Nanostructured surfaces offer opportunities to modify flow induced drag on solid objects. Measurements of the terminal velocity reveal that the drag associated with laminar Stokes flows can be reduced for spheres with nanostructured superhydrophilic as well as superhydrophobic surfaces. Numerical simulations suggest that the formation of recirculating or nearly stagnant flow zones leads to significant reduction in the friction drag. Such reduction, however, is offset by an increase in the form

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... rag that arises from nonuniform pressure distributions. Our work motivates further studies to optimally balance the friction and form drag and control resistance to laminar flows over objects with nanostructured surfaces. Controlling flow induced drag on solid objects has long been a subject of scientific as well as technological interest. Advances in microfluidics have motivated a number of recent studies on surface treatment and texturing methods for drag reduction. In particular, several studies 1-3 reported that one can achieve appreciable reduction in resistance to laminar liquid flows by using so-called superhydrophobic surfaces, which create a composite ͑solid and gas͒ interface with the liquid. This leads to apparent velocity slip and hence reduced surface friction since the viscosity of gases is orders of magnitude smaller than that of liquids. For fully wettable surfaces, in contrast, one may expect surface roughness to impede liquid flows and thereby, increase the associated drag. This was indeed demonstrated both experimentally and theoretically for laminar liquid flows along microchannels with lithographically defined microscale roughness. 4 From a simplistic consideration of increased liquid-solid contact areas, one would expect a similar trend for external liquid flows over objects with rough hydrophilic surfaces. In this article, we report a rather counterintuitive experimental observation that the drag associated with laminar Stokes flows over macroscale spheres can be reduced by forming superhydrophilic as well as superhydrophobic nanostructured surfaces. Given that the surface area of spheres increased substantially after nanostructuring, we find drag reduction, albeit small in absolute magnitude, to be remarkable for the spheres with superhydrophilic surfaces. We perform numerical simulations of Stokes flows over spheres with much simplified surface topology to gain a further physical insight. A convenient, yet precise way to characterize the flow resistance over a solid object is to drop the object in a quasiinfinite pool of liquid and measure its terminal velocity. The terminal velocity is determined by balance between the gravity force and the drag force exerted on the object by the surrounding fluid. This approach has the advantage that the terminal velocity can be measured much more precisely than flow rates or pressure. We use two groups of commercially available copper spheres of different nominal diameters. The diameters are measured using a calibrated micrometer with a precision of 0.001 mm. The average values are 1.598 and 1.980 mm, matching the nominal values provided by the supplier to within 1%. The standard deviations in the measurements are 0.002 mm and 0.001 mm, respectively. The mass of each sphere ͑19.0 and 36.4 mg͒ is determined from the measured mass of randomly selected groups of 20 spheres. The standard deviations are less than 0.05 mg, which is the estimated precision of our mass measurements. The mass values also agree with the values calculated using the density of Cu and the measured diameters of the spheres to within 0.05 mg. We perform terminal velocity measurements on spheres with three different types of surfaces such as: normally smooth surfaces of the as-received Cu spheres, nanostructured superhydrophilic surfaces, and nanostructured superhydrophobic surfaces. Lithography-based micro/ nanofabrication techniques can produce features of ordered geometries that may potentially yield more enhanced drag reduction but they are difficult, if not impossible, to apply on three-dimensional ͑3D͒ objects. We instead use a quasiselflimiting chemical oxidation scheme reported earlier 5,6 to form uniform and dense high-aspect-ratio CuO nanostructures of height approximately 1 m over the entire sphere surfaces. The scanning electron microscopy ͑SEM͒ images of an as-received Cu sphere and the same sphere after nanostructuring are shown in Fig. 1 . There are less than 0.1% changes in both the diameter and the mass of the spheres before and after oxidation. The contact angles of water and glycerin on flat Cu surfaces treated using nominally identical procedures as the spheres are measured using the sessile drop technique. 7 The measured contact angles of water and glycerin are 70°-80°for the as-received Cu samples, below 10°f or the nanostructured Cu surfaces, and 155°-165°after Teflon ® coatings are applied on the nanostructured surfaces. a͒