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Spatial investigations of nickel and cobalt atoms and of C2 and C3 radicals are performed by laser induced fluorescence (LIF) in a continuous CO2 laser-vaporization reactor during the synthesis of single-walled carbon nanotubes. The chemical composition of the gas vaporized from bimetallic Ni/Co catalysts-carbon targets is determined using a chemical kinetic model. In this model, the evolution of Ni and Co atoms is driven by kinetics of condensation/evaporation process of pure metal clusters. Metal-carbon clusters are assumed to form from soot particles (C80) and 128-atom metal clusters. Spatial profiles of Ni and Co atoms obtained by LIF are compared with the calculations to validate the modeling and to adjust the input data. The value of the initial molar fraction of carbon-metal mixture diluted in helium is determined through a parametric study. Good agreement is found between the measured and the calculated evolution of Ni for a molar fraction of the helium diluent ranging from 10 to 15%. To fit the spatial profile of Co, the activation energy is adjusted in the evaporation rate, changing the cobalt dimer bond energy. The latter is found to be largely uncertain; and three values are tested: 167, 208, and 230 kJ x mol(-1). From comparison, the activation energy is found to be 208 kJ x mol(-1). However, the C2 LIF profiles show that the depletion of C2 is accelerated when cobalt is present. The observed Co evolutions suggest that small Co-C clusters are easier and/or faster to form compared to Ni-C clusters.