based on 16 experiments.

Figure 9

Velocity of tracer particles from shadow-based, long-range micro-PTV over the baseline (left figures) and the SHS (right figures). Each row corresponds to the specified Re. The mean velocity profile (solid line) is obtained by averaging the velocity of the tracer particles in bins with a wall-normal dimension of $\mathrm{\Delta }y=10\mu \mathrm{m}$ and 75% overlap. A linear regression is applied to the mean velocity profile in the linear viscous sublayer $y^{+}<5$ as shown by the dashed line.

Figure 10

Semilogarithmic plot of velocity from micro-PTV measurement over the (a) smooth baseline and (b) the SHS.

Figure 11

Drag reduction versus $k^{+}$ of the current study in comparison with the data reported in Refs. [12] and [8]. In general, DR attenuates with increase of relative roughness $k^{+}$.

Figure 12

(a) A macroscopic image of the SHS covered with an air layer at the lowest Re of $5.0\times {10}^5$. The shiny surface is visible at the top part of the cylinder due to the shallow imaging angle. (b) An image of the same surface at the highest Re of $1.5\times {10}^6$ after 45 min operation of the flow loop. The shiny air-water interface is absent, and the surface has a matt white color.

Figure 13

(a) Plastron visualization at the lowest Re of $5.0\times {10}^5$. There is a flat air plastron covering the entire micro-roughness of the surface. (b) An image of the same surface after 45 min operation of the flow loop at the highest Re of $1.5\times {10}^6$. The thick air plastron is absent, and the surface microstructures are visible.

Figure 14

Plastron visualization under a turbulent boundary layer at Re of (a) $5.0\times {10}^5$, (b) $7.0\times {10}^5$, (c) $1.0\times {10}^6$, (d) $1.2\times {10}^6$, and (e) $1.5\times {10}^6$. The left column displays a sample image for each Re. The images of the middle show the image with the smallest level of air at the corresponding Re. The right column displays the morphology of the air plastron and pockets by subtracting the intensity of the left image from the middle image. See the Supplemental Material [26] for a sequence of the images corresponding to $\mathrm{Re}=5.0\times {10}^5$ and $1.2\times {10}^6$.