Measurement of no-slip and slip boundary conditions in confined Newtonian fluids using atomic force microscopy

We report measurements of slip length at smooth and rough hydrophilic silica surfaces, using the hydrodynamic force measurement atomic force microscope (AFM). There has been some debate in the literature as to whether the boundary condition between a solid and a wetting fluid is one of no-slip or partial-slip; in particular the results of Neto et al. (C. Neto, V. S. J. Craig and D. R. M. Williams, Eur. Phys. J. E, 2003, 12, S71-S74) and of Honig and Ducker (C. D. F. Honig and W. A. Ducker, Phys. Rev. Lett., 2007, 98, 028305) are inconsistent. Unexpectedly, the AFM cantilever geometry leads to a different measurement of hydrodynamic drainage force. Rectangular cantilevers give results consistent with a no-slip boundary condition on smooth and rough surfaces, while v-shaped cantilever measurements show variability and can produce a finding of apparent partial-slip, consistent with earlier results in the literature. Possible reasons for the discrepancy are discussed. Equilibrium force measurements show no cantilever shape dependence. We conclude that the appropriate boundary condition for aqueous solutions on smooth and nanoscale-rough hydrophilic surfaces is one of no-slip.