Effect of interface deformation and contact line motion on turbulent skin-friction drag reduction with superhydrophobic surfaces

Effect of interface deformation and contact line motion on turbulent skin-friction Drag Reduction (DR) with SuperHydrophobic (SH) surfaces is investigated by DNS using a two-phase free-energy lattice Boltzmann method. DNS studies were performed in turbulent channel flows at $Re_{\tau_0} \approx 222$ with SH longitudinal microgrooves of width $15 \le g^{+0} \le 64$ at solid fractions of $\phi_s=$1/16 \& 1/2 on both walls. Simulations were performed at viscosity ratios of $\mu_{ext}/\mu_{int}=50$, Weber numbers of $We_{\tau_0} \equiv \rho u_{\tau_0} \nu/\sigma \approx 2 \times 10^{-3}$ and dynamic contact angles of $\theta_{adv} = 112^{\circ}$ and $\theta_{rec} = 106^{\circ}$. Two initial configurations of SH interfaces were investigated, corresponding to contact angles of $\theta_c = 90^{\circ}$ and $120^{\circ}$. Contact line motion was found to magnify the apparent wetted surface area of the microgrooves, thus reducing the effective streamwise slip velocities by 7-50\%. Interface deformation was found to enhance the effective spanwise slip velocities by up to 200\% with initially curved interfaces. These combined effects lead to drops of 7-32\% and 16-50\% in the magnitude of DR with initially flat and curved interfaces, respectively, compared to `idealized' flat SH walls.