Knudsen Maximum Effect in Micro-Scale Gas Lubrication

Micro-scale gas lubrication has been studied for several decades, with extensive research on non-equilibrium flow effects like velocity slip and thermal creep. However, the Knudsen maximum effect in micro-scale gas lubrication has not been reported yet. To address this, we analyzed the load capacity characteristics of slider bearings with ultra-thin film gas lubrication equations derived from the linearized Boltzmann-Bathnagar-Gross-Krook model equation (Fukui-Kaneko lubrication model) under the condition of constant bearing number. Our study reveals that there exists a maximum value of load capacity for slider bearings when the reference Knudsen number is about unity. This happens because the dimensionless mass flowrate of micro-scale gas flows has a minimum value when the reference Knudsen number approaches unity. Understanding the Knudsen maximum effect is crucial when designing micro-nano devices related to gas lubrication, as it implies that there exists an optimum clearance for maximum load capacity.