Wall slip of complex fluids: interfacial friction or slip length?

TL;DR

This paper demonstrates that for viscoelastic fluids, boundary flow is better described by Navier's partial slip condition with an interfacial friction coefficient rather than slip length, providing a new analytical approach for experimental measurements.

Contribution

It introduces an exact analytical expression to extract interfacial friction coefficients from oscillatory drainage forces, improving understanding of boundary conditions for complex fluids.

Findings

Navier's partial slip condition accurately describes boundary flow of viscoelastic fluids.

Interfacial friction coefficient is frequency-independent and reflects interfacial depletion layers.

Model applies over a wide range of film thicknesses and frequencies.

Abstract

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 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 non-contact measurements. We use this model to investigate the boundary friction of viscoelastic polymer solutions over 5 decades of film thicknesses and one 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, not frequency dependent, and reflecting closely the dynamics of an interfacial depletion layer at the solution/solid interface.