  We study the flow of a generalized Newtonian fluid, characterized by a
power-law model, through a channel consisting of a wall with a flexible
membrane under longitudinal tension. It is assumed that at steady state the
flow through the channel admits a constant flux unidirectional flow profile,
while for the unsteady case, we employ the long wave approximation and use a
set of reduced equations to describe the variation of the shape of the membrane
(assumed to be massless and elastic) and the variation of the fluid-flux. By
means of asymptotic expansion, multiscale analysis and full numerical solutions
of the pertinent governing equations, we show that depending upon the Reynolds
number and the membrane stress, the flow behaviour for a shear-thinning,
shear-thickening and Newtonian fluid may be markedly different, being
oscillatory for one while chaotic for the other. The results presented herein
hold practical relevance for several biologically relevant processes involving
transport of rheologically complex biofluids through flexible domains.
