Transport in Superhydrophobic Microchannels: A Porous Modeling Approach

In this work we propose the use of porous flow theory to predict the behavior of the fully-developed inertia-less flow of a constant viscosity Newtonian fluid in a parallel-plate, superhydrophobic microchannel whose roughness features are composed of a square array of posts arranged transverse to the flow. The volume-averaged Navier-Stokes (VANS) equation is used to model the flow behavior in both the open and porous regions, taking into account the presence of a recirculating gas layer and the potential for partial liquid penetration into the porous and non-porous regions is coupled by imposing boundary conditions specifying the continuity of velocity and a stress jump at the interface between the two regions. An empirical factor, known as the stress jump coefficient beta, appears in the stress jump boundary condition and is shown to be correlated to the geometric properties of the porous region via a scaling law inferred from non-dimensional analysis and observed in 3D computational fluid dynamics simulations. Finally, the predictions of the model are compared with existing experimental studies.