  We investigate the laminar flow of two-fluid mixtures inside a simple network
of inter-connected tubes. The fluid system is comprised of two miscible
Newtonian fluids of different viscosity which do not mix and remain as nearly
distinct phases. Downstream of a diverging network junction the two fluids do
not necessarily split in equal fraction and thus heterogeneity is introduced
into network. We find that in the simplest network, a single loop with one
inlet and one outlet, under steady inlet conditions the flow rates and
distribution of the two fluids within the network loop can undergo persistent
spontaneous oscillations. We develop a simple model which highlights the basic
mechanism of the instability and we demonstrate that the model can predict the
region of parameter space where oscillations exist. The model predictions are
in good agreement with experimental observations.
