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For a model of a 3D coating composed of a bi-periodic system of parallelriblets with gaps we analytically derive an approximate formula for theeffective slip length (an offset from the flat surface at which the flowvelocity would extrapolate to zero) as a function of the geometry of the system(riblet period, riblet height, and relative gap size). This formula is validfor an arbitrary fraction of gaps (i.e from narrow riblets to narrow gaps) andagrees with the known analytical results for the 2D periodic coating of ribletswithout gaps. We validate our analytical results with the numerical solution ofthe equations of the viscous (creeping) flow over the riblets with gaps.

Slip length for a viscous flow over spiky surfaces