Numerical simulation of fluid flow in microchannels with superhydrophobic walls

The three-dimensional flow of a Newtonian fluid in a microchannel with superhydrophobic walls is computed using a finite element analysis. Calculations of the fully-developed laminar flow of water under a pressure gradient of 1 psi/cm in an 80 mu m high channel with superhydrophobic upper and lower surfaces containing a 2 mu m pitch array of 0.2 pro square posts shows a 40 percent flow enhancement relative to the smooth, non-patterned surface case, and an apparent slip length of 5.4 pm. A sharp gradient is observed in the axial velocity field within 0.5 mu m of the post surface and normal to the post center. The calculated axial velocity field away from the superhydrophobic surface agrees well with the analytical solution for two-dimensional channel flow with Navier's slip condition applying at the channel wall. Mesh refinement studies indicate the important role that adequate resolution of the sharp gradient in the velocity field adjacent to the post surface plays in obtaining accurate flow enhancement predictions. Decreasing the relative contact area of the fluid with the solid portion of the channel surface, either by increasing the post-to-post spacing or decreasing the post size, results in a monotonic increase in the flow enhancement. Wetting of the fluid into the post structure is shown to dramatically decrease the calculated flow enhancement. Calculations of the flow enhancement for fixed surface properties and varying channel heights result in apparent slip lengths that agree to within I percent, suggesting that the macroscopic flow behavior is adequately characterized in terms of an apparent slip model, with the magnitude of the slip length a function of the post size, post spacing and wetting behavior that characterize the local flow field.