High-precision slip length measurement via resistance analysis

We hypothesize that the large uncertainty of slip length in conventional approaches for Newtonian fluids under creeping flow and lubrication approximation conditions arises from the assumed ideal velocity distribution, and an alternative approach that does not require assuming an exact velocity distribution is of great value under the same conditions.

In this study, we developed a new methodology to quantitatively and accurately determine slip length by converting the AFM-measured hydrodynamic forces and approach rates into mass flow and velocity-independent resistances and by using the Stribeck curve to identify the appropriate data interval. To prove the concept, we employed high-precision colloidal probe atomic force microscopy (CP-AFM) technology to study water on hydrophilic, less-wetting, and unmodified silicon surfaces across six driving velocities (6.0-36.6 μm/s), and their slip length values were then obtained, compared with conventional methods combined with further discussions.

The resulting slip lengths show no dependence on the driving velocity. We further introduce an analysis of extended uncertainty, demonstrating that our method exhibits an extended uncertainty less than one-third of that from the conventional approaches. Subsequently, we quantitatively assessed the contribution of friction resistance (R_Friction, directly linked to slip) in the total resistance (R_Total). The results show that, as the separation increases, the contribution of R_Friction decreases significantly, which explains why the slip length is so difficult to measure precisely. This study reveals that the large uncertainty of slip length obtained with the conventional methods stems from underestimating the contribution of R_Friction, and this work provides a novel and reliable methodology for achieving high-precision slip length by precisely decoupling the viscous and friction flow components.