Analytical solutions for channel flows of Phan-Thien–Tanner and Giesekus fluids under slip

Abstract

Analytical and semi-analytical solutions are presented for the cases of channel and pipe flows with wall slip for viscoelastic fluids described by the simplified PTT (using both the exponential and the linearized kernel) and the Giesekus models. The slip laws used are the linear and nonlinear Navier, the Hatzikiriakos and the asymptotic models. For the nonlinear Navier slip only natural numbers can be used for the exponent of the tangent stress in order to obtain analytical solutions. For other values of the exponent and other nonlinear laws a numerical scheme is required, and thus, the solution is semi-analytical. For these cases the intervals containing the solution and the corresponding proof for the existence and uniqueness are also presented. For the Giesekus model the influence of the wall slip on the restrictions of the slip models is also investigated.