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We present a method based on the selective liquid infiltration in air holes to produce slow light in a coupled-cavity waveguide structured by two-dimensional photonic crystal and analyze the slow light propagation in the coupled-cavity waveguide with triangular lattice. The group velocity profile of different coupled-cavity waveguides, obtained by the selective liquid infiltration in the holes between the cavities in waveguide and the increased radius of the first row of holes adjacent to the waveguide, is evaluated by using both the plane-wave expansion method and a tight binding model. We determine the optimal parameters to reduce the group velocity. Using a simpler coupled-cavity waveguide structure we obtain smaller group velocity compared to most investigations.