  A pressure-driven two-layer channel flow of a Newtonian fluid with constant
viscosity (top layer) and a fluid with a time-dependent viscosity (bottom
layer) is numerically investigated. The bottom layer goes through an aging
process in which its viscosity increases due to the formation of internal
structure, which is represented by a Coussot-type relationship. The resultant
flow dynamics is the consequence of the competition between structuration and
destructuration, as characterized by the dimensionless timescale for
structuration (tau) and the dimensionless material property (beta) of the
bottom fluid. The development of Kelvin-Helmholtz type instabilities (roll-up
structures) observed in the Newtonian constant viscosity case was found to be
suppressed as the viscosity of the bottom layer increased over time. It is
found that, for the set of parameters considered in the present study, the
bottom layer almost behaves like a Newtonian fluid with constant viscosity for
tau greater than 10 and beta greater than 1. It is also shown that decreasing
the value of the Froude number stabilizes the interfacial instabilities. The
wavelength of the interfacial wave increases as the capillary number increases.
