This study develops a weighted-residual model for Oldroyd-B films on slippery substrates at moderate Reynolds number and large slippery length. Linear stability analysis reveals that wall slip promotes perturbation growth rates, increases cut-off wave numbers, and accelerates long-wave propagation speed, demonstrating a destabilizing effect. Two distinct families of traveling waves are sought, which demonstrate that varying the slippery length can alter the bifurcation type of traveling wave families. Particularly, large slippery length can cause the transition of drag-gravity regime into the drag-inertia regime. In the drag-gravity regime, slippery effect promotes the wave speed and height. However, in the drag-inertia regime, slippery effect can suppress the wave height even though the wave propagates faster. Interestingly, plateau-type waves are found in the Oldroyd-B film flow at large slippery length, which has not been reported previously.

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• Bifurcations
• Instability of free-surface flows
• Low-dimensional models
• Flow instability
• Non-Newtonian fluids