ORIGINAL PAPER Drainage of a Wetting Liquid: Effective Slippage or Polymer Depletion? J. Cayer-Barrioz Æ D. Mazuyer Æ A. Tonck Æ E. Yamaguchi Received: 21 May 2008 / Accepted: 15 September 2008 / Published online: 30 September 2008 Ó Springer Science+Business Media, LLC 2008 Abstract A surface force apparatus has been used to investigate the drainage of a viscosity improver lubricant. The characterization of the VI confined interface has been performed. Surprisingly, dynamical measurements enlighten a significant negative value of the immobile layer thickness. This result is discussed in terms of occurrence of slip at the wall, liquid–solid interface wettability, surface roughness and cleanliness, and friction experiments. Con- sequently, an interface molecular organization modelling is proposed based on polymer depletion near the solid–liquid interface. Keywords Friction  Slip  Surface force apparatus 1 Introduction In confined geometries, knowledge regarding the structure and dynamic properties of fluids located at the vicinity of solid surfaces is crucial in several technological areas including lubrication, adhesion, contact mechanics, polymer processing, wetting dynamics, colloidal hydrodynamics and microfluidics. In fluid mechanics, one usually relies on the assumption that, when a liquid flows over a solid surface, the liquid molecules adjacent to the solid are stationary relative to the solid (see Fig. 1a) and that the viscosity is equal to the bulk viscosity [1]. These no-slip boundary conditions (BC) have been demonstrated in numerous macroscopic experiments [2]. Its general acceptance is the result of a debate between eminent scientists over two centuries [2]: although early experimentalists such as Bernoulli, Stokes, du Buat, Cou- lomb, did not observe slip of liquids at solid boundaries, Navier first proposed that a liquid may slip on a solid surface. He introduced the idea of ‘‘slip length’’ which is nowadays the most commonly used concept to quantify the slip of a liquid at a solid surface [2]. The slip length, b, is the distance beyond the liquid/solid interface at which the liquid velocity extrapolates to 0 (see Fig. 1b). By the mid- twentieth century, it had been unanimously accepted that even if slip occurred, it would have been detected only using experimental techniques with resolution far beyond that reached at this time [2]. Recently with the progression of nano-technology and the development of appropriate lubricants, a demand for the understanding of physical phenomena at the nanometre scale has raised [2]. The emergence of advanced techniques with high spatial resolution capable of interfacial flow measurements such as fluorescent recovery after photo- bleaching [3, 4], atomic force microscopy [5–7], surface force apparatus (SFA) [8–12] combined with molecular dynamic simulation [13–18] has recently revolutionized these fields of investigation. In particular, the slip length model has been developed [2, 19–21]. The problem of the flow of a Newtonian liquid confined between two approaching surfaces was first treated by Reynolds neglecting inertial and gravitational terms. Moreover, for small surface separations, the thickness of the liquid film, D, separating the two surfaces is small compared with the radius of curvature R of each surface. The approximate solution of the Navier–Stokes equations in case of sphere– plane configuration leads to the following expression for J. Cayer-Barrioz (&)  D. Mazuyer  A. Tonck Ecole Centrale de Lyon, LTDS – UMR5513 CNRS, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France e-mail: juliette.cayer-barrioz@ec-lyon.fr E. Yamaguchi Chevron – Oronite Company LLC, P.O. Box 1627, Richmond, CA 94802-0627, USA 123 Tribol Lett (2008) 32:81–90 DOI 10.1007/s11249-008-9365-7