  The low-Reynolds-number Stokes flow driven by rotation of two parallel
cylinders of equal unit radius is investigated by both analytical and numerical
techniques. In Part I, the case of counter-rotating cylinders is considered. A
numerical (finite-element) solution is obtained by enclosing the system in an
outer cylinder of radius $R_{0}\!\gg\!1$, on which the no-slip condition is
imposed. A model problem with the same symmetries is first solved exactly, and
the limit of validity of the Stokes approximation is determined; this model has
some relevance for ciliary propulsion. For the two-cylinder problem, attention
is focused on the small-gap situation $\varepsilon \ll 1$. An exact analytic
solution is obtained in the contact limit $\varepsilon=0$, and a net force
$F_{c}$ acting on the pair of cylinders in this contact limit is identified;
this contributes to the torque that each cylinder experiences about its axis.
The far-field torque doublet (`torquelet') is also identified.
  Part II treats the case of co-rotating cylinders, for which again a
finite-element numerical solution is obtained for $R_{0}\!\gg \!1$. The theory
of Watson (1995) is elucidated and shown to agree well with the numerical
solution. In contrast to the counter-rotating case, inertia effects are
negligible throughout the fluid domain, however large, provided Re $\ll 1$.
  In the concluding section, the main results for both cases are summarised,
and the situation when the fluid is unbounded ($R_{0}=\infty$) is discussed.
(...)
