Introduction

Hydrophobic surfaces available naturally and their benefits have been recognised for a significant length of time. For example, the Stenocara beetle from Africa’s Namib Desert, utilises hydrophilic ridges and hydrophobic troughs on its exoskeleton to channel water towards its head for hydration. The leaves of the lotus flower are also able to remove the possibility of becoming waterlogged in a swamp like environment. This has the added benefit that water rolling off the leaves collects debris, hence cleaning the leaves [1].
The existence of slip condition at the wall, and hence the existence of drag reduction, depends on the type of flow examined. Slip velocity has been reported in both laminar [2] and turbulent flow [3]. Fukuda et al [3] investigated the flow mechanisms which can reduce drag on a horizontal flat plate under specific circumstances, such as the air layers, the addition of surface ridges or riblets etc. They observed the appearance of slip velocity at the wall which leads to drag reduction. Lee et al [4] studied the effect of surface topology and void fraction on drage reduction in detail. They found that, at low void fractions, the micro-posts outperform the micro-ridges for the same void fraction value of shear-free area. They also found that the slip length increases linearly with void fraction but increased dramatically with the gas fraction higher than 90%.
Ou & Rothstein [2] studied flow of water in a rectangular channels of 50 mm length with different cross-sectional dimensions in the range of 76x1520 µm to 254x5080 µm. They observed a slip velocity of more than 60% of the average velocity in the microchannel is found at the centre of the shear-free air-water interface whereas the no-slip boundary condition is found to hold along the surface of the hydrophobic ridges. Watanabe et al [5] studied experimentally the change in drag for tap water flowing in a 16 mm-diameter pipe under laminar flow condition. Experiments were carried out to measure the pressure drop and the velocity profile of tap water and an aqueous solution of glycerine flowing in pipes with highly water-repellent walls, by using a pressure transducer and a hot-film anemometer. They found that the main reason for the fluid slip is the reduction in the molecular attraction between the liquid and the solid surface due to the low free surface energy of the solid. The low free surface energy was attributed to lower contact area of the liquid compared to a conventional smooth surface due to the fine grooves on the solid surface. Liquid cannot flow into the fine grooves which filled with owing to surface tension which could lead to drag reduction. The validity of the term slip condition for microchannel was examined further by Tretheway & Meinhart [6] using micron-resolution particle image velocimetry for flow through 30*300μm channels of hydrophilic and hydrophobic surfaces. They found that the velocity profiles measured in a hydrophilic glass were consistent to that estimated analytically and the widely accepted non-slip condition. However, a slip velocity of 10% of the free-stream velocity and the slip length of 1μm was recorded in the channel with a hydrophobic coating. Rothstein et al [7] carried out a series of experiments to examine the effect of hydrophobic surface topology of laminar drag reduction using photolithography to fabricate silicon wafers topology into precise micro-post or micro-ridge patterns. They observed a significant drag reduction of up to 40% was slip lengths of 20μm compared to no drag reduction in smooth hydrophobic surfaces. They attributed drag reduction to an air-water interface which forms between the micro-posts and is supported by surface tension. This enables the fluid to flow while maintaining minimum contact with the channel walls, thus providing a shear-free interface.
Rothstein et al [8] used the pressure drop and particle imaging velocitimeter to study the effect of micro-patterned hydrophobic surfaces in square channel of 25 µm height and 60 µm on drag reduction in turbulent flow. They reported drag reduction up to 50% which increased with increasing feature size and spacing on the surface at a given Reynolds number. They also found that drag reduction started where a viscous sublayer thickness matched the height of the surface feature. Rothstein [9] studied the effect of ultra-hydrophobic surfaces on internal and external flows experimentally and numerically. The results showed a drag reduction of up to 75% for slip length of 120 microns for Reynolds numbers a round 4000 and increase with higher feature spacing. Zhang et al [10] examined drag reduction by measuring the pressure loss in channel of 450mm length with cross-section of 9mm width and 1.75mm height. They reported drag reduction up to 54% in laminar and turbulent flow for Reynolds numbers in the range of 500 to 5000. Rios-Rodriguez et al [11] investigated the existence slip conditions of laminar flow for Reynolds numbers in the range of 70-250 in circular hydrophobic pipe of 14.1 mm inner diameter. They reported a 20% reduction of pressure drop in the coated channel compared to the non-coated ones.
In the literature, most of the papers regarding pressure drop and drag reduction in hydrophobic pipes, are published on rectangular and micro pipes. Only a few, early investigations on pressure drop for laminar flow in hydrophobic pipes in the range of 1 – 5 mm pipes were documented. Hence, the purpose of this paper is to: i) Study the pressure drop in small pipes with hydrophobic ally coated and non-coated surfaces in the order of millimetres. ii) Understand the effect of pipe diameter (1, 2, 3, 4 and 5 mm) and Reynolds number (0 – 10000) on the drag increase/reduction of hydrophobic coated surface. iii) Use high speed camera to understand the effect of hydrophobic surface on flow behaviour.