Prediction of resistance induced by surface complexity in lubricating layers: Application to superhydrophobic surfaces

Superhydrophobic (SH) coatings have been demonstrated to reduce drag in various applications, though they have yet to be widely used or adopted due to practical issues. Various studies have demonstrated the prospect of reducing drag via SH surfaces both in turbulent and laminar flow regimes. However, the beneficial wall-slip effect produced may disappear depending on the surface geometry and flow conditions. The main mechanisms considered behind the decrease in performance are Marangoni-induced stresses and air/liquid interface deformation. In the present study, another mechanism is proposed to explain the loss of performances of SH surfaces in laminar flow regimes. Here we consider the flow of air inside the plastron and the associated momentum loss induced by roughness elements with different geometric characteristics. The effects of air motion within the plastron are coupled to the outer fluid with a homogenized boundary-condition approach. To this end, numerical simulations at the scale of the roughness elements were conducted as a function of the porosity and the tortuosity of the domain to determine the slip velocity at the air/liquid interface. The homogenized boundary condition is then implemented in a theoretical model for the outer flow to compute drag on SH spheres at low Re numbers. Experiments of laminar SH falling spheres indicate that high values of the tortuosity and low values of the porosity lead to a loss of performances when considering drag reduction. As anticipated, a three-dimensional printed sphere with low tortuosity and similar porosity demonstrated near-optimal drag reductions. A comparative study between the predicted values and experiments shows that the homogenized model is able to accurately predict the drag on SH surfaces for values of the porosity and tortuosity estimated from microscopy images of the SH textured surface.

Automated summary

In this study, a mechanism is proposed to explain the loss of performance of superhydrophobic (SH) surfaces in laminar flow regimes, considering the flow of air inside the plastron and the associated momentum loss induced by roughness elements with different geometric characteristics. Numerical simulations and experiments show that high roughness and low porosity lead to a loss of drag reduction.