Understanding Uncertainty and Error in Slip Length Measured by Atomic Force Microscopy (AFM)

Slip is a boundary condition in fluid mechanics, which is essential for understanding fluid behavior at solid-liquid interfaces. Although atomic force microscopy (AFM), especially the colloidal probe AFM (CP-AFM) technique, has been identified as a high-precision method for measuring the slip length, the results often show errors of several nanometers. To reveal the reasons behind this, in this work, the AFM slip length data reported in the literature were collected and analyzed to investigate the effects of factors, such as curvature, roughness, and velocity, on the determination of slip length. Subsequently, an error propagation analysis of the data processing using the original and simplified Vinogradova model was conducted quantitatively, together with further analysis of the interval choice. The results indicate that curvature, surface roughness, velocity, and data interval choice can all introduce significant discrepancies in the slip length, even for the same system. Moreover, both the original and simplified Vinogradova models exhibit an error-amplification trend during the slip-fitting process due to error propagation through intermediate variables such as separation, hydrodynamic force, velocity, etc. This error amplification represents a primary source of the substantial uncertainties observed in slip length determination. Subsequently, this work suggests alternatives, where (1) a resistance-based method using "hydrodynamic force/approach rate" instead of "approach rate/hydrodynamic force", which converts the error-amplification trend into an error-attenuation trend; and (2) quantitatively determining the fitting interval using the Stribeck interval screening framework is suggested.