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Measurement of frictional drag force on superhydrophobic metallic surface

  • J. R. Ley
  • Y. W. KwonEmail author
  • D. Masellas
Original Paper
  • 234 Downloads

Abstract

Material surfaces can be modified to become superhydrophobic using different techniques. Test equipment is necessary to assess the effectiveness of a superhydrophobic surface against frictional drag force. Because the frictional drag force is very small, especially for a sample size to be tested at a laboratory level, a traditional water channel system is not suitable. As a result, a new test setup was designed and fabricated to measure the reduction in the skin frictional drag force on such a superhydrophobic metallic surface. Two different types of sensors were considered. The first one was a spring-based displacement sensor and the other was a spring-less displacement sensor. The developed test setup can have the flow speed with a range of Reynolds numbers up to 70,000 with respect to the test specimen. In this range, the change in the frictional drag force was measured for superhydrophobic surfaces. A microscope was also used to check any change in the air film on the superhydrophobic surface as the flow speed was increased.

Keywords

Superhydrophobic Skin frictional force Femtosecond laser Drag reduction 

1 Introduction

One aspect of particular interest for the aqueous environment is the superhydrophobic property. A material is said to be superhydrophobic if the equilibrium contact angle of a water droplet is greater than 150\(^{\circ }\) and the contact hysteresis angle is less than 10\(^{\circ }\) (Wang and Jiang 2007). The idea of extending superhydrophobic properties to a range of materials was first inspired by observing the water repelling and self-cleaning effects of the lotus leaf (Neinhuis and Barthlott 1997) and a number of other leaves found in nature (Bhushan and Jung 2006). Due to the large contact angle, the center of mass of a water droplet is moved further above the surface causing the droplets to have a rolling action rather than a sliding action (Mahadevan and Pomeau 1999). This behavior along with the more uniform surface tension of the spherical geometry allows particles to become trapped in the droplet and carried away.

Understanding the superhydrophobic condition in the Cassie state comes from observation how a material can attain large enough contact angles to be considered superhydrophobic. When looking at the microscale roughness of a surface, if the distance between peaks is such that the static pressure of the water is not capable of overcoming the surface tension of the droplet, the valley will not become wetted. This results in an air–water interface at the material surface (Cassie and Baxter 1944).

It can be seen that, in the Cassie state, the equilibrium contact angle is a result of the proportion to the air–water interface. When the microscale peaks are combined with nanoscale features, a hierarchical structure is created and the Cassie state is improved by increasing the proportion of the air–water interface and thus increasing the equilibrium contact angle. This creates a surface that is near perfectly superhydrophobic. It is this air–water interface that is of particular interest to researchers and engineers, because a change in fluid–surface interaction by adding an air film separation alters the hydrodynamic properties.

The concept of a slip boundary condition becomes important when realizing that if a fluid does not come to rest at the interface of a solid, the resistive force of drag can be reduced on the surface, consequently, increasing the efficiency of the system. The mechanism by which this slip boundary condition is formed stems from the lotus effect, i.e., the hierarchical surface structure of superhydrophobic materials. In a hierarchical surface, under a Cassie state, there resides a layer of air that separates the solid surface from the water. Because the dynamic viscosity of air is two orders of magnitude smaller than water, the hydrodynamic skin friction is greatly reduced and the water is said to slip over the air layer (Aljallis et al. 2013).

A number of direct numerical simulations (Min and Kim 2004, 2005; Martell et al. 2009, 2010) and Computational Fluid Dynamic (CFD) simulations (Cottin-Bizonne et al. 2005; Maynes et al. 2007; Ou and Rothstein 2005) have shown that given the condition of superhydrophobicity at the surface, there could be a significant increase in slip length, resulting in higher slip velocities. Martell theorizes that the wall shear stress could be reduced as much as 50%, significantly reducing skin frictional drag. The results of these simulations are supported by experimental data, as well. Fukuda et al. (2000) and later Elbing et al. (2008) experimented by injecting an air layer over a fully submerged body to create a thin air film over the surface. This is considered an active method for achieving the same hydrodynamic benefits as a superhydrophobic surface due to the added complication of manually adding an air film layer. Elbing et al. (2008) showed that, with a continuous air film at higher injection rates, near complete elimination of skin friction drag occurred.

