Viscoelastic flow with slip in a hyperbolic channel

Abstract

We study theoretically the steady viscoelastic flow in confined and symmetric hyperbolic channels considering slip along the walls. Under the lubrication approximation and a variety of constitutive models, a high-order perturbation solution with respect to the Deborah number is calculated. The solution for all the field variables (velocity, pressure, and extra-stress) is found analytically up to eighth order and is used along with proper acceleration techniques to achieve convergence up to order one Deborah number. We reveal that even in the presence of slip, the pressure drop decreases monotonically with increasing the fluid elasticity. We evaluate the influence of slip in terms arising from two different decompositions of the pressure drop obtained with the aid of the total force balance and the mechanical energy balance of the flow system. In contrast to the nonslip Newtonian flow, our analysis also showed that the fluid slip along the walls introduces variations in the strain rate at the midplane with the distance from the inlet. However, these are small, and an effective strain rate can be well-represented using a previously developed formula [Housiadas, K. D., and A. N. Beris, Phys. Fluids 36(2), 021702 (2024)]. We also show that when the solution for the midplane velocity is used in the general formula for the Trouton ratio, instead of the Newtonian lubrication solution, there are no appreciable changes, thus confirming the validity and accuracy of our previously reported results [Housiadas, K. D., and A. N. Beris, J. Rheol. 68(3), 327–339 (2024)].