Time–Weissenberg number superposition in planar contraction microchannel flows

• We found a simple principle of time–Wi superposition in contraction flow.
• Early phase of transient flow at high Wi was the same as the steady flows at low Wi.
• When corner vortex appeared, the slope of time–Wi superposition graph changed.

The flow of viscoelastic fluids in a micro-fabricated 4:1 planar contraction channel was studied through flow visualization. As the Weissenberg number (Wi) increased, the flow developed from a Newtonian-like to vortex growth, and the transient start-up flow at high Wi was found to experience all the steady patterns at lower Wi flows. The flow sequence was different depending on the fluids and channel dimensions, however, in all the cases we could reach, the steady patterns at a low Wi flow could be matched 1:1 with the transient patterns at a high Wi flow. The plot of Wi and time when the two sets (transient and steady) were matched showed a clear functional relationship, from which the time–Weissenberg number superposition could be confirmed.