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Numerically validated analytical predictions for electro-osmosis over a charged surface decorated with a nanoscale groove pattern are developed for the situation when the electrical double layer thickness is comparable to the spatial period of the grooves. For the analytical predictions, the groove shape can be specified by any continuous periodic function, such as the triangular, trapezoidal, and sinusoidal waveforms, which are investigated as special cases. We discover that the classical Helmholtz–Smoluchowski expression for electrokinetic mobility, notwithstanding its widespread use in measurements, is rendered invalid by the presence of Debye-length-scale unevenness in the surface topography. Furthermore, we use the depth-resolved anisotropic response of oblique grooves to design and optimize a novel electro-microfluidic strategy for separating constituents of a nano-particulate mixture.