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A convenient approach to derive simple expressions for properties of Stokesflows with low levels of slip is presented. The method is based on a seriesexpansion of a Stokes-flow solution (one satisfying a Navier slip boundarycondition) with non-dimensional slip length as the small expansion parameter.Most notably, first-order predictions of surface moments of the traction force(e.g., drag and torque) can be obtained purely from no-slip solutions to thesame problem. The analysis is directly applicable to microscale rarefied gasflows in the so-called `slip regime' and relevant to a range of liquid flows atthe microscale and nanoscale. A number of application examples are considered,with expressions derived for: the drag and torque on translating and rotatingJanus particles and spheroids (prolate and oblate); the efficiency of a microjournal bearing; the speed of a self-propelled particle (a `squirmer'); and thepressure drop required to drive flow through long, straight micro/nanochannels. Where appropriate, accurate numerical calculations provideverification of the derived expressions. Certain general results are alsoobtained. For example, for low-slip Stokes flow: any surface distribution ofpositive slip length will reduce the drag on any translating particle; anyperimetric distribution of positive slip length will reduce the pressure lossthrough a straight channel flow of arbitrary cross-section; unlike in no-slipflows, the rate of work done by a bounding solid surface on the fluid is notbalanced by dissipation in the fluid volume -- there is additional dissipationat the fluid-solid interface.

First-order analysis of slip flow at the microscale and nanoscale