(469e) The Gravity Driven Motion of An Aqueous Droplet Spreading in Stokes Flow Over a Superhydrophobic Surface

?Superhydrophobic? surfaces are microtextured substrates consisting of elevations (peaks or plateaus) and depressions (valleys or cavities), with the lateral length scale of these features of the order of 1-100 microns. When the material comprising the textured surface is only partially wet by water, i.e. a smooth surface of the substrate subtends an (intrinsic) water contact angle larger than approximately 90 degrees, the microtextured surface shows two distinct behaviors as water spreads over the surface: The first is Wenzel wetting in which the three phase contact line of water moves into and out of the depressions of the topography, and an equilibrium contact angle approximately equal to that of the smooth substrate is obtained. The second is Cassie-Baxter wetting in which the three phase contact line moves over the depressions leaving air gaps behind, and the contact line comes to rest pinned at the edge of an elevation. The pinning at equilibrium creates a large contact angle (usually larger than 150 degrees) relative to the average plane of the surface. This value is usually much larger than the intrinsic angle of the substrate material, creating the appearance of a superhydropobic surface. Cassie-Baxter wetting allows for minimal contact angle hysteresis as an aqueous phase retracts or moves over the surface, and the large angles characteristic of this kind of wetting also allows droplets to easily roll over the surfaces with minimal friction. These are ideal properties for many applications such as their use as self-cleaning surfaces.

Engineering surfaces with the correct topography and intrinsic surface energies that enforce Cassie-Baxter wetting is the primary technological challenge in the development of superhydrophobic surfaces. Most research efforts have focused on static energy arguments in which the overall surface energies of the Wenzel and Cassie-Baxter wetting states are compared to discern which is favored as a function of the surface topography and intrinsic surface energy. In this presentation we will construct a more relevant picture by examining the hydrodynamics of the wetting process on the scale of the topography. Our aim is to understand how the flow interacts with the topography to determine the wetting regime. We study the two dimensional spreading due to gravity of an aqueous drop over a well defined topographical pattern consisting of a periodic array of micron-sized posts characterized by a width W, a height H and a separation distance L, with an intrinsic contact angle. The flow in the droplet is assumed to be in the Stokes flow regime of negligible fluid inertia, and a boundary integral method is used for numerical solution with slip at the contact line and a velocity dependent relation for the dynamic wetting contact angle. To construct a criteria for penetration into the gap between the posts, we assume that when the contact-line reaches the corner of a post, it remains pinned and bends over the gap until the interface either (a) touches the next post (at which point it continues to slide over the top of the post), or (b) subtends an angle with the vertical wall of the post larger than its intrinsic (static) advancing contact angle (at which point it moves into the gap). This slip-stick-jump or slip-stick-penetration movement of the three-phase contact determines the state of wetting, and we compute this state as a function of the geometric parameters of the pattern, the intrinsic wetting angle and the parameters of the contact line velocity boundary condition.