Wall slip of complex fluids: Interfacial friction versus slip length

If the slip length is an useful notion notion to describe the friction of simple fluids, we will show that the slip length is not appropriate for viscoelastic liquids. Rather, the appropriate description lies in the original Navier's partial slip boundary condition, formulated in terms of an interfacial friction coefficient. We establish an exact analytical expression to extract the interfacial friction coefficient from oscillatory drainage forces between a sphere and a plane, suitable for dynamic SFA or atomic force microscopy noncontact measurements. We use this model to investigate the boundary friction of viscoelastic polymer solutions over 5 decades of film thicknesses and 1 decade in frequency. The proper use of the original Navier's condition describes accurately the complex hydrodynamic force up to scales of tens of micrometers, with a simple Newtonian-like friction coefficient that is not frequency dependent and does reflect closely the dynamics of an interfacial depletion layer at the solution-solid interface.

REF: Cross, B., Barraud, C., Picard, C., Léger, L., Restagno, F., & Charlaix, É. (2018). Wall slip of complex fluids: Interfacial friction versus slip length. Physical Review Fluids, 3(6), 062001.