Computational sensitivity analysis of geometric parameters in laminar superhydrophobic microchannels

This talk presents 3-D numerical simulations of laminar flow through a microchannel of height $h$ containing superhydrophobic surfaces (SHS) along the top and bottom walls. The SHS is modelled as an array of longitudinal shear-free surfaces having width $w$ and inclination angle $\alpha$. The simulations allow for a phase offset $\ell$ between the shear-free surfaces on the top and bottom walls. The sensitivity of velocity, wall shear stress, and slip-length with respect to infinitesimal changes in the geometrical design parameters ($w$, $\alpha$, $\ell$, and $h$) was examined using the Sensitivity Equation Method and Complex Step Differentiation. These techniques differ from traditional parametric studies in that sensitivities are obtained more accurately by direct numerical solution of a separate set of PDEs for the sensitivity derivatives. In this manner, the present sensitivity results can be used to reliably predict the percent drag savings achievable for a unit increase in $w$ and $h$. Sensitivity results also indicate that an increase in $\alpha$ translates into enhanced mixing, albeit with a drag penalty. Finally, the talk discusses how the present sensitivity results may be incorporated in to a gradient-based optimization algorithm toward improved microchannel design.