Due to the added complications, and the inherent increase in required energy for implementation, active systems may not be a practical means of reducing drag. It is, therefore, important to investigate materials where, in the passive state, exhibit the desired qualities of superhydrophobicity. It has been understood for some time that the degree of microscale surface roughness greatly contributes to the degree of hydrophobicity (Chen et al. 1999). This knowledge, coupled with the ability to assemble and alter surfaces on the micro- and nanoscale, has given rise for the opportunity of an experimental study. Henoch et al. (2006) was able to utilize photolithography to create structures on silicon wafers known as nanograss and nanobricks. The results showed a significant reduction in drag at all fluid velocities tested, and as much as 50% in the laminar region.

In addition, Daniello et al. (2009) used a similar lithographic process to create silicon wafer molds. The results of his study showed that there is a measurable decrease in drag that becomes prominent in the turbulent region. They hypothesized that, in the turbulent region, the reduction in drag is proportional to the Reynolds number and, therefore, to the thickness of the viscous sublayer. The results also suggested that there would be an asymptotic limit in drag reduction where the thickness of the viscous sublayer decreases to less than the height of the microridges for the surface topology. This would result in the sudden onset of microroughness being exposed to the flow causing a hold on drag reduction.

In more recent years, with the development of micro- and nanoscaled chemical coatings, Aljallis et al. (2013) conducted a study in which two aluminum plates were spray coated with an acrylic base and two different types of hydrophobic nanoparticles. These results point to the conclusion that coating systems were not effective for drag reduction in practical applications.

To date, the studies that have tested the theory of reduced skin friction drag due to superhydrophobic surface conditions have been limited to samples that were manufactured by means of photolithography and made out of silicone and its derivatives (Henoch et al. 2006; Daniello et al. 2009) or polymer-based coatings (Aljallis et al. 2013).

With the use of femto-second laser surface processing (FLSP), functionalizing the surface of metallic substrates through ablation became possible. Through the control of wavelength, pulse length, and fluence, the creation of micro- and nanoscaled features on metallic surfaces could be produced to resemble the silicon and polymer coating surfaces mentioned above. Kietzig et al. (2009) was able to produce functionalized surfaces over varying metallic substrates to study the change in surface properties as it pertains to water adhesion. Both superhydrophobic and superhydrophilic samples could be fabricated by measuring the contact angles. The major difference between the superhydrophobic and superhydrophilic samples was the presence of carbons on the processed surface. Carbons created the surface topology that is superhydrophobic. Zuhlke et al. (2010, 2013) also used FLSP to create multiscale structures on metallic materials.

Due to the resiliency and durability of metal over silicon structures and polymer coatings, FLSP-functionalized metallic substrates offer a practical engineering material that can be used in commercial applications where superhydrophobic properties are desirable such as reducing drag on the hull of a ship, which, in turn, lowers the amount of fuel consumed.

The objective of this research is to develop a test apparatus to measure the change in skin frictional force on superhydrophobic surfaces. To this end, a water tunnel testing stand was designed and fabricated, such that superhydrophobic samples could be held for analysis of air film retention over a range of Reynolds numbers as well as determination of the change in the frictional drag force resulting from superhydrophobic surfaces.

2 Design and fabrication of test apparatus

The basis for the design of the water tunnel was to allow for observation and measurements of fully submerged specimens in a uniform flow at various speeds. The sample size to be tested was approximately 100 mm long and 50 mm wide. To estimate the frictional drag force on such a size of specimen, a CFD analysis was conducted for a specimen assuming no-slip condition. Using the water, the frictional drag force was in the order of mN for the flow rate available with the selected water pump.

