Measurement and Quantification of Effective Slip Length at Solid–Liquid Interface of Roughness-Induced Surfaces with Oleophobicity

Boundary conditions of the liquid–solid interface of micro/nano fluid flow are of great interest, as slippage is linked with decreased drag. However, previous studies have seldom included a systematic analysis of the effect of roughness on the measurement and quantification of slip length. For the measurement of slip length using atomic force microscopy (AFM), which is believed to be the most accurate method, a theoretical description of the drainage of thin liquid films between sphere and surface, with realistic roughness, is yet to be published. This study focuses on the measurement and quantification of slip length on rough surfaces immersed in liquids, based on AFM and laser confocal scanning microscopy. A reformulation of the boundary condition is presented, taking into account the effect of surface roughness. The correction to the effective slip length is analyzed, then surfaces with various degrees of spacing roughness Rsm were fabricated. Quantitative analysis of the effective slip length is presented. Results show that the corrected effective slip length remains constant with increased spacing roughness Rsm of surfaces. The results are discussed for the coagulation process of colloids and measurement of slip lengths on roughness-induced surfaces with AFM.