Effect of Interface Deformation and Contact Line Motion on Drag Reduction with Superhydrophobic and Liquid-Infused Surfaces in Laminar and Turbulent Flow

Effect of interface deformation and contact line motion on drag reduction (DR) with super-hydrophobic (SH) and liquid-infused (LI) surfaces is investigated in laminar and turbulent flow by direct numerical simulation (DNS) using a two-phase, single relaxation time, free-energy lattice Boltzmann method. In this method, the dynamics of a diffuse interface is incorporated into the governing equations using a Peng-Robinson free-energy functional. This obviates the need for interface tracking. DNS studies were performed in channel flows with longitudinal microgrooves of width $0.16 \le g/H \le 0.64$ in laminar flow and $15 \le g^{+0} \le 64$ in turbulent flow, at solid fractions of $\phi_s =1/16$ or $1/2$. Viscosity ratios of $\mu_{ext}/\mu_{int} = 10$, $20$ and $55$ were studied at Weber numbers of $10^{-2} \le We =\rho U_{bulk} \nu/\sigma \le 10^{-1}$ in laminar flow and $10^{-3} \le We_{\tau_0} = \rho u_{\tau_0} \nu/\sigma \le 10^{-2}$ in turbulent flow. The results show that, in both laminar and turbulent flow, interface deformation and contact line motion can significantly modify the magnitude of DR compared to results obtained with `idealized', flat SH or LI interfaces. The conditions under which the contact line depins and the interface breaks down are identified by DNS.