  A homogenised model is developed to describe the interaction between aligned
strings and an incompressible, viscous, Newtonian fluid. In the case of many
strings, the ratio of string separation to domain width gives a small parameter
which can be exploited to simplify the problem. Model derivation using
multiscale asymptotics results in a modified Darcy law for fluid flow, with
coefficients determined by averaged solutions to microscale problems. Fluid
flow is coupled to solid deformation via a homogenised force balance obtained
by coarse-graining the balance on each string. This approach offers an
alternative method to systematically derive the equations governing the
interaction of Stokes flow with many flexible structures. The resulting model
of fluid-structure interaction is reduced to a single scalar, linear, partial
differential equation by introducing a potential for the pressure. Analytical
solutions are presented for a cylindrical geometry subject to time harmonic
motion of the string ends. Scaling laws are identified that describe the
variation of shear stress exerted on the string surface with the forcing
frequency.
