First-order analysis of slip flow for micro and nanoscale applications

An existing approach for deriving analytical expressions for slip-flow properties of Stokes flow is generalised and applied to a range of micro and nanoscale applications. The technique, which exploits the reciprocal theorem, can generate first-order predictions of the impact of Navier or Maxwell slip boundary conditions on surface moments of the traction force (e.g. on drag and torque). This article brings dedicated focus to the technique, generalises it to predict first-order slip effects on arbitrary moments of the surface traction, numerically verifies the technique on a number of cases and applies the method to a range of micro and nano-scale applications. Applications include predicting: the drag on translating spheres with varying slip length; the efficiency of a micro journal bearing; the speed of a self-propelled particle (a 'squirmer'); and the pressure drop required to drive flow through long, straight micro/nano channels. Certain general results are also obtained. For example, for low-slip Stokes flow: any surface distribution of positive slip length will reduce the drag on any translating particle; and any perimetric distribution of positive slip length will reduce the pressure loss through a straight channel flow of arbitrary cross-section.