Wall slip of complex fluids: Interfacial friction versus slip length

Using a dynamic Surface Force Apparatus, we demonstrate that the notion of slip length used to describe the boundary flow of simple liquids, is not appropriate for visco-elastic liquids. Rather, the appropriate description lies in the original Navier's partial slip boundary condition, formulated in terms of an interfacial friction coefficient. We have investigated thin films of visco-elastic polymer solutions over 5 decades of thickness and one decade in frequency. The proper use of this original Navier's condition describes accurately the complex hydrodynamic force up to scales of tens of micrometers, with a simple "Newtonian-like" friction coefficient, not frequency dependent, and closely related to the existence of viscosity gradient at the solid/solution interface.