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

Abstract

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.

Influence of thermal diffusion and shear thinning during the leveling of nanoimprinted patterns in a polystyrene thin film

“…This observation is in good agreement with the rule of [22] on the generalized shear rate, which estimates the critical amplitude (below which shear-thinning is not expected) A c = 0.046 η sγs w 2 /σ ≈ 4 nm with our material and pattern, where w denotes the wavelength of the pattern. As our initial amplitude (63 nm) is higher than A c , shear-thinning has to be considered.…”

“…This assumption is relevant if the amplitude remains small enough compared to the thickness of the film and the wavelength of the sinusoidal profile. Quantitative rules have been established by Gilormini and Teyssèdre [22] who also demonstrated that, as the amplitude is reduced during the leveling, their rules are fulfilled after a certain time. As τ is a parameter of equation (6) that can be deduced from experiments and that helped [17,18,21,20] to derive the physical properties of the materials, we focus on the quantity…”

“…Section 3 introduces the leveling process and the experimental results demonstrating that improved models have to be considered to well describe the polymer reflow. Section 4 extends the code already used in a previous publication [22] to non isothermal flows and shows the impact of thermal diffusion and shearthinning on the leveling process for a Newtonian behavior. The additional effect of shear-thinning is developed in section 5 where the relevance of the leveling method and the material parameters derivation are also discussed.…”

“…This model is usually built with simplifying assumptions to be able to compute an analytic solution, but this brings restrictions to the measurements range inevitably. These limitations have been investigated numerically by Gilormini and Teyssèdre [22] for Newtonian viscous behaviors with the assumption of a uniform temperature within the film. The viscous behavior and isothermal hypotheses are examined in this paper on a periodic square wave profile with a wavelength of 2 µm and an initial height of 126 nm.…”

Leveling of Polymer Grating Structures upon Heating: Dimension Dependence on the Nanoscale and the Effect of Antiplasticizers

“…Other theoretical studies provided an understanding of how key properties for design and control, such as viscosity or slip length, change in thin polymer films. − A common practice is to measure the polymer relaxation time and seek for a correlation with those properties. From the solid mechanics perspective, Yu et al implemented a capillarity-driven surface flattening of a solid to calculate the physicochemical properties of organic glasses , using Mullins’ analytical model .…”