Three-Dimensional Numerical Simulations of Liquid Laminar Flow over Superhydrophobic Surfaces with Post Geometries

Three-Dimensional Numerical Simulations of Liquid Laminar Flow over Superhydrophobic Surfaces with Post Geometries Abolfazl Amin Department of Mechanical Engineering, BYU Doctor of Philosophy Frictional resistance reduction of liquid flow over surfaces has recently become a more important topic of research in the field of fluid dynamics. Scientific and technological progress and continued interest in nano and micro-technology have required new developments and approaches related to reducing frictional resistance, especially in liquid flow through nano and micro-channels. The application of superhydrophobic surfaces could be very effective in achieving the desired flow through such small channels. Superhydrophobic surfaces are created by intentionally creating roughnesses on the surface and applying a uniform hydrophobic coating to the entire surface. Liquid droplet tests have revealed that because of the trapped air within the cavities such surfaces could have contact angles as high as 179o. Such a property gives superhydrophobic surfaces liquid repelling characteristics making them very suitable for frictional resistance reduction in liquid flow through nano or micro-channels, provided wetting of the cavities could be avoided. This study presents 3-D numerical simulation results of liquid laminar flow over post patterned superhydrophobic surfaces. The research was performed in three phases, 1) pressure-driven flow with square micro-posts, 2) Couette flow with square micro-posts, and 3) pressure-driven flow with rectangular micro-posts at various aspect ratios. In phases (1) and (2) the influences of important parameters such as the cavity fraction, in the range of 0.0-0.9998, and the relative module width, from 0.01 to 1.5, on frictional resistance reduction in the creeping flow regime were explored. Phase (1) also addressed the effect of varying Reynolds number from 1 to 2500 on frictional resistance. Phase (3) was conducted for aspect ratios of 1/8, 1/4, 1/2, 2, 4, and 8 also in the creeping flow regime. The obtained results suggest that important parameters such as cavity fraction (relative area of the cavities), relative module width (combined post and cavity width relative to the channel hydraulic diameter), and the Reynolds number have great influence on the frictional resistance reduction. For pressure-driven flow at cavity fraction 0.9998, reductions as high as 97% in the frictional resistance were predicted compared with the classical channel flow. This reduction is directly related to the significant reduction in liquid-solid contact area. With respect to the effect of relative module width on the overall frictional resistance, a reduction of 93% in the frictional resistance was observed as the relative module width was increased from 0.1 to 1.5. This is indicative of the importance of the relative spacing size of the posts/cavities compared to the channel size in micro-channel liquid flow. The overall frictional resistance for post-patterned superhydrophobic surfaces was found to be independent of the Reynolds number up to a value of nominally 40 after which the non-dimensional frictional resistance increased at high values of the Reynolds number. However, at very high cavity fractions the frictional resistance was independent of Reynolds number only up to about 4. When the driving mechanism was a Couette flow, similar to the pressure-driven flow, as the cavity fraction and the relative module width increased the frictional resistance on the superhydrophobic surface decreased. At a cavity fraction of 0.9998 the reduction in the nondimensional frictional resistance was approximately 96%, which was only 1% different from the similar pressure-driven scenario. However, a more significant difference was observed between the slip velocities for the two flow types, and it was determined that the pressure-driven flow resulted in greater apparent slip velocities than Couette flow. A maximum difference in normalized slip between the two scenarios of approximately 20% was obtained at relative module width 0.1 and Reynolds number 1. Results for superhydrophobic surfaces with rectangular micro-posts approached those reported in the literature for micro-ribs as the aspect ratio of the posts increased. When the flow was perpendicular to the long side of the posts, and as the aspect ratio increased, the frictional resistance approached previously published transverse rib results. Similarly, when the liquid flow direction was parallel to the long side of the posts, the frictional resistance results also approached those of the previously published longitudinal ribs as the aspect ratio increased.