François Feuillebois

Effective slip over superhydrophobic surfaces in thin channels.

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a microscopic texture. Recent work has focused on specific cases, such as arrays of pillars or grooves, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g., low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. Tighter bounds for isotropic textures further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.

Dynamic effects on force measurements. I. Viscous drag on the atomic force microscope cantilever

When the atomic force microscope (AFM) is used for force measurements, the driving speed typically does not exceed a few microns per second. However, it is possible to perform the AFM force experiment at much higher speed. In this article, theoretical calculations and experimental measurements are used to show that in such a dynamic regime the AFM cantilever can be significantly deflected due to viscous drag force. This suggests that in general the force balance used in a surface force apparatus does not apply to the dynamic force measurements with an AFM. We develop a number of models that can be used to estimate the deflection caused by viscous drag on a cantilever in various experimental situations. As a result, the conditions when this effect can be minimized or even suppressed are specified. This opens up a number of new possibilities to apply the standard AFM technique for studying dynamic phenomena in a thin gap.

Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation.

We report the results of direct measurements of velocity profiles in a microchannel with hydrophobic and hydrophilic walls, using a new high-precision method of double-focus spatial fluorescence cross correlation under a confocal microscope. In the vicinity of both walls the measured velocity profiles do not go to zero by supplying a plateau of constant velocity. This apparent slip is proven to be due to a Taylor dispersion, an augmentation by shear diffusion of nanotracers in the direction of flow. Comparing the velocity profiles near the hydrophobic and hydrophilic walls for various conditions shows that there is a true slip length due to hydrophobicity. This length, of the order of several tens of nanometers, is independent of the electrolyte concentration and shear rate.