Linking Flow-Derived Local Slip Lengths to Force-Derived Effective Slip Lengths in Nanogaps

A quantitative understanding of interfacial slip is important for determining boundary conditions and evaluating fluid-flow characteristics in nanogaps relevant to fluidic devices and precision micromechanical systems. Interfacial slip has been conventionally evaluated in terms of the slip length derived from squeeze-force measurements, in which the hydrodynamic force generated within the narrowing gap between solid surfaces is compared with a hydrodynamic model assuming a spatially constant slip length. However, the slip length may depend on local flow conditions and may vary spatially within nanogaps. The relationship between such spatially distributed local slip lengths and the force-derived constant slip lengths remains unclear. In this study, we independently measured the squeeze flow and squeeze force within a nanogap formed between two solid substrates in the same experimental system and compared the constant slip length to the spatially distributed local slip lengths. Flow measurements revealed that the local slip length was not constant but depended on the local shear rate at the interface. It was zero at low shear rates, increased linearly in the transition regime, and reached a constant value at high shear rates. Consequently, the slip length varied spatially, depending on the gap height and lateral position. The measured squeeze force was successfully reproduced by calculations incorporating the spatial distribution of the local slip lengths, demonstrating that the macroscopic force response is governed by this localized variation. The force-derived constant slip length was neither the simple average nor the maximum value of the local slip lengths but rather a pressure-weighted effective quantity that reflects the local slip state in high-pressure regions. These findings clarify the physical meaning of the constant slip length obtained from conventional squeeze-force measurements, provide a framework for interpreting slip-length measurements, and demonstrate the importance of quantifying the local slip length to capture actual slip behavior in nanogap flows.