Fabrication of a micro-structured surface based on interfacial convection for drag reduction

Based on interfacial convection in the presence of solvent evaporation, a novel method for the fabrication of a micro-structured surface is proposed to facilitate drag reduction. A mixture was coated on a substrate through a specially developed spray-painting system. Micron scale pits formed spontaneously in the coated surface because of interfacial convection and deformation driven by the gradient of the interfacial tension. Experimental results indicated that particles in the mixture played a crucial role in pit formation, and with a suitable selection of particle size and dosage, the characteristic parameters of the pitting could be controlled. The drag reduction experiments were first performed in a water tunnel, and the results showed that the micro-structured surface had a remarkable drag reduction performance over a great range of flow speeds.

In practice, an interfacial instability [16][17][18][19] in the coating film may lead the surface morphology to have an unexpected structure. Applications of interfacial convection are *Corresponding author (email: jdwang@mail.tsinghua.edu.cn) numerous, especially in chemical engineering and material processing [20]. In recent years, interfacial convection in the presence of solvent evaporation has been the subject of increasing investigation because of its important role in thin-polymer-film engineering during the drying process [21]. A few applications of interfacial convection in surface micro-structure fabrication have been reported in the literature. Maruyama et al. [22] proposed a solvent-casting method for the preparation of 2-dimensional submicron scale structures. Srinivasarao et al. [23] reported a simple and robust method using evaporative cooling to fabricate ordered micro-porous polymer films.
In this study, based on interfacial convection theory, a micro-structured surface was fabricated through a spraypainting technique, and the formation mechanism was discussed. In the preliminary evaluation of the drag reduction property, samples were tested in a water tunnel, and a remarkable drag reduction performance was obtained. The proposed simple method may have promising potential in the fabrication of drag reducing micro-structured surfaces for use in engineering applications.

Surface fabrication
The paint used for spray-painting is a mixture of several components, which are listed in Table 1. After being dispersed adequately by a stirrer, the mixture is coated on a pretreated substrate through a specially developed spraypainting system, shown schematically in Figure 1. The system is feasible for both plane and cylindrical substrates. The inclination angle α is adjustable for the plane substrates.
Spray-painting parameters, such as pressure, distance, coating thickness, temperature and humidity, can be readily adjusted, and the parameter values for spray-painting are listed in Table 2.

Surface analysis methods
The characteristic parameters of a coated surface are meas ured with a non-contact surface profiler MicroXAM™ from ADE Phase-Shift, and the measurement data are analyzed using the Scanning Probe Image Processor (SPIP). The Confocal Laser Scanning Microscope (CLSM) is also used for surface analysis.
To identify the influence of micro particles and gravity direction on surface fabrication, the coating samples are  to the mixture, and by adjusting the inclination angle α from 0 and 90° to 180°, as shown in Table 3.
To analyze the formation mechanism of micron scale pits, an infrared thermometer SC660 from FLIR is used to observe the temperature changes and material transfer in the liquid film.

Drag reduction test of surface
Preliminarily drag reduction tests to evaluate the drag reduction performance of the micro-structured surface, were performed in a high-speed water tunnel with a closed circulation system as shown in Figure 2(a). The pumped water in the tunnel first flowed through an anti-revolving section to prevent rotation of the flow stream, and vertical stream-wise flow disturbance was eliminated by a honeycomb. Guide vanes in the four bends were also used to restrain flow separation and improve uniformity. All the measures taken above were to ensure the quality of the flow in the test section.
The skin friction drag on samples was measured in the test section of the water tunnel, as shown in Figure 2(b). In the test section, the sample was supported by a central axle, and two small gaps (less than 0.3 mm) were interspersed between the sample and its front and back accessories. With the aid of slip rings, the sample could glide along the central axle. When water stream flowed over the sample surface, the skin friction drag that the sample suffered was trans- Figure 1 Schematic diagram of the spray-painting system. ferred to the force sensor by slip rings and pins, and the force signal was finally acquired by a computer for data analysis. As the fairing and tail of the model were fixed to the central support, the pressure force was transferred to the support, which means that the skin friction drag could be measured independently and directly in the test section of the water tunnel. The test samples were cylindrical pipes 325 mm long and 39 mm in diameter. Five samples were tested in the water tunnel. One sample was smooth with a surface roughness (RMS) of less than 1.6 μm, while other samples were painted with coatings FC05-6, FC15-2, FC15-6 and FC30-6.
In the experiment, the flow speed of the water was 8-21 m/s, and the water temperature in the tunnel was 22.5°C (with fluctuations of less than 2°C). The relative drag reduction ratio is defined here to evaluate the drag reduction performance, compared with the smooth sample: where λ is the drag reduction ratio of micro-structured surface, F S is the friction drag of a smooth surface, and F C is the friction drag of the micro-structured surface.

