No-Slip Boundary Condition for Weak Solid−Liquid Interactions

Abstract

Lubrication forces between hydrophobized glass surfaces in alkane liquids have been measured using the atomic force microscopy colloid probe technique and compared to Reynolds lubrication theory with the aim of understanding the nature of the solid−liquid boundary condition for flow. Forces in n-hexadecane are consistent with the no-slip boundary condition. Forces in n-pentane and n-hexane are better fit when a small slip length of about 5−20 nm is included in the model. The error estimating slip length is about 10 nm, which is much greater than the error in measuring the deflection of an AFM cantilever. We rationalize the finite slip length for n-pentane and n-hexane using an activation model for shear-driven molecular motion, which predicts that only molecules with an activation energy less than about 5 kT will have their diffusion affected by applied shear. The difference in slip length between short (pentane) and long (hexadecane) molecules is then explained by the fact that the short alkanes experience a weaker attraction to the solid.