Turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves under dynamic wetting conditions*

The effect of dynamic wetting conditions on turbulent skin-friction drag reduction (DR) with superhydrophobic (SH) longitudinal microgrooves is investigated by direct numerical simulation (DNS) using free-energy lattice Boltzmann (FELB) methods. The simulations were performed in turulent channel flows at a bulk Reynolds number of Re_b=7200 (Re_τ0≈222), at a viscosity ratio of N=μ_liq/μ_vap≈55, Weber number of We_τ0= ρ_liqu_τ0ν_liq/σ≈3.65x10^-3, with arrays of SH longitudinal micrgrooves on both walls at nominal solid fractions of φ_s,n=1/2 and  φ_s,n=1/16, groove widths of 15≤g⁺⁰≤64, groove aspect ratios of d/g=1, and advancing and receding contact angles of θ_adv=112^○and θ_rec=106^○. The presence of dynamic wetting conditions is found to result in drops of ≈3-17% and ≈11-35% in the magntude of DR at φ_s,n=1/2 and φ_s,n=1/16, respectively, compared to the results obtained with stationary, flat, shear-free interfaces. These drops in DR are found to arise primarily from the motion and displacement of the contact line. Motion of the contact line is found to have two effects: (i) it increases the effective solid fraction that the fluid is exposed to from the nominal solid fraction, φ_s,n, to a wetted solid fraction, φ_s,w〉φ_s,n, and (ii) it leads to the formation of corner vortices which can act as surface roughness. The former leads to drops of ≈10-35% in the effective streamwise slip velocity, while the latter leads to enhancements of up to 200% in the effective spanwise slip. The detailed mechanisms behind these phenomena and the scaling of SH DR in the presence of dynamic wetting conditions will be discussed.