Critical entry speed versus viscosity ratio for smooth plate (solid symbols) and that decorated with vertical grooves (empty symbols). Ethanol–glycerol (square) and water–glycerol (circle) solutions are used. Gray region shows the experimental data cited from Refs. [10 and 11]. Contact angle ( θ e = θ Y ) and slipping length (λ _s) are presented according to the lubricating theory (Eq. (1)). According to the comparison, results with λ _s=10⁻⁵ are used as baselines for further analyses on rough surfaces.