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

Pierre Gilormini (1) , Hubert Teyssèdre (2, 1)

1 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux
2 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information

Measuring the relaxation time involved in the leveling of the free surface of a Newtonian fluid laid on a substrate can give access to material parameters. It is shown here how most favorable 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, special emphasis is put on the conditions required to avoid shear-thinning by controling 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 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.

Mots clés: polymers; leveling; viscosity; Navier slip; slip length

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Pierre Gilormini, Hubert Teyssèdre. On using the leveling of the free surface of a Newtonian fluid to measure viscosity and Navier slip length. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013, 469 (2160), pp.6-24. ⟨10.1098/rspa.2013.0457⟩. ⟨hal-00872587⟩