  We investigate the dynamics of pressure driven transient flows of
incompressible Newtonian fluids through circular microtubes having thin elastic
walls under the long-wavelength and small deformation assumptions, which are
valid for many industrial and biological processes. An analytical solution of
the coupled fluid and solid equations is found using Navier slip boundary
conditions and is shown to include some existing Womersley solutions as
limiting cases. The effect of the slip length at the fluid-solid interface is
analyzed for oscillatory pressure gradients using a range of slip ratio and
frequency parameters. The solutions for elastic and rigid walls are compared
for the cases with and without slip boundary conditions for a broad range of
the relevant parameters. It is shown that the elastic behavior of the microtube
couples nonlinearly with the slip velocity, which greatly enhances the
achievable flow rate and pumping efficacy compared to the inelastic case. In
addition, it is observed that increasing the slip length produces less shear
stress, which is consistent with the nearly frictionless interfaces observed in
many microscale experiments.
