Hydrodynamic resistance of close-approached slip surfaces with a nanoasperity or an entrapped nanobubble

We present a general solution of hydrodynamic resistance of close-approached slippery surfaces with a nanoasperity or a nanobubble as an idealized roughness effect. Based on Reynolds' lubrication theory and a simple slip boundary condition, the pressure distribution in the thin liquid film is predicted analytically and the total hydrodynamic resistance force at limiting cases are formulated in terms of correction functions to the Taylor's equation. Accessible parameters are included for the drainage experiment using atomic force microscope or surface force apparatus. We provide case studies to demonstrate the implication of roughness effect and the possible uncertainties involved in the dynamic force measurement. We found that in the lubrication regime, the hydrodynamic resistance is dominated by the local behavior near the asperity, thus the apparent slip length can not always represent the surface roughness.