Start-up and cessation Newtonian Poiseuille and Couette flows with dynamic wall slip

Abstract

Analytical solutions are derived for the start-up and cessation Newtonian Poiseuille and Couette flows with wall slip obeying a dynamic slip model. This slip equation allows for a relaxation time in the development of wall slip by means of a time-dependent term which forces the eigenvalue parameter to appear in the boundary conditions. The resulting spatial problem corresponds to a Sturm–Liouville problem different from that obtained using the static Navier slip condition. The orthogonality condition of the associated eigenfunctions is derived and the solutions are provided for the axisymmetric and planar Poiseuille flows and for the circular Couette flow. The effect of dynamic slip on the flow development is then discussed.