Electroosmotic phenomena in fractures have been investigated in the linear limit for various double-layer thicknesses. The effects of the geometrical parameters were systematically studied for deterministic sinusoidal and random self-affine fractures. The numerical results show a definite influence of the surface amplitude on electroosmotic processes. For self-affine fractures, the roughness or Hurst exponent has a much larger incidence than the correlation parameter between the two surfaces. All the electroosmotic coupling coefficients can be gathered in a single relationship which depends on a characteristic length scale Lambda, applicable to every configuration. Such a length was already found useful for porous media, but the relationship is different.