Article pubs.acs.org/Langmuir
Reconciling Slip Measurements in Symmetric and Asymmetric Systems Liwen Zhu, Phil Attard,* and Chiara Neto* School of Chemistry, F11, The University of Sydney, NSW 2006, Australia ABSTRACT: In the past decade, the slip of simple liquids on solid surfaces has been demonstrated by many groups. However, the slip of liquids on wettable surfaces is heavily debated. Using colloid probe atomic force microscopy (AFM), we found the slip length of di-n-octylphthalate in a symmetric wettable system (silica) to be around 11 nm, which raises the question of what the measured slip length in an asymmetric hydrophilic−hydrophobic system would be. To answer this question, we investigated liquid slip in one symmetric nonwettable system (hydrophobic DCDMS or OTS) and in one asymmetric hydrophilic (silica)− hydrophobic (DCDMS) system by the same method at driving velocities of between 10 and 80 μm/s. The slip results obtained from the three systems are in agreement with each other, and this comparison provides a means to self-assess the accuracy and reproducibility of the measured force curves and the fitted slip length in our systems. Furthermore, this method provides access to reliable values of the actual slip length on any investigated flat surface in an asymmetric system, avoiding the difficulty of preparing a symmetric probe/flat surface system in a colloid probe AFM force measurement.
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profile. The other is to fit the departure of the measured force or flow from the calculated no-slip boundary condition. The first category includes velocimetry techniques where the liquid velocity profile near the wall is measured by determining the displacement of either a particle or a molecular tracer. Examples include microparticle image velocimetry (μ-PIV),6 total internal reflection fluorescence (TIRF)-PIV,7,8 double-focus florescence cross-correlation spectroscopy (DF-FCCS),9 and TIRFfluorescence correlation spectroscopy (FCS).10 In the second category, the slip length is considered to have an effect on the flow rate, which can be measured by a high-precision volumetric flow measurement,11,12 or the draining or lubrication force in a narrow gap, which can be measured by a surface force apparatus (SFA)13,14 and AFM.15−20 On the basis of molecular interactions, liquids flowing over solvophobic surfaces are expected to be less coupled to the surface and therefore show more slip than on solvophilic surfaces. This conclusion has been supported by many experimental and simulation papers that have measured no slip on solvophilic surfaces (Table 1). However, there is no theoretical reason that the slip length should be exactly zero on solvophilic surfaces. Contradictory findings from both experiments and simulations have measured a finite slip length on solvophilic surfaces. In Table 1, we selected some slip measurements on solid surfaces with different wettabilities by different techniques. On superhydrophobic surfaces (water contact angle >150°), Joseph et al.,6 Choi et al.,12 and Bhushan et al.21 demonstrated large slip lengths on the order of micrometers or submicrometers. At solvophobic surfaces (liquid contact angle >90°,
INTRODUCTION Liquid slip at solid interfaces has been widely discussed in the past decade. The classical no-slip boundary condition has been successfully used to describe Newtonian liquids flowing on solid surfaces on macroscopic scales.1 However, this boundary condition has recently been challenged by evidence from more sensitive experiments.2−5 In these experiments, it was shown that the liquid can slip at the liquid/solid interface with a finite velocity vs and a finite slip length b, as shown in Figure 1.
Figure 1. Schematic illustration of two boundary conditions. (a) Noslip boundary condition. The velocity of the liquid relative to the solid decreases to zero at the wall. (b) Slip boundary condition. The velocity of the liquid decreases gradually toward the solid wall, but it is nonzero at the wall. The slip length b is the extrapolated distance beyond the solid surface where the liquid velocity is equal to zero.
Received: March 11, 2012 Revised: April 26, 2012 Published: April 26, 2012
The slip length can be obtained via two main categories of methods. One is to extrapolate the measured flow velocity © 2012 American Chemical Society
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dx.doi.org/10.1021/la301040d | Langmuir 2012, 28, 7768−7774
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Table 1. Summary of Experimentally Measured Values of the Slip Length Published in the Literature, as Ordered by the Wettability (Equilibrium Liquid Contact Angle θ, Advancing Contact Angle θA, and Receding Contact Angle θR) of the Solid Surfacea author 31
substrate (θ)
sphere (θ)
Ho et al. Lee et al.32 Bonaccurso et al.26 Sun et al.29 McBride and Law27 Guriyanova et al.17
MgO (30°) anodized alumina membranes (12 ± 2°) mica (θR = 0°) silica (θR = 0°) mica silica silane SAM (5−40°) silane SAM (5−40°) silica (θA
