Navier-slip boundary condition has been investigated for patterned surfaces with various grooves for the application to fluid mixing by controlling flow patterns. Simple tensorial expression is applied for anisotropically patterned surfaces and effective slip lengths for various grooves have been evaluated for a wide range of Reynolds numbers and aspect ratios using a flow rate matching technique. By doing so, the applicability of the effective tensorial slip model has been presented that replaces physical surface patterns to reduce computational cost significantly. Using a simple model agitator with a rotating disk, modification of flow characteristics with various alignment angles of the patterned surface has been investigated. We report a critical Reynolds number of O(1) for flows in agitators, below which effective slip dominates over fluid inertia. Patterned poly(dimethylsiloxane) sheets are fabricated using a compression-molding/soft-lithography technique and flow visualization with laser-induced fluorescence reveals controllability of flow patterns with the patterned surface. (c) 2016 American Institute of Chemical Engineers AIChE J, 62: 4574-4585, 2016