This poster presents the results of a numerical study of the two dimensional motion of a liquid droplet spreading by gravity over a hydrophobic microtextured surface. The surface topology consists of a periodic array of elevations in the form of rectangles or hemispheres. Spreading of aqueous drops on these surfaces has received significant attention since the droplet can move over the valleys separating the elevations by riding on air confined in the valleys. Such flows – Cassie-Wenzel wetting - are at very large contact angles relative to the plane of the surface (superhydrophobicity) and reduced friction (minimal contact angle hysteresis). The movement of the fluid at the advancing contact line is modeled by using a slip coefficient to remove the contact line singularity, and a relationship between the contact angle and the velocity of spreading to account for contact angle hysteresis. Fluid movement is analyzed in the limit of zero inertia (Stokes flow) and the boundary integral method is used to obtain numerical solutions for the motion.

For a fixed surface geometry, numerical solutions determine the critical value of the droplet wetting on the surface (or equivalently the minimum advancing contact angle) so that the droplet liquid moves within the grooves of the microtexture in a (Wenzel) wetting regime. For values of the contact angle larger than the critical value, Cassie-Baxter wetting is observed and the droplet moves over a layer of gas trapped within the grooves.

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