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 liquid-gas 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 micro-pillars arrays.