Effective slip lengths for flows over surfaces with nanobubbles: the effects of finite slip

We consider effective slip lengths for flows of simple liquids over surfaces contaminated by gaseous nanobubbles. In particular, we examine whether the effects of finite slip over the liquid-bubble interface are important in limiting effective slip lengths over such surfaces. Using an expression that interpolates between the perfect slip and finite slip regimes for flow over bubbles, we conclude that for the bubble dimensions and coverages typically reported in the literature the effects of finite slip are secondary, reducing effective slip lengths by only 10%. Further, we find that nanobubbles do not significantly increase slip lengths beyond those reported for bare hydrophobic surfaces.