Surface analysis
The characteristic parameters of the coated surface were measured with a surface profiler MicroXAM™, and the measurement results are shown in Figure 3. Micron scale pits were distributed irregularly on the coated surface. The pits were shaped truncated cones with wider upsides and narrower downsides. As shown in Figure 4, the observed results of the CLSM indicated that, at the bottom of every pit, a particle existed, and the pits were similar in size and shape to the particles below. The corresponding relationship between pits and particles indicated that particles in the mixture may play an important role in pit formation.
To further clarify the influence of particles on pit formation, coating samples were fabricated by adjusting particle sizes and dosages in the mixture, and characteristic parameters of pits, such as depth, diameter, and area percentage were measured via SPIP. Here, the depth is a statistical distance from the datum plane to the bottom of the detected pits. The diameter is a statistical mean surface diameter counted at the detection level. The area percentage is defined as the ratio of the pit area to the total area of the detected  surface. For all parameters, counts are based on the mean of nine counts, and three detected areas from three samples.
The relationship between the characteristic parameters of pits and particle sizes and dosages is shown in Figure 5. It can be seen from Figures 5(a) and (b) that, pit size, i.e. depth and diameter, increased with the increment of particle diameter from 5.27 to 29.59 μm, but was not influenced by particle dosage. As shown in Figure 5(c), the percentage area of pits increased when the particle dosage increased from 2% to 5%, but was invariable with changes in particle size. Thus, pit size is mainly determined by particle size, and is independent of particle dosage. The percentage area of pits is related to particle dosage, and is independent of particle size. Therefore, with a suitable selection of particle size and dosage, size and area percentage of micron pits can be effectively controlled. Figure 6 shows the temperature change in the wet film, which was measured by an infrared thermometer SC660. The average temperature of the surface layer was 22°C, while that of the bottom was 23.7°C. In other words, there was a temperature decrease of 1.7°C. Surface regions close to the particles had a higher temperature of 22.8°C, while regions far from the particles had a lower temperature of 22°C, which represented a visible temperature difference in the surface layer.

Formation mechanism analysis of micro-structured surface
The above analysis indicated that solvent evaporation in  the wet film resulted in a temperature decrease and temperature difference at the surface layer. Regions with a higher temperature had lower interfacial tension, while regions with a lower temperature had higher interfacial ten-sion. Therefore, the temperature gradient created an interfacial tension gradient, and the interfacial tension induced interfacial convection [16][17][18][19] at the surface layer. A sketch map of the formation mechanism of a microstructured surface is shown in Figure 7. The mixture at regions close to the particles with lower interfacial tension was driven to regions far from particles where the interfacial tension was higher. The material transfer from regions close to the particles led to subsidence compared with surrounding regions. The process was synchronous with coating solidification and viscosity increment. When the mixture became viscous enough, interfacial convection ceased, and interfacial deformation caused by convection became fixed, which resulted in micron scale pits in the coating surface.
Interfacial convection might, in fact, be driven by thermocapillary action due to the temperature dependent nature of the interfacial tensions or by the buoyancy arising from density differences. The relative size of these two effects depended on the fluid layer depth, with thermocapillary forces dominating in sufficiently thin layers [24].
To evaluate the relative importance of buoyancy and thermocapillary action in interfacial convection, coatings with different inclination angles were prepared in order to change the buoyancy direction (gravity direction), and the surface characteristic parameters were measured, as shown in Table 4.
From Table 4, characteristic parameters, such as depth,  diameter and area percentage, show small differences. Accordingly, the change of buoyancy direction has little influence on surface fabrication. In other words, compared with thermocapillary action, the effect of buoyancy was negligible during interfacial convection. Therefore, interfacial convection and deformation driven by the interface tension gradient were main factors in micro-structured surface formation.

Drag reduction performance of micro-structured surface
Four coating samples were tested in the water tunnel to evaluate the drag reduction performance, and the test results are shown in Figure 8. From the figure, the drag reduction ratio for all tested samples was over 10% in a flow speed ranging from 8 to 21 m/s. With the increase in flow speed, the drag reduction performance became more remarkable.
As the flow speed increased to 21 m/s, the average drag reduction ratio increased to 23.7%, with a highest value of 28.4% for FC15-6. Accordingly, a micro-structured surface reduces skin force effectively, and has remarkable drag reduction performance over a wide range of flow speeds. It can also be seen from the figure that the drag reduction performances of the four coating samples were different because of the surface characteristic parameters. The variance between FC15-3 and FC15-6 indicates that the area percentage of the micro scale pits has a certain influence on drag reduction, while the difference between FC05-6, FC15-6 and FC30-6 shows that pit size also plays a role in drag reduction. Therefore, with the aim of maximizing the drag reduction efficiency, systemic experiments should be carried out to clarify the relationship between drag reduction performance and surface characteristic parameters, to optimize the parameters.

Conclusions
From the above experimental results and discussion, the following conclusions are drawn.
(1) Micro-structured surfaces formed spontaneously after the solidification of the spray-painted coating. Thus particles in the mixture play a key role in surface formation. With a suitable selection of particles, the characteristic parameters of micro-structured surface can be controlled.
(2) Solvent evaporation in the wet film induces a temperature gradient and interfacial tension gradient in the surface layer, and results in interfacial convection and deformation, which are considered to be the main factors in surface formation.
(3) Comparison experiments between smooth and microstructured surfaces were performed in a high speed water tunnel. Preliminary test results indicate that the micro-structured surface fabricated by the proposed method has a remarkable drag reduction performance over a wide range of flow speeds, and the characteristic parameters have considerable influence on drag reduction efficiency.
In subsequent work, related research such as accurate control and optimization of surface characteristic parameters will be carried out to maximize drag reduction efficiency. Furthermore, drag reduction in the fields of aeronautical engineering such as air vehicles has also been the subject of increasing attention because of the significant potential practical value to both military and civil applications. Because the drag reduction tests in this paper were only performed in water flow, and a distinct change in the physical properties of fluid media may lead to unexpected results in the drag reduction performance of micro-structured surfaces, further investigation will be done on the feasibility and viability of micro-structured surface applications in air flow for drag reduction.