Effect of Nanometric-Scale Roughness on Slip at the Wall of Simple Fluids Tatiana Schmatko, ² Hubert Hervet, and Liliane Le ´ger* Laboratoire de Physique des Fluides Organise ´ s, FRE CNRS 2844, Colle ` ge de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France ReceiVed January 6, 2006. In Final Form: May 12, 2006 It is commonly acknowledged that roughness decreases the aptitude of simple liquids to exhibit flow with slip at solid interfaces. Most available studies have, however, been conducted on substrates for which both the surface chemistry and the roughness were varied simultaneously, making it difficult to identify their respective role on wall slip. To overcome this difficulty, we have developed a series of surfaces formed by grafting hyperbranched polymeric nanoparticles on a smooth, dense, self-assembled monolayer of SiH-terminated short poly(dimethylsiloxane) oligomers, allowing us to vary independently the surface density, the height, and the width of the grafted nanoparticles, and thereby the roughness parameters, while keeping similar surface chemistry. On such substrates, the boundary condition for the flow velocity of hexadecane has been characterized through near-field laser velocimetry. We demonstrate that decreasing the wavelength of the roughness at a fixed height strongly decreases slip, while increasing the height of the nanoparticles at a fixed aspect ratio of the roughness also dramatically affects slippage. Introduction Hydrodynamics usually assumes that the boundary condition for a simple liquid flowing near a solid surface is a zero velocity at the wall. During the past few years, a number of experiments have appeared showing evidence that simple liquids could slip exhibiting a nonzero velocity at the wall. This is correlated to recent improvements in detection tools for fluid velocity and the use of new setups such as the atomic force microscope (AFM) or surface force apparatus (SFA) (for a review, see ref 1). The question of a possible slip at the wall for simple liquids is not only a fundamental one. With the recent advances in microfluidics and the miniaturization of industrial processes, it is more and more important to know the exact behavior of the fluid near a solid interface. Churaev and co-workers 2 performed the first controlled experiments in 1980. Measuring the pressure drop- flow rate relation for water in microcapillaries coated with self- assembled monolayers (SAMs) of octadecyltrichlorosilane (OTS) (strongly hydrophobic substrate), they obtained flow rates higher than expected for the known bulk viscosity of water, and interpreted this result in terms of slip at the wall. A convenient parameter commonly used to characterize the flow boundary condition is the so-called slip length, b, or the distance to the wall at which the velocity profile extrapolates to zero. The average slip length in Churaev et al.’s experiments was about 200 nm, with a large uncertainty of (200 nm. The authors explained this large error as being due to an incomplete surface coating, the surface being heterogeneous, with nonwetting islands and wetting holes alternatively distributed on the substrate. Numerical simulations by Barrat 3 and Robbins 4 have indeed shown that roughness could strongly affect slip at the wall. Most often, simulations indicate that roughness decreases the slip length. Cottin et al. 5 recently showed, however, that, for a highly nonwetting surface (with advancing contact angles higher than 150°), a periodic roughness with a high enough aspect ratio may have the opposite effect. In another recent work, the same group also examined the effect of an heterogeneous pattern of nonslippy and slippy stripes on the slip length. 6 In a previous investigation from our group, using the technique of total internal reflection and fluorescence recovery after photo bleaching (TIR-FRAP), 7,8 Pit et al. showed that hexadecane exhibits slip on a bare smooth sapphire surface totally wetted by the liquid. The measured slip length, 150 nm, 9 is much larger than the dimension of the molecules. Decreasing the strength of the fluid-solid interactions by grafting a dense OTS monolayer on the sapphire surface increases the slip length, up to 400 nm. However, further decreasing the strength of the fluid-solid interaction by grafting a fluorinated SAM leads to a no-slip boundary condition (i.e., b ) 0). X-ray (XR)-reflectivity analysis of the fluorinated SAM layer showed that it was rough and incomplete. Pit et al.’s conclusions were that, as in the case of Churaev’s work, the heterogeneities of the monolayer were sufficient to kill the slippage. Along the same line, Pit et al. investigated the evolution of the slip length during the adsorption of a stearic acid monolayer on a sapphire surface 8 and observed * To whom correspondence should be addressed. E-mail: leger@lps.u- psud.fr. Current address: LPS, University Paris Sud - XI, Ba ˆtiment 510, 91405 ORSAY, France. ² Present address: FOM Institut for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1009 DB Amsterdam, The Netherlands. (1) Neto, C.; Evans, D. R.; Bonaccurso, E.; Butt, H.-J.; Craig, V. S. J. Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 2005, 68, 2859-2897. (2) Churaev, N. V.; Sobolev, V. D.; Somov, A. N. Slippage of liquids over lyophobic solid surfaces. J. Colloids Interface Sci. 1984, 97 (2), 574-581. (3) Barrat, J.-L.; Bocquet, L. Large slip effect at a nonwetting fluid-solid interface. Phys. ReV. Lett. 1999, 82 (23), 4671-4674. (4) Robbins, M. O.; Smith, E. D. Connecting molecular-scale and macroscopic tribology. Langmuir 1996, 12, 2 (19), 4543-4547. (5) Cottin-Bizonne, C.; Barrat, J.-L.; Bocquet, L.; Charlaix, E. Low friction flows of liquids at nanopatterned interfaces. Nat. Mater. 2003, 2, 237-240. (6) Cottin-Bizonne, C.; Barentin, C.; Charlaix, E.; Bocquet, L.; Barrat, J.-L. Dynamics of simple liquids at heterogeneous surfaces: Molecular-dynamics simulations and hydrodynamic description. Eur. Phys. J. E 2004, 15, 427-438. (7) Pit, R. Mesure locale de la vitesse a `l′interface solide-liquide simple: glissement et role des interactions. The `se de Doctorat, Universite ´ Paris IX, Paris, 1999. (8) Pit, R.; Hervet, H.; Le ´ger, L. Mise en e ´vidence directe d′e ´coulements avec glissement a ` la paroi a ` diverses interfaces hexade ´cane-solide. ReV. Me ´ tall.- CIT/Sci. Ge ´ nie Mate ´ r. 2001, 169-174. (9) Pit, R.; Hervet, H.; Le ´ger, L. Direct experimental evidence of slip in hexadecane: Solid interfaces. Phys. ReV. Lett. 2000, 85 (5), 980-983. 6843 Langmuir 2006, 22, 6843-6850 10.1021/la060061w CCC: $33.50 © 2006 American Chemical Society Published on Web 06/30/2006