On using the levelling of the free surface of a Newtonian fluid to measure viscosity and Navier slip length

Measuring the relaxation time involved in the levelling of a free surface of a Newtonian fluid laid on a substrate can give access to material parameters. It is shown here how most favourable pattern geometries of the free surface and film thicknesses can be defined for the measures of viscosity and Navier slip length at the fluid-solid interface, respectively. Moreover, we put special emphasis on the conditions required to avoid shear thinning by controlling the maximum shear rate. For initially sinusoidal patterns with infinitesimal amplitudes, an analytical solution including slip at the fluid-solid interface is used, and numerical simulations based on the natural element method allow one to discuss the effect of finite amplitudes. This leads to the definition of a relevance domain for the analytical solution that avoids the need for numerical simulations in practical applications. It is also shown how these results can be applied to crenelated profiles, where Fourier series expansion can be used, but with caution.