Stability Analysis of Cassie-baxter State under Pressure Driven Flow

The Cassie-Baxter state is a phenomenon in which a liquid rests on top of a textured surface with a gas layer trapped underneath the liquid layer. This gas layer introduces an effective shear free boundary that induces slip at the liquid-gas interface, allowing for friction reduction in liquid channel flows. Multiple studies have shown that different surface configurations result in different friction reduction characteristics, and most work is aimed at controlling the roughness factor and its shape in order to achieve an increased slip flow. This paper investigates the effects that different texturing geometries have on the stability of the Cassie state under pressurized microchannel flow conditions. To test the stability effects associated with the pressurized microchannel flow conditions, microfluidic channels with microstructures on the side walls were designed and fabricated. The microstructures were designed to induce the Cassie state with a liquid-air interface forming between the texturing trenches. The air trapped within the microstructure is treated as an ideal gas, with the compressibility induced pressure rise acting as a restrictive force against the Wenzel wetting transition. The model was validated against experimental flow data obtained using microchannel samples with microtextured boundaries. The microchannels were fabricated in PDMS (poly-dimethylsiloxane) using soft lithography and were baked on a hot plate to ensure the hydrophobicity of the microtexture. Pressure versus flow rate data was obtained using a constant gravitational pressure head setup and a flow meter. The liquidgas interface layer in the microchannel was visualized using bright field microscopy that allowed measurement of the liquid penetration depth into the microtexturing throughout the microhannel. The experimental results indicate that air trapped in the pockets created by micro-cavity structures prevented the liquid layer from completely filling the void. As expected, the pressure drop in the micro-cavity textured channel showed a considerable decrease compared to that in the flat surfaced channel. These results also suggest that micro-cavities can maintain the Cassie state of a liquid meniscus, resting on top of the surface, in larger pressure ranges than open spaced micropillars arrays. INTRODUCTION Superhydrophobicity has recently received attention as a means of achieving surface friction and drag reduction [1]. Other applications include frost prevention on aircraft flight surfaces to self-cleaning features on solar energy panels [2]. Superhydrophobicity can be achieved by modifying the surface geometry. Two models represent the wetting behavior of the textured surface: the Wenzel state [3] and the CassieBaxter state [4]. The Wenzel state models the amplifying effect that surface texturing has on the Young’s contact angle under fully liquid imbibed conditions. The Cassie-Baxter state models the macroscopic contact angle formed when air pockets exist within the microtexturing. The presence of these air pockets in the Cassie state can lead to friction and drag reduction [5], with research is this area being actively pursued. Such research includes modeling the fluid flow over random textured surfaces [6], studying the drag reduction of flow over carbon nano-tube forests [7], and the use of chemical coatings in microtextured surfaces to induce superhydrophobic conditions [8], among others. Despite the vast literature on friction and drag reduction from superhydrophobic surfaces there is very little work aimed at understanding the, pressure effects on the stability and characteristics of this condition. A few researchers have studied the pressure effects on the Cassie-Baxter State, concluding that textured surfaces with isolated gaps result in a lower contact Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels, and Minichannels FEDSM-ICNMM2010 August 1-5, 2010, Montreal, Canada