The CFD analysis also helped to select the cross-sectional dimensions of the water channel. The water channel should be large enough to minimize the boundary wall effects of the water channel on the flow over the specimen. On the other hand, the cross-sectional area should be small to maximize the flow rate for a fixed pump capacity. Considering both limiting aspects, the cross section of the water channel was determined to be 101.6 mm (4 in.) high, 203.2 mm (8 in.) wide, and 1524 mm (60 in.) long.

The width of the water channel was decided, such that two same sizes of plates could be tested simultaneously. Because a physical specimen has non-zero thickness, there is a form drag force on top of the frictional drag force. It is not possible to separate the two different drag forces from the total drag force which is normally measured in the test apparatus. Therefore, two test specimens of the identical size but two different surface conditions are placed in the test section in parallel. Because the two specimens are supposed to be in the same flow conditions, the form drag force would be the same for the two specimens, but the skin frictions would be different because of the surface modification. If the one is a regular specimen before the surface modification and the other is a superhydrophobic specimen, as shown in Fig. 1, the difference in the total drag forces of the two specimens would yield the change in the frictional drag force resulting from the superhydrophobic surface.
Fig. 1

Scanning electron microscope image of FLSP-treated surface

The design flow volume for this channel is selectable between 227.1 l/min (60 gpm) and 832.8 l/min (220 gpm). Using the following equation, a range of Reynolds numbers can be established:
$$\begin{aligned} Re=\frac{D_\mathrm{h} \rho u}{\mu }, \end{aligned}$$
(1)
where \(D_{\mathrm{h}}\) is the hydraulic diameter, \(\rho \) is the density of water, u is the free stream velocity, and \(\mu \) is the dynamic viscosity of water. Using the flows mentioned above, the expected span of channel Reynolds numbers is between approximately 25,000 and 91,000.

The two flow conditioners are placed near the entrance of the channel with 152.4 mm (6 in.) apart. The flow conditioners were made of honeycomb with hexagons measuring 5.842 mm (0.23 in.) from corner to corner and 5.08 mm (0.2 in.) from side to side. The effect of the flow conditioners is twofold; the primary purpose is to create a uniform flow at the inlet section. The secondary purpose is to facilitate a pressure drop in the downstream specimen testing region. The reduced pressure is desired to protect the gaskets lining of the removable cover over the specimen fixture from potential leaks.

The channel has the middle section as shown in Fig. 2, which is removable so as to allow for the placement of test specimens inside the channel. The water channel was attached to cylindrical reservoirs at its both ends for water circulation. The main focus of the design was the specimen and sensor fixture. Figure 3 shows the fixture stand which was installed at the middle section of the channel. The hole placements and patterns in both the top and bottom plates were arranged for multiple possible specimen and sensor setups.
Fig. 2

Water channel with the removable middle top

Fig. 3

Assembled specimen and sensor fixture stand

The original design called for each of FLSP-treated or -untreated plates to be supported by four styli with a ruby sphere. The plates would be placed at approximately 50% of the height of the channel, separated by 25.4 mm (1 in.), as shown in Fig. 4. These offset distances insure that there are no boundary layer interactions between the walls and test specimens.
Fig. 4

Original concept for specimen holder

The measured frictional forces for impending slip between the styli and the plates were 0.424 N for the untreated plate and 1.177 N for the treated plate. In the current design condition, the maximum flow speed attainable in the channel is 0.6723 m/s (2.21 ft/s). To estimate the expected form drag force imparted on the plates due to fluid flow, Eq. (2) was used:
$$\begin{aligned} F_\mathrm{d} =\frac{1}{2}\rho u^{2}c_\mathrm{d} A, \end{aligned}$$
(2)
where \(c_{\mathrm{d}}\) is the coefficient of drag for a flat plate perpendicular to flow estimated at 1.1, and A is the area of the plate seen by the flow. This is the form drag force for the perpendicular cross section to the flow. This equates to an estimated force of 0.045 N. On top of that, there is a frictional drag force for the surfaces parallel to the flow. However, the frictional drag force is expected to be smaller than the form drag force. Those drag forces are far below the force required to overcome static friction. Therefore, an alternate design of specimen holder was devised.
To minimize the presence of sliding friction to a negligible level, the use of a parallel pendulum setup was incorporated. Using 0.1016 mm (0.004 in.) polymer wire, two loops were attached to the top of the specimen fixture and extended down around the plate at a suspension height of 40 mm (1.57 in.) from the bottom of the channel. With the pendulum length of 61.595 mm (2.425 in.), an estimated force of approximately 0.045 N, and the mass of the plate, the resulting angle of deflection is less than \(2^{\circ }\). Therefore, the motion of the plate can be approximated as linear horizontal, since the vertical displacement is 0.032 mm (0.0013 in.). Figure 5 shows the parallel pendulum setup with the plates in place.
Fig. 5

