Boundary layer analysis of wall slip

We consider steady, plane, Poiseuille flow in a channel with wall slip for Newtonian and Maxwell fluids. Wall slip velocity is taken as a nonlinear function of shear stress. A viscoelastic boundary layer is introduced of thickness δ adjacent to a Maxwell fluid with a nonzero slip velocity between the two fluids. Fundamental qualitative conclusions are reached, based on the boundary conditions. Boundary layer equations for a Maxwell fluid are formulated using dimensional analysis, with a similar length scale δ as in the Newtonian boundary layer equations. The boundary layer equations derived in the present paper are consistent with those for the Newtonian fluid, except with different scaled magnitudes for the pressure and shear stress. A boundary condition is formulated for the nondimensional variable y*, which is finite. Several qualitative conclusions are reached by considering simple parabolic flow: for example, it may be conjectured that instability in numerical solutions of Maxwell's equations for plane, steady, viscoelastic flow is caused by the existence of a viscoelastic boundary layer.