Slippage of Water Past Superhydrophobic Carbon Nanotube Forests in Microchannels

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Original entry: Tony Orth, APPHY 226, Spring 2009

P. Joseph, C. Cottin-Bizonne, J.-M. Benoit, C. Ybert, C. Journet, P. Tabeling, and L. Bocquet, PRL 97 156104 (2006)

Abstract from paper

"We present in this Letter an experimental characterization of liquid flow slippage over superhydro- phobic surfaces made of carbon nanotube forests, incorporated in microchannels. We make use of a par- ticle image velocimetry technique to achieve the submicrometric resolution on the flow profile necessary for accurate measurement of the surface hydrodynamic properties. We demonstrate boundary slippage on the Cassie superhydrophobic state, associated with slip lengths of a few microns, while a vanishing slip length is found in the Wenzel state when the liquid impregnates the surface. Varying the lateral roughness scale L of our carbon nanotube forest-based superhydrophobic surfaces, we demonstrate that the slip length varies linearly with L in line with theoretical predictions for slippage on patterned surfaces. "

Capillary effects


Carbon nanotube forests were grown on a silicon substrate using PECVD. The nanotubes are about 50-100nm wide on the order of 1-10 mircrons tall. The nanotubes are functionalized with a carrier in the liquid phase, which upon evaporation, bundles the nanotubes together via capillary forces. The functionalization (with thiols) leaves the carbon nanotube surfaces themselves hydrophobic. This is caused by the meniscus curvature which creates a negative pressure between a collection of nanotubes leading them to bundle. The nanotubes are then made to form the floor of a microchannel into which water is driven.


The water passing through the microchannel and over top of the nanotube forest is seeded with fluorescent microspheres. These serve two purposes: The height of a few adsorbed particles above the substrate can be used to accurately identify the height of the nanotube forest which is important in properly quantifying the magnitude of fluid slippage at the boundary. More importantly, micro-PIV is used to track the fluorescent tracer particles in the microchannel. A velocity profile can then be built-up and fit to a parabolic (Poiseuille) flow.

When solving a steady pressure-driven flow in a rectangular channel, the no-slip boundary condition is essentially a universal assumption. When the bounding media are more exotic, however, this assumption fails and the fluid velocity at the boundary is non-zero. This is quantified by the "slip length" <math>b</math>, which is the distance past the wall one would need to go to reach a vanishing tangential velocity assuming a parabolic flow profile. In this paper the authors stress that some recent results which claim the observation of slip lengths on the order of 10 microns are somewhat questionable. Here, the author's attempt to make a precise measurement of this quantity (<math>b</math>) caused by the so-called "Fakir effect": It is thought that in the Cassie state, water flowing over the nanotube forest will not penetrate all the way down to the silicon substrate due to surface tension. As such, air will become trapped under the water which will only have minimal contact with the nanotubes themselves; the rest of the interface is water/air.

The authors observe up to a 2 micron slip length for carbon nanotube forests using micro-PIV. The slip length was found to increased linearly with nanotube height, as expected.