Parallel pendulum specimen holder

To facilitate the measurement of forces in the range of millinewtons or less, a highly sensitive displacement sensor should be utilized. There are two types of displacement sensors. One type has a spring, while the other type does not have a spring against a displacement. Both types of sensors have a zone where the displacement is proportional to the output voltage signal. Outside the zone such as too little or too much displacements, the output signal is not reliable. As a result, it is necessary to measure the displacement within the linear range. To do that, there should be an initial displacement to the sensor to begin with such that the displacement range stays in the linear range throughout the test. This is possible for a spring-less sensor but not possible for a spring sensor, since the spring force cannot be counter balanced without flow. As a result, two different sensor setups were carried out for the two different sensors.

Because the spring-less sensor does not require any counter balance force, it can be installed at the rear side of the specimen, as shown in Fig. 6. The movable pin of the displacement sensor was directly attached to the plate, while the sensor was hold fixed to the sensor fixture stand. Because the end of the pin has a thread, a tiny nut of the right size pair was attached to the sample plate or a female thread was machined into a sample plate, so that the displacement pin and the sample plate could move together back and forth.
Fig. 6

Setup of spring-less displacement sensors

To fully utilize the spring-based sensor, a displacement compression method was introduced, as sketched in Fig. 7. As the drag force pushes the sample plate along the flow direction, the flexible cantilever structure deforms upward. The displacement sensor was initially under compression. As the cantilever deflects up, the initial compression in the displacement sensor is increased. Because the deflection of the cantilever structure is very small, the change in the displacement sensor is linearly proportional to the drag force applied to the rigid cylinder section in Fig. 7. The correlation constant between the displacement and the force was obtained by measuring the displacement for a known force.
Fig. 7

Spring-based displacement sensor design

Upon the initial testing of the cantilever in a flowing stream of water, it was discovered that vortex-induced vibration (VIV) resulting from the pipe in Fig. 7 caused a significant instability in the cantilever system that was translated to the sensor as the flow speed increased. Therefore, the use of strakes was introduced to the pipe. A strake was used to introduce turbulence around a cylindrical body, thereby disrupting the formation of a Von Karman vortex street, the mechanism by which VIV is established (Trim et al. 2016). Figure 8 compares the voltage output from the displacement sensor with and without the strake. It clearly shows the improvement of the voltage signal with the strake as the fluid velocity increases. The signal is stable without VIV. Figure 9 shows the final construction and assembly of the cantilever system mounted in the specimen fixture.
Fig. 8

Comparison of displacement sensor voltage output with and without strake over the pipe

Fig. 9

Assembled cantilever system in the specimen fixture

To finish the water channel, a stand was developed with the goals of portability and compactness. Then, all connecting hoses, a pump, a pressure sensor, and a flow sensor were assembled, as shown in Fig. 10. The pump is a variable speed pump, with a flow range of 227.1–832.8 l/min (60–220 gpm). The outlet of the pump is monitored by a high precision 0–206.8 kPa (0–30 psig) gauge and protected from over pressurization by a compact brass pressure regulator with a selectable range between 0 and 413.7 kPa (0–60 psig) which unloads directly to the inlet. The pump inlet is monitored by a 0–101.6 kPa (0–30 in Hg) vacuum gauge. The channel flow rate is measured using a ultrasonic clamp-on flow meter with remote mounting display. The system is powered by an external 12 V DC power supply mounted next to the outlet pressure gauge.
Fig. 10

