Person:

Srinivasan, Siddarth

Skin friction drag contributes a major portion of the total drag for small and large water vehicles at high Reynolds number (Re). One emerging approach to reducing drag is to use superhydrophobic surfaces to promote slip boundary conditions. However, the air layer or “plastron” trapped on submerged superhydrophobic surfaces often diminishes quickly under hydrostatic pressure and/or turbulent pressure fluctuations. We use active heating on a superhydrophobic surface to establish a stable vapor layer or “Leidenfrost” state at a relatively low superheat temperature. The continuous film of water vapor lubricates the interface, and the resulting slip boundary condition leads to skin friction drag reduction on the inner rotor of a custom Taylor-Couette apparatus. We find that skin friction can be reduced by 80 to 90% relative to an unheated superhydrophobic surface for Re in the range 26,100 ≤ Re ≤ 52,000. We derive a boundary layer and slip theory to describe the hydrodynamics in the system and show that the plastron thickness is h = 44 ± 11 μm, in agreement with expectations for a Leidenfrost surface.

Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed nonuniform temperature field. We first determine the associated base flow by solving the long-time-scale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity α and a dimensionless width of the heating zone β. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show that the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing β, while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching while simultaneously minimizing or suppressing the out-of-plane buckling, a result that is relevant for the glass redraw method used to create ultrathin glass sheets.