Exploring plastron stability and fluid friction reduction on robust micro-textured non-wetting surfaces

Abstract

Non-wetting surfaces are characterized by the presence of stable pockets of vapor trapped within the asperities of the surface morphology. The utility of these surfaces in reducing skin friction in viscous laminar and turbulent flows is experimentally and theoretically investigated and is the main focus of this thesis. The development of a surface coating that reduces fluid drag can potentially lead to a number of practical applications such as fuel savings in marine vehicles and energy savings in pipe flows. First, a single-step, scalable spray coating technique to fabricate liquid-repellent micro-textured surfaces by depositing a blend of poly(methyl methacrylate) (PMMA) and the low surface energy molecule 1H,1H,2H,2H-heptadecafluorodecyl polyhedral oligomeric silsesquioxane (fluorodecyl POSS, [gamma]sv ~~ 10 mN/m) is presented. The surface morphology of the polymer coating was studied systematically and can be varied from a corpuscular or spherical microstructure to a beads-on-string structure and finally to bundled fibers by controlling the solution concentration c and molecular weight M of the sprayed polymer solution. A scaling law is proposed that relates the minimum necessary concentration of a polymer required to produce fibers cspf to its molecular weight M and the quality of the solvent (through the excluded volume exponent v) of the form cspi ~ M-(v+l). These POSS/PMMA coatings are shown to exhibit both superhydrophobic and superoleophobic properties due to the presence of a film of trapped air (or 'plastron') within the surface microtextures upon contact with a liquid. A combination of texture and surface chemistry is also important in the design of various biomimetic interfaces. Many species of aquatic birds dive tens of meters into water to prey on fish while entraining a 'plastron film' within the complex microstructures of their feathers, which is often thought to confer water repellency to the bird. By combining electron microscopy with contact angle measurements on specially dip-coated feathers, it is demonstrated that in fact the bird feathers are expected to be fully wetted in a typical deep dive. However, surface energy calculations and a stability analysis reveals that, depending on the geometric spacing of the barbules and hydrophobicity of the natural waxy coating, these feathers will spontaneously de-wet once the bird emerges out of water. Conversely, oils and low surface tension liquids wet the feather microstructure irreversibly. The results of this analysis can be used to design thermodynamically 'robust' coatings and fabrics that can spontaneously de-wet and recover their non-wetting properties. The vapor layer entrapped adjacent to the solid wall by the superhydrophobic coating serves to lubricate fluid flow and can potentially reduce skin friction drag. At small Reynolds numbers Re << 1, the effective Navier slip length is evaluated using torque measurements in a parallel plate rheometer resulting in a measured Navier slip length in laminar flow of b ~~ 39 [mu]m, comparable to the mean periodicity of the microstructure evaluated from confocal fluorescence microscopy. To investigate the behavior in turbulent flows (at Re >/- 10⁴), a wide gap Taylor-Couette (TC) cell was constructed. A series of global torque measurements with a spray-coated superhydrophobic inner rotor is used to establish a friction reduction varying from 6% at Re ~ 2 x 10⁴ to a maximum of 22% at Re ~ 8 x 10⁴. By applying a boundary layer theory, a modified Prandtl-von Karman type relationship of the form (Cf /2)-¹/² = Mln Re(Cf /2)¹/² + N + (b/[delta]r)Re(Cf /2)¹/² is derived, from which we extract an effective slip length of b ~ 19 m. In this manner, the presence of a finite microscopic slip length is shown to dramatically affect the bulk skin friction reduction. This result also highlights the remarkable steady enhancement in the drag reduction with increasing Re. By coupling the effective Navier slip length b (i.e., a material property characteristic of the textured surface chemistry and physics) to the hydrodynamic viscous length scale [delta]v = v/u[tau] in near-wall turbulent flows, it is established that it is the dimensionless slip length b+ = b/[delta]v which is the key parameter governing the drag reduction; we find that b+ ~ Re¹/² in the limit of high Reynolds number. The results of the experimental analysis, in combination with the theoretical framework that is developed, allows for the rational design of micro-structured surface coatings that can be applied to reduce macroscopic skin friction drag in turbulent flows.