Assembled testing stand and water channel

During the test, the voltage output of the sensors was then recorded, while the system was in a static condition to obtain the baseline position of the plates. The pump was initiated and voltage was recorded at various speeds for 30 s, following a several minute settling time to ensure that flow had reached a uniform speed through the channel. At each pump speed, the channel flow rate was recorded and the displacements of the plates were collected through the standard data collection system.

3 Results

Two superhydrophobic surfaces were compared for their skin friction. One of them had an almost twice larger average distance from valleys to peaks of the microstructures created by FLSP than the other. The former is called sample A, while the latter is called sample B. Data were recorded at various flow speeds. The tests were repeated several times while changing the positions of the plates and sensors to ensure unbiased repeatability. The Reynolds numbers were computed for two parameters for comparison. One was computed based on the hydraulic diameter of the channel, while the other was computed based on the length of the plate test specimen.

Upon filling the channel with water, the superhydrophobic properties of the surface were immediately noticeable. A thin air film formed around the plate having the appearance like a layer of ice with the surface texture of fine sand paper. Figure 11 shows an FLSP plate fully immersed in water. Both sample A and sample B had the same kind of air film over the plates upon the initial wetting, and both samples showed deterioration as head pressure rose with water level.
Fig. 11

FLSP-treated plate fully submersed in water

It took twice as long for sample A to lose its superhydrophobicity as compared to sample B. Figures 12, 13 compare the surface of sample A before and after deterioration of superhydrophobicity over the plate. The change in location and shape of the bright air bubbles from Fig. 12 to Fig. 13 indicates that some air films are replaced by water.
Fig. 12

Surface of sample A in water after the initial wetting

Fig. 13

Surface of sample A after approximately 40 min. submerged in water

Such a partial replacement of air film affected the skin frictional force. Figure 14 shows the displacement of the both samples resulting from the overall drag forces. The displacements were plotted against the Reynolds number of the water flow in terms of the specimen length. Because the form drag force is the same for both samples, the difference in the displacements is related to the change in the frictional drag force. Such a change in the skin friction is plotted in Fig. 15. That is, the skin frictional force in Fig. 15 is equal to the skin frictional force of sample B subtracted from that of sample A. In the figure, the skin frictional force was normalized in terms of a unit surface area.
Fig. 14

Plot of displacements of both sample A and sample B

Fig. 15

Plot of difference in skin frictional force between sample A and sample B

4 Conclusions

With the ability to extend superhydrophobic properties to metal surfaces through the use of FLSP, it is important to measure the effectiveness of the superhydrophobic surface against the skin friction force. To do this, an experimental apparatus was designed and fabricated.

A flow channel was designed capable of analyzing two specimens in parallel to ensure equivalent flow conditions. Two different samples to be compared were placed in the channel. The system was run at various flow rates ranging from 227.12 l/min (60 gpm) to 832.79 l/min (220 gpm). The test apparatus could measure the change in frictional drag force of the FLSP surface.

Two different superhydrophobic samples, taller and shorter microstructures on the plate surfaces, were tested and compared using the developed test apparatus. The experimental observation showed that some air films on the superhydrophobic samples disappeared resulting from water pressure on the surface. Shorter microstructures on the surface had quicker disappearance of the air films, which influenced the skin friction. As a result, the sample with longer microstructures had less skin friction than the one with shorter microstructures.

Notes

Acknowledgements

The superhydrophobic samples were fabricated and provided by Prof. Dennis Alexander at the University of Nabraska–Lincoln, and the financial support was provided by Ms. Sarwat Chappell at the Office of Naval Research. Their supports are greatly appreciated for the present research.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2018 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringNaval Postgraduate SchoolMontereyUSA

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