  A convenient approach to derive simple expressions for properties of Stokes
flows with low levels of slip is presented. The method is based on a series
expansion of a Stokes-flow solution (one satisfying a Navier slip boundary
condition) 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 the
same problem. The analysis is directly applicable to microscale rarefied gas
flows in the so-called `slip regime' and relevant to a range of liquid flows at
the microscale and nanoscale. A number of application examples are considered,
with expressions derived for: the drag and torque on translating and rotating
Janus particles and spheroids (prolate and oblate); 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. Where appropriate, accurate numerical calculations provide
verification of the derived expressions. 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; any
perimetric distribution of positive slip length will reduce the pressure loss
through a straight channel flow of arbitrary cross-section; unlike in no-slip
flows, the rate of work done by a bounding solid surface on the fluid is not
balanced by dissipation in the fluid volume -- there is additional dissipation
at the fluid-solid interface.
