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The use of membrane technologies for separation processes is an alternative approach to reduce the environmental impact and energy demand of separations. The development of new membrane materials plays a central role to overcome the limitations of membranes in terms of selectivity, permeability, and stability. Most membrane materials in the past have been engineered to control the relative magnitude of the flux of the species diffusing through the membrane. However, mass flux is a vector and controlling its direction can open new opportunities to design separation processes. In this paper we characterize the separation capabilities of metamaterial-inspired anisotropic planar membranes by studying the development of spatially dependent permeabilities and selectivities as a consequence of manipulating the flux direction within the membrane. Specifically, we show how the performance of anisotropic planar membranes for separations can be characterized in terms of permeability, selectivity, and the collected permeate proportion. In contrast to isotropic membrane materials, we show how the selectivity under single stage operation can be increased beyond the selectivities of the constituent materials by reducing the permeate proportion that is collected. Our work provides new opportunities for the design of alternative separation processes that take advantage of flux directional control within membrane materials.