Surface fluctuations of liquids confined on flat and patterned solid substrates

Abstract

We report experimental measurements of the surface fluctuations of micron-thick oil films spread onto a solid substrate. We use a recently developed optical technique based on the measurement of the deflection of a laser beam triggered by changes in the local surface slope. When the liquid is spread on a flat substrate, fluctuation dynamics slow down as the thickness is decreased, in quantitative agreement with previous predictions. In addition, we investigate the consequences on surface fluctuations of the patterning of the substrate with a rectangular grating. For liquid film thicknesses smaller than the typical wavelength probed, we demonstrate that surface fluctuations are modified by the underlying pattern: The shape of the fluctuation spectra varies periodically with the spatial position over the pattern and, in addition, the fluctuations become locally anisotropic. However, the spatially averaged spectrum is isotropic.

Thermal fluctuations of a liquid film on a heterogeneous solid substrate

“…4 for the SFSR case, with parameters similar to those of Ref. [6]. The first-order contribution S (1) ωq also obeys some scaling relation at high frequencies ω → ∞, namely S (1) ωq ∼ 1/(ηω 2 ) both for direct measurement and for SFSR.…”

“…A recent attempt to measure fluctuations over a patterned substrate has been reported in Ref. [6]. In this work, the pattern was made of gratings with a rectangular section (height 100 μm, period 250 μm), and no slip is expected.…”

“…Another interesting perspective is to measure the heterogeneity of slip lengths in the presence of Cassie-Baxter states [12,13] where a layer of gas is trapped at the substrate surface by an array of pillars (or other microstructures [14]). This perspective could be achieved with SFSR since the typical liquid film depths are of the order of several microns to tens of microns [6], and typical slip lengths can be increased up to several microns [5]. Since Cassie-Baxter states also correspond to large contact angles, thin films should easily dewet the substrates, and it is an experimental challenge to keep a stable thin liquid film in contact with a substrate in the Cassie-Baxter state.…”

“…In these two cases, we find that one can extract the substrate profile or the substrate slip length variations from the measurement of the spatial variations of the time correlation function of free-surface fluctuations. Finally, we discuss recent experiments [6], and we present some possible directions for future work.…”

Boundary Condition in Liquid Thin Films Revealed through the Thermal Fluctuations of Their Free Surfaces

“…for thickness R h >> , ) , ( k P ω only depends on the liquid properties, namely viscosity η and surface tension γ for simple liquids in an overdamped regime [28]. When the film thickness h is smaller than the beam radius R , as in the experiments reported herein, the effect of confinement has to be taken into account [29][30][31].…”