Fluid Retention in Liquid Infused Surfaces: a Direct Numerical Simulation Study

Numerical and experimental studies using super-hydrophobic and liquid infused surfaces show that they offer promise in terms of reducing frictional drag. However, to utilize them in practical conditions, these surfaces must be designed to withstand the shear of the external flow. In studies done so far, texture geometries such as infinite longitudinal bars, transverse bars and staggered cubes have been used to support the infused fluid within the cavities. However, these geometries fall short in terms of retaining the infused fluid and sustaining drag reduction for long periods of time. Therefore, in this study, we have tried to address this issue by modeling texture geometries which can retain the infused fluid. We have designed surface geometries of mesh configurations having rectangular shaped cavities containing the infused fluid and restricting the infused fluid flow. While the pitch along the spanwise direction between longitudinal riblets was maintained constant, three pitch lengths of 11k,22k and 44k, where k is the height of roughness, were used between the transverse bars in the streamwise direction. These geometries have been modelled at the lower wall of a channel and turbulent channel flow has been simulated over them by direct numerical simulations (DNS). A viscosity ratio m = µ2/µ1 of 0.4 ( subscript 2 indicates the fluid in cavities and subscript 1 indicates external flowing fluid) mimicking the viscosity ratio of liquid infused surfaces (LIS) is considered. The first set of simulations was performed with W e = 0 to obtain perfect slip at the interface. The results agree well with those in literature for perfect slip conditions. A second set of simulations was performed at W e = 100 (W e+ = 3.6 × 10−4 ) to assess the deformation of the interface. A simulation with a streamwise pitch length of 11k and W e = 500 (W e+ = 2 × 10−3 ) was also performed to analyse the effect of large interface deformation on the external flow. This deformation of the interface is fully coupled with the Navier-Stokes equation and tracked in time using a Level set method. In comparison with the geometry having only longitudinal riblets, we observe an increase in drag and decrease in slip length. However, a minimum drag reduction of 5% can still be achieved under realistic conditions with finite surface tension (W e+ = 3.6 × 10−4 ) applied at the interface. However, when the surface tension was reduced, a drag increase was observed. As these modeled texture geometries retain the infused fluid, they offer a long term gain over the ideal geometries mentioned before. Compared to flat channel flow, there is a decrease in turbulent Reynolds stresses and kinetic energy production showing promise for further studies.