Two-layer channel flow involving a fluid with time-dependent viscosity

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