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Basedon classical density functional theory, we study the sizeselectivity for ternary colloidal mixtures in the presence of a Gaussbarrier. The competition between the external potential and the depletionpotential is also investigated. The effects of bulk fraction of eachspecies, the size asymmetry, and the strength and width of the Gaussbarrier on the selectivity of the big species are calculated and analyzedin detail. The results in different conditions of bulk fraction suggestthat the larger the bulk fraction for the small species, the strongerselectivity of big particles. On the contrary, increase of bulk fractionfor the big species leads to a reduction in selectivity. In addition,results under different conditions of size asymmetry suggest thatthe medium particles can also be selected by the Gauss barrier whenthey are sufficiently large in comparison to the small particles.We also demonstrate the effect of barrier geometry on the selectivityof the big species and the competition between the depletion and theexternal potential. [ABSTRACT FROM AUTHOR]