Slip-controlled crossover in pressure-driven viscoelastic channel flow

Pressure-driven flows of viscoelastic fluids frequently exhibit wall slip, yet the combined influence of slip and elastic stress generation on macroscopic transport remains poorly understood. In this work, we investigate fully developed creeping flow of polymer solutions in a planar channel with explicit wall slip, focusing on how slip interacts with bulk viscoelasticity across different constitutive models. We consider Oldroyd-B and three finitely extensible nonlinear elastic (FENE) models, including the FENE-P model, its conformation-dependent-drag variant (FENE-P-CD), and the Phan-Thien–Manero–Leal variant (FENE-PTML); and impose a Navier-type slip law in which the slip velocity is proportional to the total wall shear stress. By introducing slip-corrected and uncorrected excess flow rate measures, we separate boundary contributions from bulk elastic effects. The slip-corrected flow rate collapses onto model-specific master curves independent of slip strength, recovering known asymptotic scalings, while the uncorrected flow rate exhibits pronounced non-monotonic behavior. This behavior is characterized by a slip-controlled crossover Deborah number, marking a transition between elasticity-dominated and boundary-dominated transport. The location and scaling of this crossover depend sensitively on the constitutive model and slip strength, revealing qualitative differences between FENE-type models that are absent in no-slip theories. These results demonstrate that wall slip does not merely offset classical viscoelastic flow rate predictions but introduces new transport regimes governed by the competition between bulk elastic resistance and boundary slip.